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FM","link":"/"}},"mindshift_63615":{"type":"posts","id":"mindshift_63615","meta":{"index":"posts_1591205157","site":"mindshift","id":"63615","score":null,"sort":[1713780042000]},"guestAuthors":[],"slug":"stanfords-jo-boaler-talks-about-her-new-book-math-ish-and-takes-on-her-critics","title":"Stanford’s Jo Boaler Discusses Her New Book ‘MATH-ish’ and Takes On Her Critics","publishDate":1713780042,"format":"standard","headTitle":"Stanford’s Jo Boaler Discusses Her New Book ‘MATH-ish’ and Takes On Her Critics | KQED","labelTerm":{"site":"mindshift"},"content":"\u003cp>\u003cspan style=\"font-weight: 400\">Jo Boaler is a professor at the Stanford Graduate School of Education with a devoted following of teachers who cheer her call to make math education more exciting. But despite all her fans, she has sparked controversy at nearly every stage of her career. Critics say she misrepresents research to make her case and her ideas actually impede students. Now, with a new book coming out in May, provocatively titled “MATH-\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">ish\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">,” Boaler is fighting back. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“This is a whole effort to shut me down, my research and my writing,” said Boaler. “I see it as a form of knowledge suppression.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Academic fights usually don’t make it beyond the ivory tower. But Boaler’s popularity and influence have made her a focal point in the current math wars, which also seem to reflect the broader culture wars. In the last few months, \u003c/span>\u003ca href=\"https://nypost.com/2024/03/22/opinion/dei-math-ed-prof-who-helped-get-algebra-banned-in-frisco-is-accused-of-faulty-research/\">\u003cspan style=\"font-weight: 400\">tabloids\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and \u003c/span>\u003ca href=\"https://www.piratewires.com/p/jo-boaler-misrepresented-citations\">\u003cspan style=\"font-weight: 400\">conservative publications\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> have turned Boaler into something of an education villain who’s captured the attention of \u003c/span>\u003ca href=\"https://twitter.com/elonmusk/status/1770663755149656458\">\u003cspan style=\"font-weight: 400\">Elon Musk\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and \u003c/span>\u003ca href=\"https://twitter.com/tedcruz/status/1770659605774786758\">\u003cspan style=\"font-weight: 400\">Texas Sen. Ted Cruz\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> on social media. Critics have even questioned Boaler’s association with a \u003c/span>\u003ca href=\"https://www.piratewires.com/p/yolande-beckles-scammer-california-education-system\">\u003cspan style=\"font-weight: 400\">former reality tv star\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“I am the next target,” Boaler said, describing the death threats and abusive email she’s been receiving.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">This controversy matters on a much larger level because there is a legitimate debate about how math should be taught in American schools. Cognitive science research suggests that students need a lot of practice and memorization to master math. And once students achieve success through practice, this success will motivate them to learn and enjoy math. In other words, success increases motivation at least as much as motivation produces success. \u003c/span>\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Yet, from Boaler’s perspective, too many students feel like failures in math class and hate the subject. That leaves us with millions of Americans who are innumerate. Nearly 2 out of every 5 eighth graders don’t even have the most basic math skills, according to the \u003c/span>\u003ca href=\"https://www.nationsreportcard.gov/highlights/mathematics/2022/\">\u003cspan style=\"font-weight: 400\">2022 National Assessment of Educational Progress\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> (NAEP). On the \u003c/span>\u003ca href=\"https://hechingerreport.org/proof-points-there-is-a-worldwide-problem-in-math-and-its-not-just-about-the-pandemic/\">\u003cspan style=\"font-weight: 400\">Program for International Student Assessment (PISA)\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, American 15-year-olds rank toward the bottom of economically advanced nations in math achievement. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler draws upon a different body of research about student motivation that looks at the root causes of why students don’t like math based on surveys and interviews. Students who are tracked into low-level classes feel discouraged. Struggling math students often describe feelings of anxiety from timed tests. Many students express frustration that math is just a collection of meaningless procedures. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler seeks to fix these root causes. She advocates for ending tracking by ability in math classes, getting rid of timed tests and starting with conceptual understanding before introducing procedures. Most importantly, she wants to elevate the work that students tackle in math classes with more interesting questions that spark genuine curiosity and encourage students to think and wonder. Her goal is to expose students to the beauty of mathematical thinking as mathematicians enjoy the subject. Whether students actually learn more math the Boaler way is where this dispute centers. In other words, how strong is the evidence base?\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The latest battle over Boaler’s work began with an anonymous complaint published in March by the \u003c/span>\u003ca href=\"https://freebeacon.com/california/san-francisco-cited-this-professor-to-end-8th-grade-algebra-her-research-had-reckless-disregard-for-accuracy-complaint-alleges/\">\u003cspan style=\"font-weight: 400\">Washington Free Beacon\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, the same conservative website that first surfaced plagiarism accusations against Claudine Gay, the former president of Harvard University. The \u003c/span>\u003ca href=\"https://drive.proton.me/urls/P7BYBG7E6R#VCfOpReAcH9F\">\u003cspan style=\"font-weight: 400\">complaint\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> accuses Boaler of a “reckless disregard for accuracy” by misrepresenting research citations 52 times and asks Stanford to discipline Boaler, a full professor with an endowed chair. Stanford has said it’s reviewing the complaint and hasn’t decided whether to open an investigation, according to news reports. Boaler \u003ca href=\"https://joboaler.people.stanford.edu/\">stands by her research\u003c/a> (other than one citation that she says has been fixed) and calls the anonymous complaint “bogus.” \u003cspan style=\"color: #111111;font-family: Tiempos,Georgia,serif;font-size: medium\">(\u003c/span>\u003cspan style=\"color: #111111;font-family: Tiempos,Georgia,serif;font-size: medium\">\u003ci>UPDATE: The Hechinger Report learned after this article was published that Stanford has decided \u003c/i>\u003c/span>\u003ca href=\"https://url.us.m.mimecastprotect.com/s/7e_rCXDM32FOJLk3SkNtc7?domain=stanforddaily.com\" target=\"_blank\" rel=\"noopener noreferrer\">\u003cspan style=\"font-family: Tiempos,Georgia,serif;font-size: medium\">\u003ci>not to open an investigation\u003c/i>\u003c/span>\u003c/a>\u003cspan style=\"color: #111111;font-family: Tiempos,Georgia,serif;font-size: medium\">\u003ci>.\u003c/i>\u003c/span>\u003cspan style=\"color: #111111;font-family: Tiempos,Georgia,serif;font-size: medium\">)\u003c/span>\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“They haven’t even got the courage to put their name on accusations like this,” Boaler said. “That tells us something.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler first drew fire from critics in 2005, when she presented new \u003c/span>\u003ca href=\"https://nrich.maths.org/content/id/7011/nrich%20paper.pdf\">\u003cspan style=\"font-weight: 400\">research claiming that students at a low-income school\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> who were behind grade level had outperformed students at higher achieving schools when they were taught in classrooms that combined students of different math achievement levels. The supposed secret sauce was an unusual curriculum that emphasized group work and de-emphasized lectures. Critics disparaged the findings and hounded her to release her data. Math professors at Stanford and Cal State University \u003c/span>\u003ca href=\"https://nonpartisaneducation.org/Review/Articles/v8n1.pdf\">\u003cspan style=\"font-weight: 400\">re-crunched the numbers\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and declared they’d found the opposite result.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler, who is originally from England, retreated to an academic post back in the U.K., but returned to Stanford in 2010 with a fighting spirit. She had written a book, “What’s Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject,” which explained to a general audience why challenging, open-ended problems would help more children to embrace math and how the current approach of boring drills and formulas was turning too many kids off. Teachers loved it.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler accused her earlier critics of academic \u003c/span>\u003ca href=\"https://www.insidehighered.com/news/2012/10/15/stanford-professor-goes-public-attacks-over-her-math-education-research\">\u003cspan style=\"font-weight: 400\">bullying and harassment\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. But she didn’t address their legitimate research questions. Instead, she focused on changing classrooms. Tens of thousands of teachers and parents flocked to her 2013 online course on how to teach math. Building on this new fan base, she founded a nonprofit organization at Stanford called youcubed to train teachers, conduct research and spread her gospel. Boaler says a half million teachers now visit youcubed’s website each month.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler also saw math as a lever to promote social justice. She lamented that too many low-income Black and Hispanic children were stuck in discouraging, low-level math classes. She advocated for change. In 2014, San Francisco \u003c/span>\u003ca href=\"https://sanfrancisco.granicus.com/player/clip/19433?view_id=47&redirect=true\">\u003cspan style=\"font-weight: 400\">heeded that call\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, mixing different achievement levels in middle school classrooms and delaying algebra until ninth grade. Parents, especially in the city’s large Asian community, protested that delaying algebra was holding their children back. Without starting algebra in middle school, it was difficult to progress to high school calculus, an important course for college applications. Parents blamed Boaler, who applauded San Francisco for \u003c/span>\u003ca href=\"https://hechingerreport.org/opinion-how-one-city-got-math-right/\">\u003cspan style=\"font-weight: 400\">getting math right\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Ten years later, the city is slated to \u003c/span>\u003ca href=\"https://www.sfusd.edu/about-sfusd/sfusd-news/press-releases/2024-02-14-sfusd-offer-algebra-1-8th-grade-beginning-2024-25-school-year#:~:text=San%20Francisco%20(February%2014%2C%202024,at%20its%20regular%20meeting%20Tuesday.\">\u003cspan style=\"font-weight: 400\">reinstate algebra for eighth graders\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> this fall. Boaler denies any involvement in the unpopular San Francisco reforms.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Before that math experiment unraveled in San Francisco, California education policymakers tapped Boaler to be one of the lead writers of a new math framework, which would guide math instruction throughout the state. The first draft discouraged tracking children into separate math classes by achievement levels, and proposed delaying algebra until high school. It emphasized “social justice” and suggested that students could take data science instead of advanced algebra in high school. Traditional math proponents worried that the document would water down math instruction in California, hinder advanced students and make it harder to pursue STEM careers. And they were concerned that California’s proposed reforms could spread across the nation. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">In the battle to quash the framework, critics attacked Boaler for trying to institute “\u003c/span>\u003ca href=\"https://blog.independent.org/2023/07/10/californias-flawed-k-12-math-framework/\">\u003cspan style=\"font-weight: 400\">woke\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">” mathematics. The battle became personal, with some criticizing her \u003c/span>\u003ca href=\"https://www.oxnardsd.org/site/default.aspx?PageType=3&ModuleInstanceID=16044&ViewID=DEDCCD34-7C24-4AF2-812A-33C0075398BC&RenderLoc=0&FlexDataID=25705&PageID=10939&Tag=&Comments=true\">\u003cspan style=\"font-weight: 400\">$5,000-an-hour\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> consulting and speaking fees at public schools while sending her own children to private school. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Critics also dug into the weeds of the framework document, which is how this also became a research story. A Stanford mathematics professor catalogued a list of what he saw as \u003c/span>\u003ca href=\"https://sites.google.com/view/publiccommentsonthecmf/\">\u003cspan style=\"font-weight: 400\">research misrepresentations\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Those citations, together with additional characterizations of research findings throughout Boaler’s writings, eventually grew into the anonymous complaint that’s now at Stanford.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">By the time the most recent complaint against Boaler was lodged, the framework had already been revised in substantial ways. Boaler’s critics had arguably won their main policy battles. College-bound students still need the traditional course sequence and cannot substitute data science for advanced algebra. California’s middle schools will continue to have the option to track children into separate classes and start algebra in eighth grade. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">But the attacks on Boaler continue. In addition to seeking sanctions from Stanford, her anonymous critics have asked academic journals to pull down her papers, according to Boaler. They’ve written to conference organizers to stop Boaler from speaking and, she says, they’ve told her funders to stop giving money to her. At least one, the Valhalla Foundation, the family foundation of billionaire Scott Cook (co-founder of the software giant Intuit), stopped funding youcubed in 2024. In 2022 and 2023, it gave Boaler’s organization more than $560,000. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler sees the continued salvos against her as part of the larger right-wing attack on diversity, equity and inclusion, or DEI. She also sees a misogynistic pattern of taking down women who have power in education, such as Claudine Gay. “You’re basically hung, drawn and quartered by the court of Twitter,” she said.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">From my perch as a journalist who covers education research, I see that Boaler has a tendency to \u003c/span>\u003ca href=\"http://www.danielwillingham.com/daniel-willingham-science-and-education-blog/march-13th-2019\">\u003cspan style=\"font-weight: 400\">overstate the implications\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> of a narrow study. Sometimes she cites a theory that’s been written about in an academic journal but hasn’t been proven and labels it research. While technically true – most academic writing falls under the broad category of research – that’s not the same as evidence from a well-designed classroom experiment. And she tends not to factor in evidence that runs counter to her views or adjust her views as new studies arise. Some of her numerical claims seem grandiose. For example, she says one of her 18-lesson summer courses raised achievement by \u003c/span>\u003ca href=\"https://www.youcubed.org/pd/\">\u003cspan style=\"font-weight: 400\">2.8 years\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“People have raised questions for a long time about the rigor and the care in which Jo makes claims related to both her own research and others,” said Jon Star, a professor of math education at Harvard Graduate School of Education. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">But Star says many other education researchers have done exactly the same, and the “liberties” Boaler takes are common in the field. “That’s not to suggest that taking these liberties is okay,” Star said, “but she is being called out for it.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler is getting more scrutiny than her colleagues, he said, because she’s influential, has a large following of devoted teachers and has been involved in policy changes at schools. Many other scholars of math education share Boaler’s views. But Boaler has become the public face of nontraditional teaching ideas in math. And in today’s polarized political climate, that’s a dangerous public face to be.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The citation controversy reflects bigger issues with the state of education research. It’s often not as precise as the hard sciences or even social sciences like economics. Academic experts are prone to make wide, sweeping statements. And there are too few studies in real classrooms or randomized controlled trials that could settle some of the big debates. Star argues that \u003c/span>\u003ca href=\"https://pubs.nctm.org/view/journals/jrme/49/1/article-p98.xml\">\u003cspan style=\"font-weight: 400\">more replication studies\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> could improve the quality of evidence for math instruction. We can’t know which teaching methods are most effective unless the method can be reproduced in different settings with different students.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">It’s also possible that more research may never settle these big math debates and we may continue to generate conflicting evidence. There’s the real possibility that traditional methods could be more effective for short-term achievement gains, while nontraditional methods might attract more students to the subject, and potentially lead to more creative problem solvers in the future. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Even if \u003c/span>\u003ca href=\"https://notepad.michaelpershan.com/youcubed-is-more-than-just-sloppy-about-research/\">\u003cspan style=\"font-weight: 400\">Boaler is loose\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> with the details of research studies, she could still be right about the big picture. Maybe advanced students would be better off slowing down on the current racetrack to calculus to learn math with more depth and breadth. Her fun, hands-on approach to math might spark just enough motivation to inspire more kids to do their homework. Might we trade off a bit of short-term math achievement for a greater good of a numerate, civic society?\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">In her new book, “\u003c/span>\u003ca href=\"https://www.harpercollins.com/products/math-ish-jo-boaler?variant=41226038083618\">\u003cspan style=\"font-weight: 400\">MATH-\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">ish\u003c/span>\u003c/i>\u003c/a>\u003cspan style=\"font-weight: 400\">,” Boaler is doubling down on her approach to math with a title that seems to encourage inexactitude. She argues that approaching a problem in a “math-ish” way gives students the freedom to take a guess and make mistakes, to step back and think rather than jumping to numerical calculations. Boaler says she’s hearing from teachers that “ish” is far more fun than making estimates.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“I’m hoping this book is going to be my salvation,” she said, “that I have something exciting to do and focus on and not focus on the thousands of abusive messages I’m getting.”\u003c/span>\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">This story about \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/proof-points-stanfords-jo-boaler-book-math-ish-critics/\">\u003ci>\u003cspan style=\"font-weight: 400\">Jo Boaler\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> was written by Jill Barshay and produced by \u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">The Hechinger Report\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/proofpoints/\">\u003ci>\u003cspan style=\"font-weight: 400\">Proof Points newsletter\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/i>\u003c/p>\n\n","blocks":[],"excerpt":"With a new book coming out in May, titled “MATH-ish,” Jo Boaler is fighting back against her critics in the current math wars.","status":"publish","parent":0,"modified":1713883570,"stats":{"hasAudio":false,"hasVideo":false,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":32,"wordCount":2235},"headData":{"title":"Stanford’s Jo Boaler Discusses Her New Book ‘MATH-ish’ and Takes On Her Critics | KQED","description":"With a new book coming out in May, titled “MATH-ish,” Jo Boaler is fighting back against her critics in the current math wars.","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","socialDescription":"With a new book coming out in May, titled “MATH-ish,” Jo Boaler is fighting back against her critics in the current math wars.","schema":{"@context":"http://schema.org","@type":"Article","headline":"Stanford’s Jo Boaler Discusses Her New Book ‘MATH-ish’ and Takes On Her Critics","datePublished":"2024-04-22T10:00:42.000Z","dateModified":"2024-04-23T14:46:10.000Z","image":"https://cdn.kqed.org/wp-content/uploads/2020/02/KQED-OG-Image@1x.png"}},"sticky":false,"nprByline":"Jill Barshay, \u003ca href=\"https://hechingerreport.org/\" target=\"_blank\">The Hechinger Report\u003c/a>","excludeFromSiteSearch":"Include","showOnAuthorArchivePages":"No","articleAge":"0","path":"/mindshift/63615/stanfords-jo-boaler-talks-about-her-new-book-math-ish-and-takes-on-her-critics","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>\u003cspan style=\"font-weight: 400\">Jo Boaler is a professor at the Stanford Graduate School of Education with a devoted following of teachers who cheer her call to make math education more exciting. But despite all her fans, she has sparked controversy at nearly every stage of her career. Critics say she misrepresents research to make her case and her ideas actually impede students. Now, with a new book coming out in May, provocatively titled “MATH-\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">ish\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">,” Boaler is fighting back. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“This is a whole effort to shut me down, my research and my writing,” said Boaler. “I see it as a form of knowledge suppression.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Academic fights usually don’t make it beyond the ivory tower. But Boaler’s popularity and influence have made her a focal point in the current math wars, which also seem to reflect the broader culture wars. In the last few months, \u003c/span>\u003ca href=\"https://nypost.com/2024/03/22/opinion/dei-math-ed-prof-who-helped-get-algebra-banned-in-frisco-is-accused-of-faulty-research/\">\u003cspan style=\"font-weight: 400\">tabloids\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and \u003c/span>\u003ca href=\"https://www.piratewires.com/p/jo-boaler-misrepresented-citations\">\u003cspan style=\"font-weight: 400\">conservative publications\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> have turned Boaler into something of an education villain who’s captured the attention of \u003c/span>\u003ca href=\"https://twitter.com/elonmusk/status/1770663755149656458\">\u003cspan style=\"font-weight: 400\">Elon Musk\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and \u003c/span>\u003ca href=\"https://twitter.com/tedcruz/status/1770659605774786758\">\u003cspan style=\"font-weight: 400\">Texas Sen. Ted Cruz\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> on social media. Critics have even questioned Boaler’s association with a \u003c/span>\u003ca href=\"https://www.piratewires.com/p/yolande-beckles-scammer-california-education-system\">\u003cspan style=\"font-weight: 400\">former reality tv star\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“I am the next target,” Boaler said, describing the death threats and abusive email she’s been receiving.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">This controversy matters on a much larger level because there is a legitimate debate about how math should be taught in American schools. Cognitive science research suggests that students need a lot of practice and memorization to master math. And once students achieve success through practice, this success will motivate them to learn and enjoy math. In other words, success increases motivation at least as much as motivation produces success. \u003c/span>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Yet, from Boaler’s perspective, too many students feel like failures in math class and hate the subject. That leaves us with millions of Americans who are innumerate. Nearly 2 out of every 5 eighth graders don’t even have the most basic math skills, according to the \u003c/span>\u003ca href=\"https://www.nationsreportcard.gov/highlights/mathematics/2022/\">\u003cspan style=\"font-weight: 400\">2022 National Assessment of Educational Progress\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> (NAEP). On the \u003c/span>\u003ca href=\"https://hechingerreport.org/proof-points-there-is-a-worldwide-problem-in-math-and-its-not-just-about-the-pandemic/\">\u003cspan style=\"font-weight: 400\">Program for International Student Assessment (PISA)\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, American 15-year-olds rank toward the bottom of economically advanced nations in math achievement. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler draws upon a different body of research about student motivation that looks at the root causes of why students don’t like math based on surveys and interviews. Students who are tracked into low-level classes feel discouraged. Struggling math students often describe feelings of anxiety from timed tests. Many students express frustration that math is just a collection of meaningless procedures. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler seeks to fix these root causes. She advocates for ending tracking by ability in math classes, getting rid of timed tests and starting with conceptual understanding before introducing procedures. Most importantly, she wants to elevate the work that students tackle in math classes with more interesting questions that spark genuine curiosity and encourage students to think and wonder. Her goal is to expose students to the beauty of mathematical thinking as mathematicians enjoy the subject. Whether students actually learn more math the Boaler way is where this dispute centers. In other words, how strong is the evidence base?\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The latest battle over Boaler’s work began with an anonymous complaint published in March by the \u003c/span>\u003ca href=\"https://freebeacon.com/california/san-francisco-cited-this-professor-to-end-8th-grade-algebra-her-research-had-reckless-disregard-for-accuracy-complaint-alleges/\">\u003cspan style=\"font-weight: 400\">Washington Free Beacon\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, the same conservative website that first surfaced plagiarism accusations against Claudine Gay, the former president of Harvard University. The \u003c/span>\u003ca href=\"https://drive.proton.me/urls/P7BYBG7E6R#VCfOpReAcH9F\">\u003cspan style=\"font-weight: 400\">complaint\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> accuses Boaler of a “reckless disregard for accuracy” by misrepresenting research citations 52 times and asks Stanford to discipline Boaler, a full professor with an endowed chair. Stanford has said it’s reviewing the complaint and hasn’t decided whether to open an investigation, according to news reports. Boaler \u003ca href=\"https://joboaler.people.stanford.edu/\">stands by her research\u003c/a> (other than one citation that she says has been fixed) and calls the anonymous complaint “bogus.” \u003cspan style=\"color: #111111;font-family: Tiempos,Georgia,serif;font-size: medium\">(\u003c/span>\u003cspan style=\"color: #111111;font-family: Tiempos,Georgia,serif;font-size: medium\">\u003ci>UPDATE: The Hechinger Report learned after this article was published that Stanford has decided \u003c/i>\u003c/span>\u003ca href=\"https://url.us.m.mimecastprotect.com/s/7e_rCXDM32FOJLk3SkNtc7?domain=stanforddaily.com\" target=\"_blank\" rel=\"noopener noreferrer\">\u003cspan style=\"font-family: Tiempos,Georgia,serif;font-size: medium\">\u003ci>not to open an investigation\u003c/i>\u003c/span>\u003c/a>\u003cspan style=\"color: #111111;font-family: Tiempos,Georgia,serif;font-size: medium\">\u003ci>.\u003c/i>\u003c/span>\u003cspan style=\"color: #111111;font-family: Tiempos,Georgia,serif;font-size: medium\">)\u003c/span>\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“They haven’t even got the courage to put their name on accusations like this,” Boaler said. “That tells us something.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler first drew fire from critics in 2005, when she presented new \u003c/span>\u003ca href=\"https://nrich.maths.org/content/id/7011/nrich%20paper.pdf\">\u003cspan style=\"font-weight: 400\">research claiming that students at a low-income school\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> who were behind grade level had outperformed students at higher achieving schools when they were taught in classrooms that combined students of different math achievement levels. The supposed secret sauce was an unusual curriculum that emphasized group work and de-emphasized lectures. Critics disparaged the findings and hounded her to release her data. Math professors at Stanford and Cal State University \u003c/span>\u003ca href=\"https://nonpartisaneducation.org/Review/Articles/v8n1.pdf\">\u003cspan style=\"font-weight: 400\">re-crunched the numbers\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and declared they’d found the opposite result.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler, who is originally from England, retreated to an academic post back in the U.K., but returned to Stanford in 2010 with a fighting spirit. She had written a book, “What’s Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject,” which explained to a general audience why challenging, open-ended problems would help more children to embrace math and how the current approach of boring drills and formulas was turning too many kids off. Teachers loved it.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler accused her earlier critics of academic \u003c/span>\u003ca href=\"https://www.insidehighered.com/news/2012/10/15/stanford-professor-goes-public-attacks-over-her-math-education-research\">\u003cspan style=\"font-weight: 400\">bullying and harassment\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. But she didn’t address their legitimate research questions. Instead, she focused on changing classrooms. Tens of thousands of teachers and parents flocked to her 2013 online course on how to teach math. Building on this new fan base, she founded a nonprofit organization at Stanford called youcubed to train teachers, conduct research and spread her gospel. Boaler says a half million teachers now visit youcubed’s website each month.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler also saw math as a lever to promote social justice. She lamented that too many low-income Black and Hispanic children were stuck in discouraging, low-level math classes. She advocated for change. In 2014, San Francisco \u003c/span>\u003ca href=\"https://sanfrancisco.granicus.com/player/clip/19433?view_id=47&redirect=true\">\u003cspan style=\"font-weight: 400\">heeded that call\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, mixing different achievement levels in middle school classrooms and delaying algebra until ninth grade. Parents, especially in the city’s large Asian community, protested that delaying algebra was holding their children back. Without starting algebra in middle school, it was difficult to progress to high school calculus, an important course for college applications. Parents blamed Boaler, who applauded San Francisco for \u003c/span>\u003ca href=\"https://hechingerreport.org/opinion-how-one-city-got-math-right/\">\u003cspan style=\"font-weight: 400\">getting math right\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Ten years later, the city is slated to \u003c/span>\u003ca href=\"https://www.sfusd.edu/about-sfusd/sfusd-news/press-releases/2024-02-14-sfusd-offer-algebra-1-8th-grade-beginning-2024-25-school-year#:~:text=San%20Francisco%20(February%2014%2C%202024,at%20its%20regular%20meeting%20Tuesday.\">\u003cspan style=\"font-weight: 400\">reinstate algebra for eighth graders\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> this fall. Boaler denies any involvement in the unpopular San Francisco reforms.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Before that math experiment unraveled in San Francisco, California education policymakers tapped Boaler to be one of the lead writers of a new math framework, which would guide math instruction throughout the state. The first draft discouraged tracking children into separate math classes by achievement levels, and proposed delaying algebra until high school. It emphasized “social justice” and suggested that students could take data science instead of advanced algebra in high school. Traditional math proponents worried that the document would water down math instruction in California, hinder advanced students and make it harder to pursue STEM careers. And they were concerned that California’s proposed reforms could spread across the nation. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">In the battle to quash the framework, critics attacked Boaler for trying to institute “\u003c/span>\u003ca href=\"https://blog.independent.org/2023/07/10/californias-flawed-k-12-math-framework/\">\u003cspan style=\"font-weight: 400\">woke\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">” mathematics. The battle became personal, with some criticizing her \u003c/span>\u003ca href=\"https://www.oxnardsd.org/site/default.aspx?PageType=3&ModuleInstanceID=16044&ViewID=DEDCCD34-7C24-4AF2-812A-33C0075398BC&RenderLoc=0&FlexDataID=25705&PageID=10939&Tag=&Comments=true\">\u003cspan style=\"font-weight: 400\">$5,000-an-hour\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> consulting and speaking fees at public schools while sending her own children to private school. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Critics also dug into the weeds of the framework document, which is how this also became a research story. A Stanford mathematics professor catalogued a list of what he saw as \u003c/span>\u003ca href=\"https://sites.google.com/view/publiccommentsonthecmf/\">\u003cspan style=\"font-weight: 400\">research misrepresentations\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Those citations, together with additional characterizations of research findings throughout Boaler’s writings, eventually grew into the anonymous complaint that’s now at Stanford.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">By the time the most recent complaint against Boaler was lodged, the framework had already been revised in substantial ways. Boaler’s critics had arguably won their main policy battles. College-bound students still need the traditional course sequence and cannot substitute data science for advanced algebra. California’s middle schools will continue to have the option to track children into separate classes and start algebra in eighth grade. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">But the attacks on Boaler continue. In addition to seeking sanctions from Stanford, her anonymous critics have asked academic journals to pull down her papers, according to Boaler. They’ve written to conference organizers to stop Boaler from speaking and, she says, they’ve told her funders to stop giving money to her. At least one, the Valhalla Foundation, the family foundation of billionaire Scott Cook (co-founder of the software giant Intuit), stopped funding youcubed in 2024. In 2022 and 2023, it gave Boaler’s organization more than $560,000. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler sees the continued salvos against her as part of the larger right-wing attack on diversity, equity and inclusion, or DEI. She also sees a misogynistic pattern of taking down women who have power in education, such as Claudine Gay. “You’re basically hung, drawn and quartered by the court of Twitter,” she said.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">From my perch as a journalist who covers education research, I see that Boaler has a tendency to \u003c/span>\u003ca href=\"http://www.danielwillingham.com/daniel-willingham-science-and-education-blog/march-13th-2019\">\u003cspan style=\"font-weight: 400\">overstate the implications\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> of a narrow study. Sometimes she cites a theory that’s been written about in an academic journal but hasn’t been proven and labels it research. While technically true – most academic writing falls under the broad category of research – that’s not the same as evidence from a well-designed classroom experiment. And she tends not to factor in evidence that runs counter to her views or adjust her views as new studies arise. Some of her numerical claims seem grandiose. For example, she says one of her 18-lesson summer courses raised achievement by \u003c/span>\u003ca href=\"https://www.youcubed.org/pd/\">\u003cspan style=\"font-weight: 400\">2.8 years\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“People have raised questions for a long time about the rigor and the care in which Jo makes claims related to both her own research and others,” said Jon Star, a professor of math education at Harvard Graduate School of Education. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">But Star says many other education researchers have done exactly the same, and the “liberties” Boaler takes are common in the field. “That’s not to suggest that taking these liberties is okay,” Star said, “but she is being called out for it.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Boaler is getting more scrutiny than her colleagues, he said, because she’s influential, has a large following of devoted teachers and has been involved in policy changes at schools. Many other scholars of math education share Boaler’s views. But Boaler has become the public face of nontraditional teaching ideas in math. And in today’s polarized political climate, that’s a dangerous public face to be.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The citation controversy reflects bigger issues with the state of education research. It’s often not as precise as the hard sciences or even social sciences like economics. Academic experts are prone to make wide, sweeping statements. And there are too few studies in real classrooms or randomized controlled trials that could settle some of the big debates. Star argues that \u003c/span>\u003ca href=\"https://pubs.nctm.org/view/journals/jrme/49/1/article-p98.xml\">\u003cspan style=\"font-weight: 400\">more replication studies\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> could improve the quality of evidence for math instruction. We can’t know which teaching methods are most effective unless the method can be reproduced in different settings with different students.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">It’s also possible that more research may never settle these big math debates and we may continue to generate conflicting evidence. There’s the real possibility that traditional methods could be more effective for short-term achievement gains, while nontraditional methods might attract more students to the subject, and potentially lead to more creative problem solvers in the future. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Even if \u003c/span>\u003ca href=\"https://notepad.michaelpershan.com/youcubed-is-more-than-just-sloppy-about-research/\">\u003cspan style=\"font-weight: 400\">Boaler is loose\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> with the details of research studies, she could still be right about the big picture. Maybe advanced students would be better off slowing down on the current racetrack to calculus to learn math with more depth and breadth. Her fun, hands-on approach to math might spark just enough motivation to inspire more kids to do their homework. Might we trade off a bit of short-term math achievement for a greater good of a numerate, civic society?\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">In her new book, “\u003c/span>\u003ca href=\"https://www.harpercollins.com/products/math-ish-jo-boaler?variant=41226038083618\">\u003cspan style=\"font-weight: 400\">MATH-\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">ish\u003c/span>\u003c/i>\u003c/a>\u003cspan style=\"font-weight: 400\">,” Boaler is doubling down on her approach to math with a title that seems to encourage inexactitude. She argues that approaching a problem in a “math-ish” way gives students the freedom to take a guess and make mistakes, to step back and think rather than jumping to numerical calculations. Boaler says she’s hearing from teachers that “ish” is far more fun than making estimates.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“I’m hoping this book is going to be my salvation,” she said, “that I have something exciting to do and focus on and not focus on the thousands of abusive messages I’m getting.”\u003c/span>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">This story about \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/proof-points-stanfords-jo-boaler-book-math-ish-critics/\">\u003ci>\u003cspan style=\"font-weight: 400\">Jo Boaler\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> was written by Jill Barshay and produced by \u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">The Hechinger Report\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/proofpoints/\">\u003ci>\u003cspan style=\"font-weight: 400\">Proof Points newsletter\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/i>\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/63615/stanfords-jo-boaler-talks-about-her-new-book-math-ish-and-takes-on-her-critics","authors":["byline_mindshift_63615"],"categories":["mindshift_21504"],"tags":["mindshift_21341","mindshift_20943","mindshift_392","mindshift_20893","mindshift_20841"],"featImg":"mindshift_63616","label":"mindshift"},"mindshift_61712":{"type":"posts","id":"mindshift_61712","meta":{"index":"posts_1591205157","site":"mindshift","id":"61712","score":null,"sort":[1685440859000]},"guestAuthors":[],"slug":"do-math-drills-help-children-learn","title":"Do math drills help children learn?","publishDate":1685440859,"format":"standard","headTitle":"Do math drills help children learn? | KQED","labelTerm":{"site":"mindshift"},"content":"\u003cp>\u003cspan style=\"font-weight: 400\">One of the most hotly contested teaching practices concerns a single minute of math class. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Should teachers pull out their stopwatches and administer one-page worksheets in addition, subtraction, multiplication and division? Speed drills are such a routine part of the weekly rhythms of many math classrooms that they’re often called Mad Minute Mondays. Critics say these timed drills aren’t useful and instead provoke math anxiety in many children. The National Council of Teachers of Mathematics urges teachers to “\u003c/span>\u003ca href=\"https://www.nctm.org/uploadedFiles/Standards_and_Positions/Position_Statements/PROCEDURAL_FLUENCY.pdf\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">avoid” timed tests\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. But advocates insist that these tests, which last one to five minutes, help children memorize math facts, freeing up their brains to tackle more challenging math problems. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">This long-running debate captured my attention again because a group of more than a dozen education researchers, who founded an organization they call the “\u003c/span>\u003ca href=\"https://www.thescienceofmath.com/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">Science of Math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">,” declared that the stopwatch skeptics are wrong. The researchers built an \u003c/span>\u003ca href=\"https://www.thescienceofmath.com/timed-tests-cause-math-anxiety\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">entire webpage\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> to set the record straight and devoted a section of a 2022 paper to explaining why it’s a \u003c/span>\u003ca href=\"https://www.cis.org.au/publication/myths-that-undermine-maths-teaching/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">myth that timed tests cause anxiety\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. A few readers contacted me after I first wrote about the \u003c/span>\u003ca href=\"https://hechingerreport.org/proof-points-how-a-debate-over-the-science-of-math-could-reignite-the-math-wars/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">Science of Math movement\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> earlier in May 2023, urging me to look at the group’s claims about timed tests. After looking at the research, I think the evidence is not quite as clear as the Science of Math group indicates. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The group argues there is no evidence that timed tests cause math anxiety. They also contend that timed tests improve math performance. Some researchers contest both points.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“Time tests don’t cause math anxiety?” said Jo Boaler, an education professor at Stanford University who is a prominent opponent of timed tests. “I could counter their studies with many more that show the opposite. And yes, you could conclude it’s a contested field, that there’s different evidence. But you can’t conclude that this is a myth.”\u003c/span>\u003c/p>\n\u003ch2>Dueling evidence\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">There isn’t much dispute about the lack of empirical evidence. I interviewed more than a half dozen math experts who confirmed there aren’t well-designed experiments that prove timed tests cause math anxiety. The Science of Math group could find only \u003c/span>\u003ca href=\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2806671/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">two experimental studies\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> that have attempted to \u003c/span>\u003ca href=\"https://link.springer.com/article/10.1007/s10864-016-9251-6\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">test the hypothesis\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and neither concluded that tests produce anxiety. \u003c/span>\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Math anxiety is difficult to measure, and even children who enjoy timed drills may experience an elevated heart rate, an aspect of anxiety, as they race through a sheet of sums. Distinguishing productive adrenaline rush from detrimental anxiety isn’t easy. It’s also complicated to disentangle whether timed tests are making matters worse for children who already have math anxiety from other causes. There’s \u003c/span>\u003ca href=\"https://news.uchicago.edu/story/math-anxiety-causes-trouble-students-early-first-grade\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">evidence for and against\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> even within studies. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Ideally, you would need to design a multi-year study — where some children were randomly given speed drills and others not, but were all taught the same way — and see what their math achievement and math anxiety levels were at the end of high school. That study doesn’t exist. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">What does exist are dozens, perhaps hundreds, of studies that document the stories of people who describe how much they hated timed tests. Interview excerpts like this one from a \u003c/span>\u003ca href=\"https://go.gale.com/ps/i.do?id=GALE%7CA62839422&sid=googleScholar&v=2.1&it=r&linkaccess=abs&issn=01463934&p=AONE&sw=w&userGroupName=nysl_oweb&isGeoAuthType=true&aty=geo\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">1999 study\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> of college students who were training to become math teachers are typical:\u003c/span>\u003c/p>\n\u003cp>\u003cem>\u003cspan style=\"font-weight: 400\">“If I am timed, I get nervous and forget everything. I do the ones I know, but then I get stressed that I’m not thinking fast enough and forget. I worry about finishing, and I can’t remember it even if I do know it. It is horrible. I get nervous just thinking about it.”\u003c/span>\u003c/em>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Others explained how they decided they weren’t a “math person” during these time-pressured moments and lost interest in the subject. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">First-person testimonials are sufficient evidence for some that timed tests are harmful. For others, subjective reflections like this, no matter how many and how emotionally compelling, still fall short of scientific proof. At the same time, we also don’t have compelling scientific evidence to prove that timed tests aren’t harming children. I think it remains unknown. \u003c/span>\u003c/p>\n\u003ch2>Citation clash\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">Several math education experts questioned the Science of Math group’s scientific evidence on their second claim, that “timed tactics improve math performance.” One critic, Rachel Lambert, an associate professor in both special education and mathematics education at University of California Santa Barbara, had one of her classes analyze the group’s citations about timed tests, as an assignment on how to analyze education research. She showed me a spreadsheet of instances where the citations didn’t back their claims. In some cases, the studies contradicted their claims and found that students performed worse under timed conditions. “They’re calling themselves the Science of Math,” said Lambert. “But they’re not being careful in their citations.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">I found several of the citations confusing, too. Corey Peltier, an assistant professor of special education at the University of Oklahoma and one of the founders of the Science of Math group, explained that the primary purpose of the webpage and the article was to dispel the myth that timed tests and other timed activities cause anxiety. “We weren’t writing about how timing affects math performance,” he said via email. “Rather we were writing about whether timing causes math anxiety.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Confusing citations or not, the more pressing question for math teachers and parents is whether there is evidence in favor of timed tests. The U.S. Department of Education seems to side with the Science of Math folks and against the National Council of Teachers of Mathematics. A \u003c/span>\u003ca href=\"https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/WWC2021006-Math-PG.pdf\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">2021 guide for teachers on how to assist elementary school students who struggle with math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> recommends regular timed activities – not necessarily tests – to help children build fluency with addition, subtraction, multiplication and division. The What Works Clearinghouse, a unit of the Department of Education that vets research, and an expert panel found 27 studies to back timed practice and called that a “strong” level of evidence.\u003c/span>\u003c/p>\n\u003ch2>Games vs. the stopwatch\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">These 27 studies suggest that timed activities – not in isolation, but in conjunction with larger interventions – help children learn math. In one 2013 \u003c/span>\u003ca href=\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3779611/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">study\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, struggling first graders received math tutoring three times a week and were split into two groups. One played untimed games to reinforce the lessons. The other was subjected to speed practice, where the children worked in groups to try to answer as many math flashcards correctly as possible within 60 seconds. Each time they were encouraged to “meet or beat” their previous score. After 16 weeks, the children in the speed practice group had much higher math achievement than the children who had played untimed games.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Children in the speed group answered more math facts correctly each day, the researchers found. The sheer volume of correct responses helped the children commit more math facts to long-term memory, according to Lynn Fuchs, who led the study. Cognitive scientists call that spaced retrieval practice, a proven way of building long-term memories, and children in the speed group got more of it. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“That gives children an advantage as they progress through the math curriculum,” said Fuchs, a professor of education at Vanderbilt University. “A lot of kids will develop fluency on their own without any fluency building practice. But to say we can’t do that in classrooms is to deny the opportunity to develop fluency for a significant portion of children.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Fuchs and other advocates question why timed practice is so controversial in math when it’s common in other fields. Musicians repeat scales by the rapid tick of a metronome and athletes do speed drills to build muscle memory. “In all walks of life, the strongest musicians, the most skillful athletes, they do drills and practice, drill and practice,” said Fuchs.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Opponents of timed tests also want children to automatically know that seven times eight is 56 instead of conceptually thinking it out each time (7+7+7+7+7+7+7+7), but they say that there are games and other less stressful ways to do it. Fuchs’s study is one of the few to directly test timed versus untimed conditions and we need more studies to replicate her findings before we can conclude that speed is considerably more effective and harmless to children.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Both sides of this debate are concerned with working memory, the ability to temporarily hold information in your head in order to process it, think and solve. One side worries that timed tests can produce so much anxiety that it overwhelms the working memory and prevents a child from learning. The other side wants to free up working memory to handle more complicated math problems by making basic arithmetic calculations automatic, and it believes the most effective road to automaticity is through speed drills. While the causes of math anxiety are debated and mysterious, many in the pro-drill camp suspect that children might feel less math anxiety if they became more proficient in the subject, which is something that drills might help accomplish.\u003c/span>\u003c/p>\n\u003ch2>Advice for math teachers\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">What can classroom teachers take away from this debate? I turned to a veteran researcher, Art Baroody, professor emeritus at the University of Illinois at Urbana-Champaign, who spent his career studying the best ways to teach counting, numbers and arithmetic concepts to young children.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">He agrees that timed tests can be used effectively, but he is apprehensive about a blanket recommendation for teachers to use them. “Timed tests are an educational tool and like any tool can be used to good, no, or bad effect,” he said. “Unfortunately, the tool is often misused with poor or even devastating results. I have seen the damage timed tests can do to some children.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Baroody thinks it’s critical that children first understand conceptually what addition and subtraction mean and develop number sense before they are given timed tests. Too often students are taught mathematical operations through rote memorization, like random numbers, he said, and arithmetic learned this way is easily forgotten, no matter how much it’s drilled.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">But once a child understands the math, he believes that timed worksheets are beneficial. Baroody said that if he were teaching in an elementary school classroom, he would administer timed tests at least once a week, and even more often depending on the topic and how much children have learned.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Fuchs is even more circumspect in her advice to teachers on how to use timed tests effectively without harming children in the process. Not only should students first master concepts, they should have already demonstrated that they know the correct answers in an untimed setting. “You don’t want to give students a page full of problems and they’re kind of lost,” said Fuchs. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Immediate feedback is important too. “When you make an error, your teacher or your partner can say, ‘Hey, let’s fix that’,” said Fuchs. “You want to stop a student when they make an error because what you’re trying to do is practice correct responses. You don’t want students to practice incorrect responses.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Advocates of timed practice disagree about the details. Some say students should be given long lists of calculations so that no one can finish in time and slam their pencils down, which leaves slower children feeling bad about themselves. However, Fuchs favors flashcards because she fears the sight of a long list of problems overwhelms some children. This is an area that needs more research to guide teachers on best practices.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The Science of Math group concurs that not all timed practice is good, and says the research shows that timed activities or tests shouldn’t start until after a child can calculate accurately. They also say that teachers should never count these tests toward students’ grades; the tests should be low-stakes practice.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“Much like any instructional activity, if it is used inappropriately, it will yield minimal benefits and in some cases could be harmful,” said Peltier. Timing students on “a skill they don’t know – not only is this a waste of time, it also can be demoralizing and harmful. Imagine being timed to parallel park a car at the age of 16!” \u003c/span>\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">This story about \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/proof-points-do-math-drills-help-children-learn/\" target=\"_blank\" rel=\"noopener\">\u003ci>\u003cspan style=\"font-weight: 400\">math drills\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> was written by Jill Barshay and produced by \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/special-reports/higher-education/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">The Hechinger Report\u003c/span>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/proofpoints/\" target=\"_blank\" rel=\"noopener\">\u003ci>\u003cspan style=\"font-weight: 400\">Proof Points\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> and other \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/newsletters/\" target=\"_blank\" rel=\"noopener\">\u003ci>\u003cspan style=\"font-weight: 400\">Hechinger newsletters\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\"> \u003c/span>\u003c/p>\n\n","blocks":[],"excerpt":"Advocates insist that timed tests help children memorize math facts, while opponents say they cause math anxiety.","status":"publish","parent":0,"modified":1685240378,"stats":{"hasAudio":false,"hasVideo":false,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":33,"wordCount":2177},"headData":{"title":"Do math drills help children learn? | KQED","description":"Timed tests might be a more efficient way to memorize multiplication tables, but even advocates caution that there are many pitfalls.","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","socialDescription":"Timed tests might be a more efficient way to memorize multiplication tables, but even advocates caution that there are many pitfalls.","schema":{"@context":"http://schema.org","@type":"Article","headline":"Do math drills help children learn?","datePublished":"2023-05-30T10:00:59.000Z","dateModified":"2023-05-28T02:19:38.000Z","image":"https://cdn.kqed.org/wp-content/uploads/2020/02/KQED-OG-Image@1x.png"}},"nprByline":"Jill Barshay, \u003ca href=\"https://hechingerreport.org/\" target=\"_blank\">The Hechinger Report\u003c/a>","excludeFromSiteSearch":"Include","showOnAuthorArchivePages":"No","articleAge":"0","path":"/mindshift/61712/do-math-drills-help-children-learn","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>\u003cspan style=\"font-weight: 400\">One of the most hotly contested teaching practices concerns a single minute of math class. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Should teachers pull out their stopwatches and administer one-page worksheets in addition, subtraction, multiplication and division? Speed drills are such a routine part of the weekly rhythms of many math classrooms that they’re often called Mad Minute Mondays. Critics say these timed drills aren’t useful and instead provoke math anxiety in many children. The National Council of Teachers of Mathematics urges teachers to “\u003c/span>\u003ca href=\"https://www.nctm.org/uploadedFiles/Standards_and_Positions/Position_Statements/PROCEDURAL_FLUENCY.pdf\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">avoid” timed tests\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. But advocates insist that these tests, which last one to five minutes, help children memorize math facts, freeing up their brains to tackle more challenging math problems. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">This long-running debate captured my attention again because a group of more than a dozen education researchers, who founded an organization they call the “\u003c/span>\u003ca href=\"https://www.thescienceofmath.com/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">Science of Math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">,” declared that the stopwatch skeptics are wrong. The researchers built an \u003c/span>\u003ca href=\"https://www.thescienceofmath.com/timed-tests-cause-math-anxiety\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">entire webpage\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> to set the record straight and devoted a section of a 2022 paper to explaining why it’s a \u003c/span>\u003ca href=\"https://www.cis.org.au/publication/myths-that-undermine-maths-teaching/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">myth that timed tests cause anxiety\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. A few readers contacted me after I first wrote about the \u003c/span>\u003ca href=\"https://hechingerreport.org/proof-points-how-a-debate-over-the-science-of-math-could-reignite-the-math-wars/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">Science of Math movement\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> earlier in May 2023, urging me to look at the group’s claims about timed tests. After looking at the research, I think the evidence is not quite as clear as the Science of Math group indicates. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The group argues there is no evidence that timed tests cause math anxiety. They also contend that timed tests improve math performance. Some researchers contest both points.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“Time tests don’t cause math anxiety?” said Jo Boaler, an education professor at Stanford University who is a prominent opponent of timed tests. “I could counter their studies with many more that show the opposite. And yes, you could conclude it’s a contested field, that there’s different evidence. But you can’t conclude that this is a myth.”\u003c/span>\u003c/p>\n\u003ch2>Dueling evidence\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">There isn’t much dispute about the lack of empirical evidence. I interviewed more than a half dozen math experts who confirmed there aren’t well-designed experiments that prove timed tests cause math anxiety. The Science of Math group could find only \u003c/span>\u003ca href=\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2806671/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">two experimental studies\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> that have attempted to \u003c/span>\u003ca href=\"https://link.springer.com/article/10.1007/s10864-016-9251-6\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">test the hypothesis\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and neither concluded that tests produce anxiety. \u003c/span>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Math anxiety is difficult to measure, and even children who enjoy timed drills may experience an elevated heart rate, an aspect of anxiety, as they race through a sheet of sums. Distinguishing productive adrenaline rush from detrimental anxiety isn’t easy. It’s also complicated to disentangle whether timed tests are making matters worse for children who already have math anxiety from other causes. There’s \u003c/span>\u003ca href=\"https://news.uchicago.edu/story/math-anxiety-causes-trouble-students-early-first-grade\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">evidence for and against\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> even within studies. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Ideally, you would need to design a multi-year study — where some children were randomly given speed drills and others not, but were all taught the same way — and see what their math achievement and math anxiety levels were at the end of high school. That study doesn’t exist. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">What does exist are dozens, perhaps hundreds, of studies that document the stories of people who describe how much they hated timed tests. Interview excerpts like this one from a \u003c/span>\u003ca href=\"https://go.gale.com/ps/i.do?id=GALE%7CA62839422&sid=googleScholar&v=2.1&it=r&linkaccess=abs&issn=01463934&p=AONE&sw=w&userGroupName=nysl_oweb&isGeoAuthType=true&aty=geo\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">1999 study\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> of college students who were training to become math teachers are typical:\u003c/span>\u003c/p>\n\u003cp>\u003cem>\u003cspan style=\"font-weight: 400\">“If I am timed, I get nervous and forget everything. I do the ones I know, but then I get stressed that I’m not thinking fast enough and forget. I worry about finishing, and I can’t remember it even if I do know it. It is horrible. I get nervous just thinking about it.”\u003c/span>\u003c/em>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Others explained how they decided they weren’t a “math person” during these time-pressured moments and lost interest in the subject. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">First-person testimonials are sufficient evidence for some that timed tests are harmful. For others, subjective reflections like this, no matter how many and how emotionally compelling, still fall short of scientific proof. At the same time, we also don’t have compelling scientific evidence to prove that timed tests aren’t harming children. I think it remains unknown. \u003c/span>\u003c/p>\n\u003ch2>Citation clash\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">Several math education experts questioned the Science of Math group’s scientific evidence on their second claim, that “timed tactics improve math performance.” One critic, Rachel Lambert, an associate professor in both special education and mathematics education at University of California Santa Barbara, had one of her classes analyze the group’s citations about timed tests, as an assignment on how to analyze education research. She showed me a spreadsheet of instances where the citations didn’t back their claims. In some cases, the studies contradicted their claims and found that students performed worse under timed conditions. “They’re calling themselves the Science of Math,” said Lambert. “But they’re not being careful in their citations.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">I found several of the citations confusing, too. Corey Peltier, an assistant professor of special education at the University of Oklahoma and one of the founders of the Science of Math group, explained that the primary purpose of the webpage and the article was to dispel the myth that timed tests and other timed activities cause anxiety. “We weren’t writing about how timing affects math performance,” he said via email. “Rather we were writing about whether timing causes math anxiety.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Confusing citations or not, the more pressing question for math teachers and parents is whether there is evidence in favor of timed tests. The U.S. Department of Education seems to side with the Science of Math folks and against the National Council of Teachers of Mathematics. A \u003c/span>\u003ca href=\"https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/WWC2021006-Math-PG.pdf\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">2021 guide for teachers on how to assist elementary school students who struggle with math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> recommends regular timed activities – not necessarily tests – to help children build fluency with addition, subtraction, multiplication and division. The What Works Clearinghouse, a unit of the Department of Education that vets research, and an expert panel found 27 studies to back timed practice and called that a “strong” level of evidence.\u003c/span>\u003c/p>\n\u003ch2>Games vs. the stopwatch\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">These 27 studies suggest that timed activities – not in isolation, but in conjunction with larger interventions – help children learn math. In one 2013 \u003c/span>\u003ca href=\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3779611/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">study\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, struggling first graders received math tutoring three times a week and were split into two groups. One played untimed games to reinforce the lessons. The other was subjected to speed practice, where the children worked in groups to try to answer as many math flashcards correctly as possible within 60 seconds. Each time they were encouraged to “meet or beat” their previous score. After 16 weeks, the children in the speed practice group had much higher math achievement than the children who had played untimed games.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Children in the speed group answered more math facts correctly each day, the researchers found. The sheer volume of correct responses helped the children commit more math facts to long-term memory, according to Lynn Fuchs, who led the study. Cognitive scientists call that spaced retrieval practice, a proven way of building long-term memories, and children in the speed group got more of it. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“That gives children an advantage as they progress through the math curriculum,” said Fuchs, a professor of education at Vanderbilt University. “A lot of kids will develop fluency on their own without any fluency building practice. But to say we can’t do that in classrooms is to deny the opportunity to develop fluency for a significant portion of children.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Fuchs and other advocates question why timed practice is so controversial in math when it’s common in other fields. Musicians repeat scales by the rapid tick of a metronome and athletes do speed drills to build muscle memory. “In all walks of life, the strongest musicians, the most skillful athletes, they do drills and practice, drill and practice,” said Fuchs.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Opponents of timed tests also want children to automatically know that seven times eight is 56 instead of conceptually thinking it out each time (7+7+7+7+7+7+7+7), but they say that there are games and other less stressful ways to do it. Fuchs’s study is one of the few to directly test timed versus untimed conditions and we need more studies to replicate her findings before we can conclude that speed is considerably more effective and harmless to children.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Both sides of this debate are concerned with working memory, the ability to temporarily hold information in your head in order to process it, think and solve. One side worries that timed tests can produce so much anxiety that it overwhelms the working memory and prevents a child from learning. The other side wants to free up working memory to handle more complicated math problems by making basic arithmetic calculations automatic, and it believes the most effective road to automaticity is through speed drills. While the causes of math anxiety are debated and mysterious, many in the pro-drill camp suspect that children might feel less math anxiety if they became more proficient in the subject, which is something that drills might help accomplish.\u003c/span>\u003c/p>\n\u003ch2>Advice for math teachers\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">What can classroom teachers take away from this debate? I turned to a veteran researcher, Art Baroody, professor emeritus at the University of Illinois at Urbana-Champaign, who spent his career studying the best ways to teach counting, numbers and arithmetic concepts to young children.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">He agrees that timed tests can be used effectively, but he is apprehensive about a blanket recommendation for teachers to use them. “Timed tests are an educational tool and like any tool can be used to good, no, or bad effect,” he said. “Unfortunately, the tool is often misused with poor or even devastating results. I have seen the damage timed tests can do to some children.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Baroody thinks it’s critical that children first understand conceptually what addition and subtraction mean and develop number sense before they are given timed tests. Too often students are taught mathematical operations through rote memorization, like random numbers, he said, and arithmetic learned this way is easily forgotten, no matter how much it’s drilled.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">But once a child understands the math, he believes that timed worksheets are beneficial. Baroody said that if he were teaching in an elementary school classroom, he would administer timed tests at least once a week, and even more often depending on the topic and how much children have learned.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Fuchs is even more circumspect in her advice to teachers on how to use timed tests effectively without harming children in the process. Not only should students first master concepts, they should have already demonstrated that they know the correct answers in an untimed setting. “You don’t want to give students a page full of problems and they’re kind of lost,” said Fuchs. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Immediate feedback is important too. “When you make an error, your teacher or your partner can say, ‘Hey, let’s fix that’,” said Fuchs. “You want to stop a student when they make an error because what you’re trying to do is practice correct responses. You don’t want students to practice incorrect responses.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Advocates of timed practice disagree about the details. Some say students should be given long lists of calculations so that no one can finish in time and slam their pencils down, which leaves slower children feeling bad about themselves. However, Fuchs favors flashcards because she fears the sight of a long list of problems overwhelms some children. This is an area that needs more research to guide teachers on best practices.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The Science of Math group concurs that not all timed practice is good, and says the research shows that timed activities or tests shouldn’t start until after a child can calculate accurately. They also say that teachers should never count these tests toward students’ grades; the tests should be low-stakes practice.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“Much like any instructional activity, if it is used inappropriately, it will yield minimal benefits and in some cases could be harmful,” said Peltier. Timing students on “a skill they don’t know – not only is this a waste of time, it also can be demoralizing and harmful. Imagine being timed to parallel park a car at the age of 16!” \u003c/span>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">This story about \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/proof-points-do-math-drills-help-children-learn/\" target=\"_blank\" rel=\"noopener\">\u003ci>\u003cspan style=\"font-weight: 400\">math drills\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> was written by Jill Barshay and produced by \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/special-reports/higher-education/\" target=\"_blank\" rel=\"noopener\">\u003cspan style=\"font-weight: 400\">The Hechinger Report\u003c/span>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/proofpoints/\" target=\"_blank\" rel=\"noopener\">\u003ci>\u003cspan style=\"font-weight: 400\">Proof Points\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> and other \u003c/span>\u003c/i>\u003ca href=\"https://hechingerreport.org/newsletters/\" target=\"_blank\" rel=\"noopener\">\u003ci>\u003cspan style=\"font-weight: 400\">Hechinger newsletters\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\"> \u003c/span>\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/61712/do-math-drills-help-children-learn","authors":["byline_mindshift_61712"],"categories":["mindshift_21504"],"tags":["mindshift_20943","mindshift_392","mindshift_20893","mindshift_21641","mindshift_21640","mindshift_21541","mindshift_21094","mindshift_21642"],"featImg":"mindshift_61716","label":"mindshift"},"mindshift_54389":{"type":"posts","id":"mindshift_54389","meta":{"index":"posts_1591205157","site":"mindshift","id":"54389","score":null,"sort":[1570087359000]},"guestAuthors":[],"slug":"3-ways-to-shape-math-into-a-positive-experience","title":"3 Ways to Shape Math Into a Positive Experience","publishDate":1570087359,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp>\u003cspan style=\"font-weight: 400\">As a teenager, Vanessa Vakharia never expected math to factor into her future.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“I wanted to be a rock star and marry Keanu Reeves. Still do,”\u003c/span>\u003cspan style=\"font-weight: 400\"> Vakharia says in a phone interview as \u003c/span>\u003ca href=\"https://www.goodnightsunrise.com/\">\u003cspan style=\"font-weight: 400\">her band\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> drives across Canada for a multi-week tour.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Aside from her Keanu fantasies, there were other signs that a career in numbers wasn’t in the cards — like the two times she failed 11th-grade math.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Because she was into art and music, Vakharia considered herself a “creative type.” When she enrolled in an alternative high school, she told her teacher that she was \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/42825/not-a-math-person-how-to-remove-obstacles-to-learning-math\">\u003cspan style=\"font-weight: 400\">not a math person\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The educator rebuffed the notion. “She was like, ‘That’s not a thing,’ ” Vakharia recalls. \u003c/span>\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">That’s when Vakharia’s math story began to shift. Fast forward two decades, and she is a certified math teacher who runs \u003c/span>\u003ca href=\"https://www.themathguru.ca/\">\u003cspan style=\"font-weight: 400\">a Toronto tutoring business\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> with 40 employees. (She hasn’t given up hope on Keanu, though, pointing out that he’s still unmarried.) She is also the author of the book \"\u003c/span>\u003ca href=\"https://www.amazon.ca/Math-Hacks-Stress-Better-Marks/dp/1443163163\">\u003cspan id=\"productTitle\" class=\"a-size-large\">Math Hacks: Cool Tips + Less Stress = Better Marks.\" \u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">After transforming her own math narrative, Vakharia now strives to abolish the widespread view that math is “this innate super power that people are born with.”\u003c/span>\u003c/p>\n\u003cfigure id=\"attachment_54582\" class=\"wp-caption alignnone\" style=\"max-width: 2000px\">\u003cimg class=\"wp-image-54582 size-full\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/10/Vakharia2.jpg\" alt=\"\" width=\"2000\" height=\"1858\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2.jpg 2000w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-160x149.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-800x743.jpg 800w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-768x713.jpg 768w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-1020x948.jpg 1020w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-1200x1115.jpg 1200w\" sizes=\"(max-width: 2000px) 100vw, 2000px\">\u003cfigcaption class=\"wp-caption-text\">Courtesy of Vanessa Vakharia.\u003c/figcaption>\u003c/figure>\n\u003cp>\u003cspan style=\"font-weight: 400\">Research supports her stance. As with other subjects, having a \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/41700/growth-mindset-how-to-normalize-mistake-making-and-struggle-in-class\">\u003cspan style=\"font-weight: 400\">growth mindset\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> in math matters — and not just for kids. A range of parent and teacher beliefs and attitudes toward math have been linked with children’s beliefs and performance in the subject, especially among girls. In \u003c/span>\u003ca href=\"https://psycnet.apa.org/search/display?id=ad67cf96-e312-e79b-f972-5057555c5505&recordId=1&tab=PA&page=1&display=25&sort=PublicationYearMSSort%20desc,AuthorSort%20asc&sr=1\">\u003cspan style=\"font-weight: 400\">a recent study\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> of Chilean kindergartners and their families, for example, mothers’ math self-concepts positively predicted girls’ math self-concepts, while fathers’ math self-concepts negatively predicted girls’ math self-concepts. (The latter effect was reduced in cases where fathers engaged in home math activities with their daughters.)\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">In the same study, parents’ math self-concepts did not predict kindergarten boys’ math self-concepts. Adults’ gender stereotypes and \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/32223/why-kids-take-on-adults-math-anxiety\">\u003cspan style=\"font-weight: 400\">math anxiety\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, too, have been found to influence children’s math attitudes and performance. Jo Boaler, a Stanford University education professor and author of \"\u003c/span>\u003ca href=\"https://www.youcubed.org/resources/mathematical-mindsets/\">\u003cspan style=\"font-weight: 400\">Mathematical Mindsets\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">,\" says that when she talks to parents she tells them that “the most important thing whenever they approach maths is to be very positive about it with their kids.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">But many adults have to overcome their own negative histories with the subject first. At the end of a recent summer program that Boaler taught, 98 out of 100 undergraduates wrote about their past math traumas and how differently they felt about the subject after discovering that \u003c/span>\u003ca href=\"https://www.youcubed.org/resources/brain-science/\">\u003cspan style=\"font-weight: 400\">anyone can learn math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">So how can adults who have long-held negative beliefs about math begin to \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/52749/how-to-make-sure-your-math-anxiety-doesnt-make-your-kids-hate-math\">\u003cspan style=\"font-weight: 400\">think and talk differently\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">? Based on her own myth-busting talks with parents and teachers, Vakharia recommends three steps.\u003c/span>\u003c/p>\n\u003cp>\u003cb>1. Unpack the cultural narrative\u003c/b>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Shifting your math narrative requires recognition of the societal math narratives in which it is enmeshed. “As a society we have an obsession with categorizing...boy/girl, left-brained/right-brained,” says Vakharia. Those binaries get repeated in \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/46772/how-one-school-changed-its-math-culture-starting-with-teachers\">\u003cspan style=\"font-weight: 400\">schools\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, families, workplaces, media and pop culture.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Vakharia likes to ask people if they have ever seen a cheerleader on TV or in a movie who is good at math. The answer, of course, is “no.” Not only does popular culture show math as being for certain types of people, it often portrays those people as geniuses and prodigies, like Matt Damon’s character in \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Good Will Hunting\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">. That’s harmful, Vakharia says, because it discourages a more productive, \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/53524/how-revising-math-exams-turns-students-into-learners-not-processors\">\u003cspan style=\"font-weight: 400\">growth-focused approach toward math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“We also have this narrative that if it takes work to do something, you’re not good at something,” she says. “You weren’t born knowing calculus. You work at it, and some people have to \u003c/span>\u003ca href=\"https://www.youcubed.org/resource/visual-mathematics/\">\u003cspan style=\"font-weight: 400\">work at it in different ways\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.”\u003c/span>\u003c/p>\n\u003cfigure id=\"attachment_54583\" class=\"wp-caption alignnone\" style=\"max-width: 1920px\">\u003cimg class=\"wp-image-54583 size-full\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/10/Vakharia_TheMathGuru.jpg\" alt=\"\" width=\"1920\" height=\"1080\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru.jpg 1920w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-160x90.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-800x450.jpg 800w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-768x432.jpg 768w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-1020x574.jpg 1020w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-1200x675.jpg 1200w\" sizes=\"(max-width: 1920px) 100vw, 1920px\">\u003cfigcaption class=\"wp-caption-text\">Courtesy of Vanessa Vakharia.\u003c/figcaption>\u003c/figure>\n\u003cp>\u003cb>2. Drill down into your experience\u003c/b>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Once you debunk the social messages surrounding math, it’s time to make it personal. If you say you’re not a math person, break that down. Why do you think that?\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Most of the time, when Vakharia asks that question, she hears common themes: The person never did their homework, they had a demeaning teacher, their parents said it wasn’t in their genes, and so on. When Vakharia asks follow-up questions about how the person tried to improve, such as seeking extra resources or teacher support, the response is usually that they tried one type of remediation but gave up when it didn’t work.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“When you really peel it back, there’s nothing in any of these stories that someone was truly incapable of doing math,” Vakharia says.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">At this point, analogies can help. Think about something you have learned as an adult. Maybe it’s watercolors or CrossFit. Before taking up that practice, did you consider yourself an artist or an athlete? Probably not, and maybe you still don’t, but you know that painting and weightlifting are skills that can be learned.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">It’s the same with math.\u003c/span>\u003c/p>\n\u003cp>\u003cb>3. Try again\u003c/b>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Once a person has re-examined their math history, Vakharia likes to ask whether they’re open to learning math now. If they say “yes,” she asks them to pick a topic they want to learn and recommends a tutor or other resources.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The key is to make it manageable. You don’t need to commit to learning an entire math course. If geometry confounded you, give the Pythagorean Theorem another shot. If your math problems began in elementary school, try something more fundamental, such as times tables or fractions.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">\u003ca href=\"https://www.goodreads.com/book/show/42286436-math-hacks\">\u003cimg class=\"alignright wp-image-54585\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/10/Math-Hacks.jpg\" alt=\"\" width=\"250\" height=\"299\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2019/10/Math-Hacks.jpg 318w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Math-Hacks-160x191.jpg 160w\" sizes=\"(max-width: 250px) 100vw, 250px\">\u003c/a>In a June 2019 episode of the \"\u003c/span>\u003ca href=\"https://unladylike.co/episodes/052/math\">\u003cspan style=\"font-weight: 400\">Unladylike\" podcast\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, co-host Caroline Ervin talked about her childhood math traumas with Vakharia and her lasting perception that she was incapable of doing math. At the end of the conversation, Vakharia asked Ervin to commit to learning one aspect of math that troubled her. Ervin assigned herself the task of revisiting SohCahToa, a mnemonic device used to understand how sine, cosine and tangent work in trigonometry.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Ervin followed through on her homework. In an interview with MindShift, she said that she set up a Skype session with one of the tutors from Vakharia’s tutoring center, The Math Guru. Though she felt some familiar math anxiety creep in at the start, ultimately, Ervin said, she “had a blast” and conquered SohCahToa.\u003c/span>\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“Approaching math as a set of skills that simply require learning and practice helps me chill out about it,” she said. “Math isn't mystical; it's practical, and it's something I now feel I can easily revisit if there's some sort of practical puzzle to solve.”\u003c/span>\u003c/p>\n\n","blocks":[],"excerpt":"It's not uncommon for kids and adults to have a negative experience learning math. Learning about how the brain works and unpacking some stereotypes can help learners reframe the narrative they tell themselves about math. ","status":"publish","parent":0,"modified":1589422682,"stats":{"hasAudio":false,"hasVideo":false,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":28,"wordCount":1177},"headData":{"title":"3 Ways to Shape Math Into a Positive Experience | KQED","description":"It's not uncommon for kids and adults to have a negative experience learning math. Learning about how the brain works and unpacking some stereotypes can help learners reframe the narrative they tell themselves about math. ","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","schema":{"@context":"http://schema.org","@type":"Article","headline":"3 Ways to Shape Math Into a Positive Experience","datePublished":"2019-10-03T07:22:39.000Z","dateModified":"2020-05-14T02:18:02.000Z","image":"https://cdn.kqed.org/wp-content/uploads/2020/02/KQED-OG-Image@1x.png"}},"disqusIdentifier":"54389 https://ww2.kqed.org/mindshift/?p=54389","disqusUrl":"https://ww2.kqed.org/mindshift/2019/10/03/3-ways-to-shape-math-into-a-positive-experience/","disqusTitle":"3 Ways to Shape Math Into a Positive Experience","path":"/mindshift/54389/3-ways-to-shape-math-into-a-positive-experience","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>\u003cspan style=\"font-weight: 400\">As a teenager, Vanessa Vakharia never expected math to factor into her future.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“I wanted to be a rock star and marry Keanu Reeves. Still do,”\u003c/span>\u003cspan style=\"font-weight: 400\"> Vakharia says in a phone interview as \u003c/span>\u003ca href=\"https://www.goodnightsunrise.com/\">\u003cspan style=\"font-weight: 400\">her band\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> drives across Canada for a multi-week tour.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Aside from her Keanu fantasies, there were other signs that a career in numbers wasn’t in the cards — like the two times she failed 11th-grade math.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Because she was into art and music, Vakharia considered herself a “creative type.” When she enrolled in an alternative high school, she told her teacher that she was \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/42825/not-a-math-person-how-to-remove-obstacles-to-learning-math\">\u003cspan style=\"font-weight: 400\">not a math person\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The educator rebuffed the notion. “She was like, ‘That’s not a thing,’ ” Vakharia recalls. \u003c/span>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">That’s when Vakharia’s math story began to shift. Fast forward two decades, and she is a certified math teacher who runs \u003c/span>\u003ca href=\"https://www.themathguru.ca/\">\u003cspan style=\"font-weight: 400\">a Toronto tutoring business\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> with 40 employees. (She hasn’t given up hope on Keanu, though, pointing out that he’s still unmarried.) She is also the author of the book \"\u003c/span>\u003ca href=\"https://www.amazon.ca/Math-Hacks-Stress-Better-Marks/dp/1443163163\">\u003cspan id=\"productTitle\" class=\"a-size-large\">Math Hacks: Cool Tips + Less Stress = Better Marks.\" \u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">After transforming her own math narrative, Vakharia now strives to abolish the widespread view that math is “this innate super power that people are born with.”\u003c/span>\u003c/p>\n\u003cfigure id=\"attachment_54582\" class=\"wp-caption alignnone\" style=\"max-width: 2000px\">\u003cimg class=\"wp-image-54582 size-full\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/10/Vakharia2.jpg\" alt=\"\" width=\"2000\" height=\"1858\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2.jpg 2000w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-160x149.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-800x743.jpg 800w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-768x713.jpg 768w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-1020x948.jpg 1020w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia2-1200x1115.jpg 1200w\" sizes=\"(max-width: 2000px) 100vw, 2000px\">\u003cfigcaption class=\"wp-caption-text\">Courtesy of Vanessa Vakharia.\u003c/figcaption>\u003c/figure>\n\u003cp>\u003cspan style=\"font-weight: 400\">Research supports her stance. As with other subjects, having a \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/41700/growth-mindset-how-to-normalize-mistake-making-and-struggle-in-class\">\u003cspan style=\"font-weight: 400\">growth mindset\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> in math matters — and not just for kids. A range of parent and teacher beliefs and attitudes toward math have been linked with children’s beliefs and performance in the subject, especially among girls. In \u003c/span>\u003ca href=\"https://psycnet.apa.org/search/display?id=ad67cf96-e312-e79b-f972-5057555c5505&recordId=1&tab=PA&page=1&display=25&sort=PublicationYearMSSort%20desc,AuthorSort%20asc&sr=1\">\u003cspan style=\"font-weight: 400\">a recent study\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> of Chilean kindergartners and their families, for example, mothers’ math self-concepts positively predicted girls’ math self-concepts, while fathers’ math self-concepts negatively predicted girls’ math self-concepts. (The latter effect was reduced in cases where fathers engaged in home math activities with their daughters.)\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">In the same study, parents’ math self-concepts did not predict kindergarten boys’ math self-concepts. Adults’ gender stereotypes and \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/32223/why-kids-take-on-adults-math-anxiety\">\u003cspan style=\"font-weight: 400\">math anxiety\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, too, have been found to influence children’s math attitudes and performance. Jo Boaler, a Stanford University education professor and author of \"\u003c/span>\u003ca href=\"https://www.youcubed.org/resources/mathematical-mindsets/\">\u003cspan style=\"font-weight: 400\">Mathematical Mindsets\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">,\" says that when she talks to parents she tells them that “the most important thing whenever they approach maths is to be very positive about it with their kids.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">But many adults have to overcome their own negative histories with the subject first. At the end of a recent summer program that Boaler taught, 98 out of 100 undergraduates wrote about their past math traumas and how differently they felt about the subject after discovering that \u003c/span>\u003ca href=\"https://www.youcubed.org/resources/brain-science/\">\u003cspan style=\"font-weight: 400\">anyone can learn math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">So how can adults who have long-held negative beliefs about math begin to \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/52749/how-to-make-sure-your-math-anxiety-doesnt-make-your-kids-hate-math\">\u003cspan style=\"font-weight: 400\">think and talk differently\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">? Based on her own myth-busting talks with parents and teachers, Vakharia recommends three steps.\u003c/span>\u003c/p>\n\u003cp>\u003cb>1. Unpack the cultural narrative\u003c/b>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Shifting your math narrative requires recognition of the societal math narratives in which it is enmeshed. “As a society we have an obsession with categorizing...boy/girl, left-brained/right-brained,” says Vakharia. Those binaries get repeated in \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/46772/how-one-school-changed-its-math-culture-starting-with-teachers\">\u003cspan style=\"font-weight: 400\">schools\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, families, workplaces, media and pop culture.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Vakharia likes to ask people if they have ever seen a cheerleader on TV or in a movie who is good at math. The answer, of course, is “no.” Not only does popular culture show math as being for certain types of people, it often portrays those people as geniuses and prodigies, like Matt Damon’s character in \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Good Will Hunting\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">. That’s harmful, Vakharia says, because it discourages a more productive, \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/53524/how-revising-math-exams-turns-students-into-learners-not-processors\">\u003cspan style=\"font-weight: 400\">growth-focused approach toward math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“We also have this narrative that if it takes work to do something, you’re not good at something,” she says. “You weren’t born knowing calculus. You work at it, and some people have to \u003c/span>\u003ca href=\"https://www.youcubed.org/resource/visual-mathematics/\">\u003cspan style=\"font-weight: 400\">work at it in different ways\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.”\u003c/span>\u003c/p>\n\u003cfigure id=\"attachment_54583\" class=\"wp-caption alignnone\" style=\"max-width: 1920px\">\u003cimg class=\"wp-image-54583 size-full\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/10/Vakharia_TheMathGuru.jpg\" alt=\"\" width=\"1920\" height=\"1080\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru.jpg 1920w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-160x90.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-800x450.jpg 800w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-768x432.jpg 768w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-1020x574.jpg 1020w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Vakharia_TheMathGuru-1200x675.jpg 1200w\" sizes=\"(max-width: 1920px) 100vw, 1920px\">\u003cfigcaption class=\"wp-caption-text\">Courtesy of Vanessa Vakharia.\u003c/figcaption>\u003c/figure>\n\u003cp>\u003cb>2. Drill down into your experience\u003c/b>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Once you debunk the social messages surrounding math, it’s time to make it personal. If you say you’re not a math person, break that down. Why do you think that?\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Most of the time, when Vakharia asks that question, she hears common themes: The person never did their homework, they had a demeaning teacher, their parents said it wasn’t in their genes, and so on. When Vakharia asks follow-up questions about how the person tried to improve, such as seeking extra resources or teacher support, the response is usually that they tried one type of remediation but gave up when it didn’t work.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“When you really peel it back, there’s nothing in any of these stories that someone was truly incapable of doing math,” Vakharia says.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">At this point, analogies can help. Think about something you have learned as an adult. Maybe it’s watercolors or CrossFit. Before taking up that practice, did you consider yourself an artist or an athlete? Probably not, and maybe you still don’t, but you know that painting and weightlifting are skills that can be learned.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">It’s the same with math.\u003c/span>\u003c/p>\n\u003cp>\u003cb>3. Try again\u003c/b>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Once a person has re-examined their math history, Vakharia likes to ask whether they’re open to learning math now. If they say “yes,” she asks them to pick a topic they want to learn and recommends a tutor or other resources.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The key is to make it manageable. You don’t need to commit to learning an entire math course. If geometry confounded you, give the Pythagorean Theorem another shot. If your math problems began in elementary school, try something more fundamental, such as times tables or fractions.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">\u003ca href=\"https://www.goodreads.com/book/show/42286436-math-hacks\">\u003cimg class=\"alignright wp-image-54585\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/10/Math-Hacks.jpg\" alt=\"\" width=\"250\" height=\"299\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2019/10/Math-Hacks.jpg 318w, https://ww2.kqed.org/app/uploads/sites/23/2019/10/Math-Hacks-160x191.jpg 160w\" sizes=\"(max-width: 250px) 100vw, 250px\">\u003c/a>In a June 2019 episode of the \"\u003c/span>\u003ca href=\"https://unladylike.co/episodes/052/math\">\u003cspan style=\"font-weight: 400\">Unladylike\" podcast\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, co-host Caroline Ervin talked about her childhood math traumas with Vakharia and her lasting perception that she was incapable of doing math. At the end of the conversation, Vakharia asked Ervin to commit to learning one aspect of math that troubled her. Ervin assigned herself the task of revisiting SohCahToa, a mnemonic device used to understand how sine, cosine and tangent work in trigonometry.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Ervin followed through on her homework. In an interview with MindShift, she said that she set up a Skype session with one of the tutors from Vakharia’s tutoring center, The Math Guru. Though she felt some familiar math anxiety creep in at the start, ultimately, Ervin said, she “had a blast” and conquered SohCahToa.\u003c/span>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“Approaching math as a set of skills that simply require learning and practice helps me chill out about it,” she said. “Math isn't mystical; it's practical, and it's something I now feel I can easily revisit if there's some sort of practical puzzle to solve.”\u003c/span>\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/54389/3-ways-to-shape-math-into-a-positive-experience","authors":["11487"],"categories":["mindshift_192"],"tags":["mindshift_20784","mindshift_1040","mindshift_20825","mindshift_20512","mindshift_20943","mindshift_392","mindshift_20893","mindshift_391"],"featImg":"mindshift_54584","label":"mindshift"},"mindshift_54486":{"type":"posts","id":"mindshift_54486","meta":{"index":"posts_1591205157","site":"mindshift","id":"54486","score":null,"sort":[1569305261000]},"guestAuthors":[],"slug":"how-collaboration-unlocks-learning-and-lessens-student-isolation","title":"How Collaboration Unlocks Learning and Lessens Student Isolation","publishDate":1569305261,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp class=\"p1\">\u003cem>Excerpted from \u003ca href=\"https://www.youcubed.org/limitless-mind/\">LIMITLESS MIND\u003c/a> by Jo Boaler, copyright 2019. Reprinted with permission by HarperOne, an imprint of HarperCollins Publishers.\u003c/em>\u003c/p>\n\u003cp>\u003cstrong>By Jo Boaler\u003c/strong>\u003c/p>\n\u003cp class=\"p2\">Why Is Collaboration Important?\u003c/p>\n\u003cp class=\"p2\">Over my lifetime I have encountered a small number of fascinating situations, some through research and some through personal experience, in which collaboration and connection produced surprising outcomes. Some of these have related to learning, some to the pursuit of equity, and some to the advancement of ideas, even in the face of severe opposition. These different cases all shed light on something that neuroscience is also showing—when we connect with other people’s ideas there are multiple benefits for our brains and for our lives.\u003c/p>\n\u003cp class=\"p2\">Uri Treisman, a mathematician at the University of Texas at Austin, used to teach at the University of California, Berkeley. While Uri was at Berkeley, he noticed that 60 percent of African American students who took calculus were failing the class. This caused many to drop out of college altogether. Uri began looking at more university data and saw that no Chinese American students were failing calculus, so he asked the question: What is the difference between these two cultural groups that seems to be causing this discrepancy?\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp class=\"p2\">Uri at first asked the other mathematics faculty what they thought the reason was. They came up with a range of reasons: perhaps African American students came into the university with lower math scores or an insufficient mathematical background; perhaps they were from less wealthy homes. None of these suggested reasons were correct. What Uri found, through studying the students at work, was that there was one difference—the African American students worked on math problems by themselves, whereas the Chinese American students worked collaboratively. The Chinese American students worked on their assigned math problems in their dormitories and in the dining halls, thinking about them together. By contrast the African American students worked alone in their dormitory rooms and when they struggled on problems, they decided they were just not “math people” and gave up.\u003c/p>\n\u003cp class=\"p2\">\u003ca href=\"https://www.youcubed.org/limitless-mind/\">\u003cimg class=\"alignright size-full wp-image-54489\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/09/BOALER_LimitlessMind_HC-e1569303153159.jpg\" alt=\"\" width=\"250\" height=\"375\">\u003c/a>Uri and his team set up workshops for the more vulnerable students, including students of color. They created what Uri describes as a “challenging yet emotionally supportive academic environment.” In the workshops students worked on math problems together, considering together what it would take to achieve at the highest levels on different problems. The academic improvement that resulted from the workshops was significant. Within two years, the failure rate of African American students had dropped to zero, and the African American and Latino students who attended the workshops were outperforming their white and Asian classmates. This was an impressive result, and Uri has continued this approach at Austin. His approach has now been used in over two hundred different institutions of higher education. In writing about the experience, Uri says:\u003c/p>\n\u003cp class=\"p2\">\u003cem>We were able to convince the students in our orientation that success in college would require them to work with their peers, to create for themselves a community based on shared intellectual interests and common professional aims. How‐ ever, it took some work to teach them how to work together. After that it was really rather elementary pedagogy.\u003c/em>\u003c/p>\n\u003cp class=\"p2\">The fact that it took work to teach students how to collaborate with each other after they had spent thirteen years in school speaks to the problems in our school system, where the common pattern is that teachers lecture and students work through problems alone. The team leading the work‐ shops was right to point out that success in college requires working with others and making good connections. Many people know this, but they still see no role for collaboration in learning. When Uri and his team encouraged students to work together, their mathematical learning paths changed and they found success. This success story was about learning calculus in college, but we could substitute any other subject and expect similar results.\u003c/p>\n\u003cp class=\"p2\">Part of the reason students give up on learning is because they find it difficult and think they are alone in their struggle. An important change takes place when students work together and discover that everybody finds some or all of the work difficult. This is a critical moment for students, and one that helps them know that for everyone learning is a process and that obstacles are common.\u003c/p>\n\u003cp class=\"p2\">Another reason that students’ learning pathways change is because they receive an opportunity to connect ideas. Connecting with another person’s idea both requires and develops a higher level of understanding. When students work together (learning math, science, languages, English— anything), they get opportunities to make connections be‐ tween ideas, which is inherently valuable for them.\u003c/p>\n\u003cp class=\"p2\">A similarly noteworthy finding came from the results of a large‐scale testing program. In 2012, PISA assessments (international tests given to fifteen‐year‐olds worldwide, as mentioned earlier) showed that boys achieved at higher levels than girls in mathematics in thirty‐eight countries.\u003c/p>\n\u003cp class=\"p2\">This result was disappointing and surprising. In the US and in most other countries, the achievement of girls and boys in school is equal. This reminded me again of the ways that tests distort what students actually know and can do.\u003c/p>\n\u003cfigure id=\"attachment_54492\" class=\"wp-caption alignright\" style=\"max-width: 250px\">\u003cimg class=\"wp-image-54492\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2.jpg\" alt=\"\" width=\"250\" height=\"319\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2.jpg 1440w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-160x204.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-800x1020.jpg 800w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-768x979.jpg 768w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-1020x1301.jpg 1020w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-941x1200.jpg 941w\" sizes=\"(max-width: 250px) 100vw, 250px\">\u003cfigcaption class=\"wp-caption-text\">Jo Boaler \u003ccite>(Robert Houser Photography)\u003c/cite>\u003c/figcaption>\u003c/figure>\n\u003cp class=\"p2\">This was underscored when the PISA team issued a report showing that when anxiety was factored into the analysis, the gap in achievement between girls and boys was fully explained by the lower confidence of girls.\u003cspan class=\"s1\"> \u003c/span>What appeared to be a gender difference in mathematics achievement was in reality a difference in mathematics confidence levels. Girls became more anxious when they took the individual math tests, a phenomenon that is well established,\u003cspan class=\"s1\"> \u003c/span>and one that should make any educator pause before basing decisions on test performance.\u003c/p>\n\u003cp class=\"p2\">The impact of the different testing conditions as well as the potential of collaboration for reducing inequalities were also shown by another assessment the PISA team conducted. In addition to the usual individual mathematics test, they did an assessment of collaborative problem solving. In this assessment students did not collaborate with other students but with a computer agent. They had to take on the ideas of the agent and connect with and build upon them to collaboratively solve complex problems.\u003cspan class=\"s1\"> \u003c/span>This, to me, gauges something much more valuable than what a student produces on an individual math test. Instead of reproducing knowledge individually, students are asked to consider another’s ideas and work with them to solve a complex problem. This is also more consistent with the world of work students are being prepared for.\u003c/p>\n\u003cp class=\"p2\">In the test of collaborative problem solving, administered in fifty‐one countries, girls outperformed boys in every country. This notable result was accompanied by two others—there were no significant differences in outcomes between advantaged and disadvantaged students, a rare and important finding. And in some countries diversity boosted performance. The team found that in some countries “non‐ immigrant” students achieved at higher levels when they were in schools with larger numbers of “immigrant” students, a fantastic result, suggesting that diverse communities of learners help students become better collaborators.\u003c/p>\n\u003cp class=\"p2\">The results of the PISA assessment of collaborative problem solving shine a light on the pursuit of equity, revealing also the discriminatory nature of individual testing, something that anyone who gets anxious about high‐stakes testing fully understands. What does it mean that for girls collaboration, even with a computer agent, increases their confidence levels and causes them to achieve at higher levels? Similarly, what does it mean that African American students go from failing calculus to outperforming other, previously more successful, students when they collaborate? This research reveals the potential of collaboration, not only for girls or students of color, but for all learners and thinkers. When you connect with someone else’s ideas, you enhance your brain, your understanding, and your perspective.\u003c/p>\n\u003cp class=\"p2\">Neuroscientists also know the importance of collaboration. Research shows that when people collaborate, the medial orbitofrontal cortex and the frontoparietal network are activated, the latter of which aids in the development of executive functions. Neuroscientists refer to these different brain areas as the “social brain.” When we collaborate, our brains are charged with the complex task of making sense of another’s thinking and learning to interact. Social cognition is the topic of much current neuroscientific investigation.\u003c/p>\n\u003cp class=\"p2\">Collaboration is vital for learning, for college success, for brain development, and for creating equitable outcomes. Beyond all of this, it is beneficial to establish interpersonal connections, especially in times of conflict and need.\u003c/p>\n\u003cp class=\"p2\">Victor and Mildred Goertzel studied seven hundred people who had made huge contributions to society, choosing those who had been the subject of at least two biographies, people such as Marie Curie and Henry Ford. They found, in‐ credibly, that less than 15 percent of the famous men and women had been raised in supportive families; 75 percent had grown up in families with severe problems such as “poverty, abuse, absent parents, alcoholism, serious illness,” and other major issues. Their study was conducted in the 1960s. Clinical psychologist Meg Jay, in her interesting Wall Street Journal article on resilience, reports that similar results would be found today and cites Oprah Winfrey, Howard Schultz, and LeBron James as examples of people who grew up in extreme hardship.\u003c/p>\n\u003cp class=\"p2\">Jay has studied resilience over many years and points out that people who survive hardship often do better, but not through “bouncing back,” as some think, because the recovery process takes time and is more of a battle than a bounce. She also points out those who ultimately benefit from hardship, becoming stronger and resilient, do so when they maintain self‐belief, when they “own the fighter within,” and when they connect with other people. The thing that people who overcome hardship and do not become defeated by it have in common is that in times of need they all reached out to someone—a friend, a family member, or a colleague—and those connections helped them survive and develop strength.\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp class=\"p1\">\u003cem>Jo Boaler is the Nomellini-Olivier Professor of Education at Stanford, cofounder of \u003ca href=\"https://www.youcubed.org/\">youcubed.org\u003c/a> and author of \u003ca href=\"https://www.youcubed.org/limitless-mind/\">Limitless Mind: Learn, Lead & Live without Barriers\u003c/a> by HarperOne, an imprint of HarperCollins Publishers.\u003c/em>\u003c/p>\n\n","blocks":[],"excerpt":"Working together helps students know that obstacles are a shared experience and that they're not alone in their struggles. Collaboration also helps deepen connections to learning. ","status":"publish","parent":0,"modified":1569305261,"stats":{"hasAudio":false,"hasVideo":false,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":3,"wordCount":1733},"headData":{"title":"How Collaboration Unlocks Learning and Lessens Student Isolation | KQED","description":"Working together helps students know that obstacles are a shared experience and that they're not alone in their struggles. Collaboration also helps deepen connections to learning. ","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","schema":{"@context":"http://schema.org","@type":"Article","headline":"How Collaboration Unlocks Learning and Lessens Student Isolation","datePublished":"2019-09-24T06:07:41.000Z","dateModified":"2019-09-24T06:07:41.000Z","image":"https://cdn.kqed.org/wp-content/uploads/2020/02/KQED-OG-Image@1x.png"}},"disqusIdentifier":"54486 https://ww2.kqed.org/mindshift/?p=54486","disqusUrl":"https://ww2.kqed.org/mindshift/2019/09/23/how-collaboration-unlocks-learning-and-lessens-student-isolation/","disqusTitle":"How Collaboration Unlocks Learning and Lessens Student Isolation","path":"/mindshift/54486/how-collaboration-unlocks-learning-and-lessens-student-isolation","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp class=\"p1\">\u003cem>Excerpted from \u003ca href=\"https://www.youcubed.org/limitless-mind/\">LIMITLESS MIND\u003c/a> by Jo Boaler, copyright 2019. Reprinted with permission by HarperOne, an imprint of HarperCollins Publishers.\u003c/em>\u003c/p>\n\u003cp>\u003cstrong>By Jo Boaler\u003c/strong>\u003c/p>\n\u003cp class=\"p2\">Why Is Collaboration Important?\u003c/p>\n\u003cp class=\"p2\">Over my lifetime I have encountered a small number of fascinating situations, some through research and some through personal experience, in which collaboration and connection produced surprising outcomes. Some of these have related to learning, some to the pursuit of equity, and some to the advancement of ideas, even in the face of severe opposition. These different cases all shed light on something that neuroscience is also showing—when we connect with other people’s ideas there are multiple benefits for our brains and for our lives.\u003c/p>\n\u003cp class=\"p2\">Uri Treisman, a mathematician at the University of Texas at Austin, used to teach at the University of California, Berkeley. While Uri was at Berkeley, he noticed that 60 percent of African American students who took calculus were failing the class. This caused many to drop out of college altogether. Uri began looking at more university data and saw that no Chinese American students were failing calculus, so he asked the question: What is the difference between these two cultural groups that seems to be causing this discrepancy?\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp class=\"p2\">Uri at first asked the other mathematics faculty what they thought the reason was. They came up with a range of reasons: perhaps African American students came into the university with lower math scores or an insufficient mathematical background; perhaps they were from less wealthy homes. None of these suggested reasons were correct. What Uri found, through studying the students at work, was that there was one difference—the African American students worked on math problems by themselves, whereas the Chinese American students worked collaboratively. The Chinese American students worked on their assigned math problems in their dormitories and in the dining halls, thinking about them together. By contrast the African American students worked alone in their dormitory rooms and when they struggled on problems, they decided they were just not “math people” and gave up.\u003c/p>\n\u003cp class=\"p2\">\u003ca href=\"https://www.youcubed.org/limitless-mind/\">\u003cimg class=\"alignright size-full wp-image-54489\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/09/BOALER_LimitlessMind_HC-e1569303153159.jpg\" alt=\"\" width=\"250\" height=\"375\">\u003c/a>Uri and his team set up workshops for the more vulnerable students, including students of color. They created what Uri describes as a “challenging yet emotionally supportive academic environment.” In the workshops students worked on math problems together, considering together what it would take to achieve at the highest levels on different problems. The academic improvement that resulted from the workshops was significant. Within two years, the failure rate of African American students had dropped to zero, and the African American and Latino students who attended the workshops were outperforming their white and Asian classmates. This was an impressive result, and Uri has continued this approach at Austin. His approach has now been used in over two hundred different institutions of higher education. In writing about the experience, Uri says:\u003c/p>\n\u003cp class=\"p2\">\u003cem>We were able to convince the students in our orientation that success in college would require them to work with their peers, to create for themselves a community based on shared intellectual interests and common professional aims. How‐ ever, it took some work to teach them how to work together. After that it was really rather elementary pedagogy.\u003c/em>\u003c/p>\n\u003cp class=\"p2\">The fact that it took work to teach students how to collaborate with each other after they had spent thirteen years in school speaks to the problems in our school system, where the common pattern is that teachers lecture and students work through problems alone. The team leading the work‐ shops was right to point out that success in college requires working with others and making good connections. Many people know this, but they still see no role for collaboration in learning. When Uri and his team encouraged students to work together, their mathematical learning paths changed and they found success. This success story was about learning calculus in college, but we could substitute any other subject and expect similar results.\u003c/p>\n\u003cp class=\"p2\">Part of the reason students give up on learning is because they find it difficult and think they are alone in their struggle. An important change takes place when students work together and discover that everybody finds some or all of the work difficult. This is a critical moment for students, and one that helps them know that for everyone learning is a process and that obstacles are common.\u003c/p>\n\u003cp class=\"p2\">Another reason that students’ learning pathways change is because they receive an opportunity to connect ideas. Connecting with another person’s idea both requires and develops a higher level of understanding. When students work together (learning math, science, languages, English— anything), they get opportunities to make connections be‐ tween ideas, which is inherently valuable for them.\u003c/p>\n\u003cp class=\"p2\">A similarly noteworthy finding came from the results of a large‐scale testing program. In 2012, PISA assessments (international tests given to fifteen‐year‐olds worldwide, as mentioned earlier) showed that boys achieved at higher levels than girls in mathematics in thirty‐eight countries.\u003c/p>\n\u003cp class=\"p2\">This result was disappointing and surprising. In the US and in most other countries, the achievement of girls and boys in school is equal. This reminded me again of the ways that tests distort what students actually know and can do.\u003c/p>\n\u003cfigure id=\"attachment_54492\" class=\"wp-caption alignright\" style=\"max-width: 250px\">\u003cimg class=\"wp-image-54492\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2.jpg\" alt=\"\" width=\"250\" height=\"319\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2.jpg 1440w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-160x204.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-800x1020.jpg 800w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-768x979.jpg 768w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-1020x1301.jpg 1020w, https://ww2.kqed.org/app/uploads/sites/23/2019/09/Jo-Boaler-author-photo-Photo-Credit-Robert-Houser-Photography-2-941x1200.jpg 941w\" sizes=\"(max-width: 250px) 100vw, 250px\">\u003cfigcaption class=\"wp-caption-text\">Jo Boaler \u003ccite>(Robert Houser Photography)\u003c/cite>\u003c/figcaption>\u003c/figure>\n\u003cp class=\"p2\">This was underscored when the PISA team issued a report showing that when anxiety was factored into the analysis, the gap in achievement between girls and boys was fully explained by the lower confidence of girls.\u003cspan class=\"s1\"> \u003c/span>What appeared to be a gender difference in mathematics achievement was in reality a difference in mathematics confidence levels. Girls became more anxious when they took the individual math tests, a phenomenon that is well established,\u003cspan class=\"s1\"> \u003c/span>and one that should make any educator pause before basing decisions on test performance.\u003c/p>\n\u003cp class=\"p2\">The impact of the different testing conditions as well as the potential of collaboration for reducing inequalities were also shown by another assessment the PISA team conducted. In addition to the usual individual mathematics test, they did an assessment of collaborative problem solving. In this assessment students did not collaborate with other students but with a computer agent. They had to take on the ideas of the agent and connect with and build upon them to collaboratively solve complex problems.\u003cspan class=\"s1\"> \u003c/span>This, to me, gauges something much more valuable than what a student produces on an individual math test. Instead of reproducing knowledge individually, students are asked to consider another’s ideas and work with them to solve a complex problem. This is also more consistent with the world of work students are being prepared for.\u003c/p>\n\u003cp class=\"p2\">In the test of collaborative problem solving, administered in fifty‐one countries, girls outperformed boys in every country. This notable result was accompanied by two others—there were no significant differences in outcomes between advantaged and disadvantaged students, a rare and important finding. And in some countries diversity boosted performance. The team found that in some countries “non‐ immigrant” students achieved at higher levels when they were in schools with larger numbers of “immigrant” students, a fantastic result, suggesting that diverse communities of learners help students become better collaborators.\u003c/p>\n\u003cp class=\"p2\">The results of the PISA assessment of collaborative problem solving shine a light on the pursuit of equity, revealing also the discriminatory nature of individual testing, something that anyone who gets anxious about high‐stakes testing fully understands. What does it mean that for girls collaboration, even with a computer agent, increases their confidence levels and causes them to achieve at higher levels? Similarly, what does it mean that African American students go from failing calculus to outperforming other, previously more successful, students when they collaborate? This research reveals the potential of collaboration, not only for girls or students of color, but for all learners and thinkers. When you connect with someone else’s ideas, you enhance your brain, your understanding, and your perspective.\u003c/p>\n\u003cp class=\"p2\">Neuroscientists also know the importance of collaboration. Research shows that when people collaborate, the medial orbitofrontal cortex and the frontoparietal network are activated, the latter of which aids in the development of executive functions. Neuroscientists refer to these different brain areas as the “social brain.” When we collaborate, our brains are charged with the complex task of making sense of another’s thinking and learning to interact. Social cognition is the topic of much current neuroscientific investigation.\u003c/p>\n\u003cp class=\"p2\">Collaboration is vital for learning, for college success, for brain development, and for creating equitable outcomes. Beyond all of this, it is beneficial to establish interpersonal connections, especially in times of conflict and need.\u003c/p>\n\u003cp class=\"p2\">Victor and Mildred Goertzel studied seven hundred people who had made huge contributions to society, choosing those who had been the subject of at least two biographies, people such as Marie Curie and Henry Ford. They found, in‐ credibly, that less than 15 percent of the famous men and women had been raised in supportive families; 75 percent had grown up in families with severe problems such as “poverty, abuse, absent parents, alcoholism, serious illness,” and other major issues. Their study was conducted in the 1960s. Clinical psychologist Meg Jay, in her interesting Wall Street Journal article on resilience, reports that similar results would be found today and cites Oprah Winfrey, Howard Schultz, and LeBron James as examples of people who grew up in extreme hardship.\u003c/p>\n\u003cp class=\"p2\">Jay has studied resilience over many years and points out that people who survive hardship often do better, but not through “bouncing back,” as some think, because the recovery process takes time and is more of a battle than a bounce. She also points out those who ultimately benefit from hardship, becoming stronger and resilient, do so when they maintain self‐belief, when they “own the fighter within,” and when they connect with other people. The thing that people who overcome hardship and do not become defeated by it have in common is that in times of need they all reached out to someone—a friend, a family member, or a colleague—and those connections helped them survive and develop strength.\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp class=\"p1\">\u003cem>Jo Boaler is the Nomellini-Olivier Professor of Education at Stanford, cofounder of \u003ca href=\"https://www.youcubed.org/\">youcubed.org\u003c/a> and author of \u003ca href=\"https://www.youcubed.org/limitless-mind/\">Limitless Mind: Learn, Lead & Live without Barriers\u003c/a> by HarperOne, an imprint of HarperCollins Publishers.\u003c/em>\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/54486/how-collaboration-unlocks-learning-and-lessens-student-isolation","authors":["4354"],"categories":["mindshift_193"],"tags":["mindshift_20589","mindshift_1028","mindshift_121","mindshift_939","mindshift_20784","mindshift_1040","mindshift_20512","mindshift_20943","mindshift_392","mindshift_20893","mindshift_46","mindshift_205"],"featImg":"mindshift_54495","label":"mindshift"},"mindshift_49042":{"type":"posts","id":"mindshift_49042","meta":{"index":"posts_1591205157","site":"mindshift","id":"49042","score":null,"sort":[1504591502000]},"guestAuthors":[],"slug":"how-the-google-suite-can-enhance-open-ended-math-exploration","title":"How the Google Suite Can Enhance Open-Ended Math Exploration","publishDate":1504591502,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp>Stanford education professor Jo Boaler’s message about teaching math in visual ways that don’t emphasize one right procedure has become a rallying cry for many math educators ready for a seismic shift in how American schools teach mathematics. But \u003ca href=\"https://ww2.kqed.org/mindshift/2015/11/30/not-a-math-person-how-to-remove-obstacles-to-learning-math/\" target=\"_blank\" rel=\"noopener noreferrer\">her ideas\u003c/a> also challenge much of what has been done in classrooms for decades, including the ways that current teachers and parents learned themselves. \u003ca href=\"http://alicekeeler.com/\" target=\"_blank\" rel=\"noopener noreferrer\">Alice Keeler\u003c/a> is one of the converted, despite the fact she taught math traditionally for many years.\u003c/p>\n\u003cp>“I was a math teacher, and I’ll be honest,\" Keeler said, \"I didn’t teach it to be creative.\" She always felt pressure to move more quickly through the curriculum. Every day brought a new topic, whether or not students had deeply understood what came before. When Keeler read Boaler’s book, \u003cem>\u003ca href=\"https://www.goodreads.com/book/show/26067736-mathematical-mindsets\" target=\"_blank\" rel=\"noopener noreferrer\">Mathematical Mindsets\u003c/a>\u003c/em>, she saw herself as a young student in much of what Boaler described. With tears in her eyes, she told a group of educators at the \u003ca href=\"https://www.iste.org/\" target=\"_blank\" rel=\"noopener noreferrer\">International Society for Technology in Education (ISTE)\u003c/a> that since fourth grade she secretly thought she was dumb because she couldn’t pass timed math tests. Boaler’s message that fast is not the same thing as smart was liberating to her as a person and as a math teacher.\u003c/p>\n\u003cp>“When we work on a math problem, any type of problem, there are five different pathways in the brain that light up and are working,” Boaler said by video call at the same presentation. “Two of them are visual.” She argues that much of traditional math teaching focuses on numerical representations, teachers demonstrating procedures, and memorization, when it would be more effective to try to \u003ca href=\"https://ww2.kqed.org/mindshift/2016/11/21/what-neuroscience-can-tell-us-about-making-fractions-stick/\" target=\"_blank\" rel=\"noopener noreferrer\">strengthen connections between the various parts of the brain\u003c/a> needed when working on math.\u003c/p>\n\u003cp>“That comes about by showing information in different ways,” Boaler said. Representations of math problems using words, images and numbers each use different parts of the brain, so the concept gets hardwired in a neural network drawing on multiple brain faculties instead of one numerical pathway.\u003c/p>\n\u003cp>“The least likely way of helping kids have those brain connections is having kids sit and listen to lectures,” Boaler said. That doesn’t mean all math classes need to be project-based or that direct instruction is always bad, but when lecture is the default classroom mode, it doesn’t require students to use their brains to make sense of the new ideas.\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>Boaler’s website \u003ca href=\"https://www.youcubed.org/\" target=\"_blank\" rel=\"noopener noreferrer\">YouCubed\u003c/a> has many \u003ca href=\"https://www.youcubed.org/tasks/\" target=\"_blank\" rel=\"noopener noreferrer\">activities\u003c/a> to help teachers learn to open up the exploration of math from one of closed questions with a right and wrong answer, to one where \u003ca href=\"https://ww2.kqed.org/mindshift/2017/04/05/five-ways-to-shift-teaching-practice-so-students-feel-less-math-anxious/\" target=\"_blank\" rel=\"noopener noreferrer\">different ways of seeing and articulating math \u003c/a>are valued. When teachers ask students to explain why their thinking makes sense, students are forced to articulate their thought process, how it compares and contrasts to ideas peers have shared, and in doing so may help the teacher identify any \u003ca href=\"https://ww2.kqed.org/mindshift/2016/04/18/getting-inside-students-minds-why-misconceptions-are-so-powerful/\" target=\"_blank\" rel=\"noopener noreferrer\">misconceptions\u003c/a>.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe src=\"https://player.vimeo.com/video/129139086?title=0&byline=0&portrait=0\" width=\"640\" height=\"360\" frameborder=\"0\" scrolling=\"yes\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>A simple example of opening up math in this way starts with a closed question: Divide one by two-thirds. But rather than asking students to apply a rule, ask students to come up with a visual proof. “What happens is the kids have these amazing discussions with different visual proofs, and it’s such a great way of taking a very closed question and opening it up,” Boaler said.\u003c/p>\n\u003cp>As a math teacher Alice Keeler loves the ideas on YouCubed and readily admits most of them can be done without technology. However, Keeler sees many ways that technology could enhance the visual and collaboration elements of the work, so she has adapted several YouCubed activities for the Google Suite. While Keeler spent 14 years in the classroom, she now has her own consulting business and teaches at California State University Fresno. She also co-wrote \u003ca href=\"http://alicekeeler.com/google-classroom/\">two books on using Google Classroom\u003c/a> with Libbi Miller: \u003cem>50 Things You Can Do with Google Classroom\u003c/em> and \u003cem>50 Things To Go Further With Google Classroom.\u003c/em>\u003c/p>\n\u003cp>“It’s not about being digital and it’s not about being paperless,” Keeler said. “That doesn’t make learning better. But collaboration does.” She likes doing open-ended math activities in Google Slides because each student can play with visual representations, give feedback to peers, and receive ongoing feedback from the teacher. She usually makes blank slides and gives editing power to students.\u003c/p>\n\u003cp>“I ask each student to add their own slides explaining how they did it, how they visualized it, and we’re all doing it together in the Google Slides,” Keeler said. She’s found that when students can see how a peer visualized the problem, they then reflect on different approaches. She also values her ability to comment in real time with students because it becomes a conversation, not a static comment on returned work that the student may or may not look at again.\u003c/p>\n\u003cp>“I can have conversations with them around the ideas and help them to develop their thinking rather than just marking things right and wrong,” Keeler said. A math teacher who isn’t using G-Suite in class could also have these kinds of formative conversations by circling the room and talking with students working in groups, but Keeler likes using the technology because she can easily see how each individual is thinking about the problem. And students can interact with one another’s ideas, even when they aren’t physically in her class.\u003c/p>\n\u003cfigure id=\"attachment_49164\" class=\"wp-caption alignnone\" style=\"max-width: 754px\">\u003cimg class=\"wp-image-49164 size-full\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2017/09/how-close-to-100.jpg\" alt='An adaptation of the <a href=\"https://www.youcubed.org/tasks/how-close-to-100/\">\"How Close to 100\"</a> YouCubed activity that can be done in Google Sheets. (<a href=\"http://alicekeeler.com/\">Alice Keeler</a>' width=\"754\" height=\"424\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100.jpg 754w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100-160x90.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100-240x135.jpg 240w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100-375x211.jpg 375w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100-520x292.jpg 520w\" sizes=\"(max-width: 754px) 100vw, 754px\">\u003cfigcaption class=\"wp-caption-text\">An adaptation of the \u003ca href=\"https://www.youcubed.org/tasks/how-close-to-100/\">\"How Close to 100\"\u003c/a> YouCubed activity that can be done in Google Sheets. (\u003ca href=\"http://alicekeeler.com/\">Alice Keeler)\u003c/a>\u003c/figcaption>\u003c/figure>\n\u003cp>Keeler often tells students not to delete mistakes from the slides, instead telling them to duplicate the slide and keep working. That way she can see the progression of their thinking. This also helps students to see how far they’ve come.\u003c/p>\n\u003cp>A \u003ca href=\"https://www.youcubed.org/tasks/the-four-4s/\" target=\"_blank\" rel=\"noopener noreferrer\">popular YouCubed problem \u003c/a>asks students to take exactly four 4s and use any combination of operations to come up with the numbers 1-20. Keeler often \u003ca href=\"http://www.alicekeeler.com/four4s\" target=\"_blank\" rel=\"noopener noreferrer\">does this in Google Slides\u003c/a>, where each slide is a place for students to show how they combined four 4s to get “1” and then on the next slide the work for “2,” etc.\u003c/p>\n\u003cp>She likes working in Google Slides because students can add media or even do work on paper and upload an image. This gives different types of learners options. Students with disabilities or who benefit from speech-to-text help can also participate using \u003ca href=\"https://chrome.google.com/webstore/detail/equatio-math-made-digital/hjngolefdpdnooamgdldlkjgmdcmcjnc?hl=en-US\" target=\"_blank\" rel=\"noopener noreferrer\">EquatIO\u003c/a>, a Chrome add-on that has voice typing capabilities, as well as handwriting recognition. EquatIO used to be g(Math), and now also makes it possible to use math symbols in slides and other Google apps.\u003c/p>\n\u003cfigure id=\"attachment_49170\" class=\"wp-caption alignnone\" style=\"max-width: 753px\">\u003cimg class=\"size-full wp-image-49170\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2017/09/pixelart-math-1.jpg\" alt=\"\" width=\"753\" height=\"421\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1.jpg 753w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1-160x89.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1-240x134.jpg 240w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1-375x210.jpg 375w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1-520x291.jpg 520w\" sizes=\"(max-width: 753px) 100vw, 753px\">\u003cfigcaption class=\"wp-caption-text\">Alice Keeler adapted a YouCubed activity, asking students to visualize the math using pixel art. \u003ccite>(\u003ca href=\"http://alicekeeler.com/2016/07/17/modeling-division-brownies-joboaler/\">Alice Keeler\u003c/a> )\u003c/cite>\u003c/figcaption>\u003c/figure>\n\u003cp>Another popular YouCubed activity asks students to visualize division by divvying up a pan of brownies equally among friends. Keeler does this activity in \u003ca href=\"http://alicekeeler.com/2016/07/17/modeling-division-brownies-joboaler/\" target=\"_blank\" rel=\"noopener noreferrer\">a spreadsheet\u003c/a>, and often asks students to create their own brownie pans -- their own problems -- in the next tab. “It allows them to experiment and play,” she said.\u003c/p>\n\u003cp>Keeler has become something of an \u003ca href=\"http://alicekeeler.com/2016/02/10/teaching-math-with-google-googlemath/\" target=\"_blank\" rel=\"noopener noreferrer\">evangelist for technology in math classrooms\u003c/a>, learning how to set up conditional statements and even simple code in Google Sheets to aid her purposes (she also shares these ideas regularly on \u003ca href=\"http://@alicekeeler\" target=\"_blank\" rel=\"noopener noreferrer\">Twitter\u003c/a>, including activity templates). Over time her teaching evolved and by the time she left the K-12 classroom she had upended some of the practices she once considered fundamental, like assigning \u003ca href=\"https://ww2.kqed.org/mindshift/2012/11/16/parents-wonder-why-so-much-homework/\" target=\"_blank\" rel=\"noopener noreferrer\">homework\u003c/a>.\u003c/p>\n\u003cp>One of the most controversial ideas in math education revolves around \u003ca href=\"https://ww2.kqed.org/mindshift/2013/02/22/can-repetitive-exercises-actually-feed-the-creative-process/\" target=\"_blank\" rel=\"noopener noreferrer\">how, when and how much students should practice\u003c/a>. Many teachers believe it is important for students to do homework so they can practice new concepts learned in class. Boaler agrees that practice is important, but doesn’t think that requires doing the same type of rote problem over and over. Boaler explained this to her daughter’s teacher and was pleasantly surprised at how she used the feedback. After their discussion, the teacher started giving students four problems to practice the calculations and then asked them to represent the concept some other way. They could write a story, make a drawing or come up with something else. The key was showing their knowledge in different ways.\u003c/p>\n\u003cp>Many elementary school educators are willing to consider that homework is not necessary for the young learners they teach, but far fewer high school teachers agree. Keeler taught Algebra and AP Statistics when she was in the classroom. She found that “the only kids who did the homework were the ones who didn’t need to,” so she stopped assigning homework. “It didn’t make a lick of difference” in terms of achievement, she said, but kids started enjoying class more. When she eliminated homework, Keeler found she had much more positive relationships with students and parents, a benefit that far outweighed what she called the “marginal gains of more rote practice.”\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>Ultimately both Keeler and Boaler hope that by making math a subject that’s about \u003ca href=\"https://ww2.kqed.org/mindshift/2016/12/18/what-can-we-learn-from-countries-that-effectively-teach-math/\" target=\"_blank\" rel=\"noopener noreferrer\">ideas, discussion, differing viewpoints \u003c/a>and visual representations, students will learn they can not only do math, but excel at it. Too many students don’t feel that way now, which is why teachers are beginning to see the need for a new approach.\u003c/p>\n\n","blocks":[],"excerpt":"Math educator Alice Keeler teams up with Stanford math education professor Jo Boaler to look at how open-ended math tasks can be enhanced with technology.","status":"publish","parent":0,"modified":1504640165,"stats":{"hasAudio":false,"hasVideo":true,"hasChartOrMap":true,"iframeSrcs":["https://player.vimeo.com/video/129139086"],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":22,"wordCount":1597},"headData":{"title":"How the Google Suite Can Enhance Open-Ended Math Exploration | KQED","description":"Math educator Alice Keeler teams up with Stanford math education professor Jo Boaler to look at how open-ended math tasks can be enhanced with technology.","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","schema":{"@context":"http://schema.org","@type":"Article","headline":"How the Google Suite Can Enhance Open-Ended Math Exploration","datePublished":"2017-09-05T06:05:02.000Z","dateModified":"2017-09-05T19:36:05.000Z","image":"https://cdn.kqed.org/wp-content/uploads/2020/02/KQED-OG-Image@1x.png"}},"disqusIdentifier":"49042 https://ww2.kqed.org/mindshift/?p=49042","disqusUrl":"https://ww2.kqed.org/mindshift/2017/09/04/how-the-google-suite-can-enhance-open-ended-math-exploration/","disqusTitle":"How the Google Suite Can Enhance Open-Ended Math Exploration","path":"/mindshift/49042/how-the-google-suite-can-enhance-open-ended-math-exploration","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>Stanford education professor Jo Boaler’s message about teaching math in visual ways that don’t emphasize one right procedure has become a rallying cry for many math educators ready for a seismic shift in how American schools teach mathematics. But \u003ca href=\"https://ww2.kqed.org/mindshift/2015/11/30/not-a-math-person-how-to-remove-obstacles-to-learning-math/\" target=\"_blank\" rel=\"noopener noreferrer\">her ideas\u003c/a> also challenge much of what has been done in classrooms for decades, including the ways that current teachers and parents learned themselves. \u003ca href=\"http://alicekeeler.com/\" target=\"_blank\" rel=\"noopener noreferrer\">Alice Keeler\u003c/a> is one of the converted, despite the fact she taught math traditionally for many years.\u003c/p>\n\u003cp>“I was a math teacher, and I’ll be honest,\" Keeler said, \"I didn’t teach it to be creative.\" She always felt pressure to move more quickly through the curriculum. Every day brought a new topic, whether or not students had deeply understood what came before. When Keeler read Boaler’s book, \u003cem>\u003ca href=\"https://www.goodreads.com/book/show/26067736-mathematical-mindsets\" target=\"_blank\" rel=\"noopener noreferrer\">Mathematical Mindsets\u003c/a>\u003c/em>, she saw herself as a young student in much of what Boaler described. With tears in her eyes, she told a group of educators at the \u003ca href=\"https://www.iste.org/\" target=\"_blank\" rel=\"noopener noreferrer\">International Society for Technology in Education (ISTE)\u003c/a> that since fourth grade she secretly thought she was dumb because she couldn’t pass timed math tests. Boaler’s message that fast is not the same thing as smart was liberating to her as a person and as a math teacher.\u003c/p>\n\u003cp>“When we work on a math problem, any type of problem, there are five different pathways in the brain that light up and are working,” Boaler said by video call at the same presentation. “Two of them are visual.” She argues that much of traditional math teaching focuses on numerical representations, teachers demonstrating procedures, and memorization, when it would be more effective to try to \u003ca href=\"https://ww2.kqed.org/mindshift/2016/11/21/what-neuroscience-can-tell-us-about-making-fractions-stick/\" target=\"_blank\" rel=\"noopener noreferrer\">strengthen connections between the various parts of the brain\u003c/a> needed when working on math.\u003c/p>\n\u003cp>“That comes about by showing information in different ways,” Boaler said. Representations of math problems using words, images and numbers each use different parts of the brain, so the concept gets hardwired in a neural network drawing on multiple brain faculties instead of one numerical pathway.\u003c/p>\n\u003cp>“The least likely way of helping kids have those brain connections is having kids sit and listen to lectures,” Boaler said. That doesn’t mean all math classes need to be project-based or that direct instruction is always bad, but when lecture is the default classroom mode, it doesn’t require students to use their brains to make sense of the new ideas.\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>Boaler’s website \u003ca href=\"https://www.youcubed.org/\" target=\"_blank\" rel=\"noopener noreferrer\">YouCubed\u003c/a> has many \u003ca href=\"https://www.youcubed.org/tasks/\" target=\"_blank\" rel=\"noopener noreferrer\">activities\u003c/a> to help teachers learn to open up the exploration of math from one of closed questions with a right and wrong answer, to one where \u003ca href=\"https://ww2.kqed.org/mindshift/2017/04/05/five-ways-to-shift-teaching-practice-so-students-feel-less-math-anxious/\" target=\"_blank\" rel=\"noopener noreferrer\">different ways of seeing and articulating math \u003c/a>are valued. When teachers ask students to explain why their thinking makes sense, students are forced to articulate their thought process, how it compares and contrasts to ideas peers have shared, and in doing so may help the teacher identify any \u003ca href=\"https://ww2.kqed.org/mindshift/2016/04/18/getting-inside-students-minds-why-misconceptions-are-so-powerful/\" target=\"_blank\" rel=\"noopener noreferrer\">misconceptions\u003c/a>.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe src=\"https://player.vimeo.com/video/129139086?title=0&byline=0&portrait=0\" width=\"640\" height=\"360\" frameborder=\"0\" scrolling=\"yes\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>A simple example of opening up math in this way starts with a closed question: Divide one by two-thirds. But rather than asking students to apply a rule, ask students to come up with a visual proof. “What happens is the kids have these amazing discussions with different visual proofs, and it’s such a great way of taking a very closed question and opening it up,” Boaler said.\u003c/p>\n\u003cp>As a math teacher Alice Keeler loves the ideas on YouCubed and readily admits most of them can be done without technology. However, Keeler sees many ways that technology could enhance the visual and collaboration elements of the work, so she has adapted several YouCubed activities for the Google Suite. While Keeler spent 14 years in the classroom, she now has her own consulting business and teaches at California State University Fresno. She also co-wrote \u003ca href=\"http://alicekeeler.com/google-classroom/\">two books on using Google Classroom\u003c/a> with Libbi Miller: \u003cem>50 Things You Can Do with Google Classroom\u003c/em> and \u003cem>50 Things To Go Further With Google Classroom.\u003c/em>\u003c/p>\n\u003cp>“It’s not about being digital and it’s not about being paperless,” Keeler said. “That doesn’t make learning better. But collaboration does.” She likes doing open-ended math activities in Google Slides because each student can play with visual representations, give feedback to peers, and receive ongoing feedback from the teacher. She usually makes blank slides and gives editing power to students.\u003c/p>\n\u003cp>“I ask each student to add their own slides explaining how they did it, how they visualized it, and we’re all doing it together in the Google Slides,” Keeler said. She’s found that when students can see how a peer visualized the problem, they then reflect on different approaches. She also values her ability to comment in real time with students because it becomes a conversation, not a static comment on returned work that the student may or may not look at again.\u003c/p>\n\u003cp>“I can have conversations with them around the ideas and help them to develop their thinking rather than just marking things right and wrong,” Keeler said. A math teacher who isn’t using G-Suite in class could also have these kinds of formative conversations by circling the room and talking with students working in groups, but Keeler likes using the technology because she can easily see how each individual is thinking about the problem. And students can interact with one another’s ideas, even when they aren’t physically in her class.\u003c/p>\n\u003cfigure id=\"attachment_49164\" class=\"wp-caption alignnone\" style=\"max-width: 754px\">\u003cimg class=\"wp-image-49164 size-full\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2017/09/how-close-to-100.jpg\" alt='An adaptation of the <a href=\"https://www.youcubed.org/tasks/how-close-to-100/\">\"How Close to 100\"</a> YouCubed activity that can be done in Google Sheets. (<a href=\"http://alicekeeler.com/\">Alice Keeler</a>' width=\"754\" height=\"424\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100.jpg 754w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100-160x90.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100-240x135.jpg 240w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100-375x211.jpg 375w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/how-close-to-100-520x292.jpg 520w\" sizes=\"(max-width: 754px) 100vw, 754px\">\u003cfigcaption class=\"wp-caption-text\">An adaptation of the \u003ca href=\"https://www.youcubed.org/tasks/how-close-to-100/\">\"How Close to 100\"\u003c/a> YouCubed activity that can be done in Google Sheets. (\u003ca href=\"http://alicekeeler.com/\">Alice Keeler)\u003c/a>\u003c/figcaption>\u003c/figure>\n\u003cp>Keeler often tells students not to delete mistakes from the slides, instead telling them to duplicate the slide and keep working. That way she can see the progression of their thinking. This also helps students to see how far they’ve come.\u003c/p>\n\u003cp>A \u003ca href=\"https://www.youcubed.org/tasks/the-four-4s/\" target=\"_blank\" rel=\"noopener noreferrer\">popular YouCubed problem \u003c/a>asks students to take exactly four 4s and use any combination of operations to come up with the numbers 1-20. Keeler often \u003ca href=\"http://www.alicekeeler.com/four4s\" target=\"_blank\" rel=\"noopener noreferrer\">does this in Google Slides\u003c/a>, where each slide is a place for students to show how they combined four 4s to get “1” and then on the next slide the work for “2,” etc.\u003c/p>\n\u003cp>She likes working in Google Slides because students can add media or even do work on paper and upload an image. This gives different types of learners options. Students with disabilities or who benefit from speech-to-text help can also participate using \u003ca href=\"https://chrome.google.com/webstore/detail/equatio-math-made-digital/hjngolefdpdnooamgdldlkjgmdcmcjnc?hl=en-US\" target=\"_blank\" rel=\"noopener noreferrer\">EquatIO\u003c/a>, a Chrome add-on that has voice typing capabilities, as well as handwriting recognition. EquatIO used to be g(Math), and now also makes it possible to use math symbols in slides and other Google apps.\u003c/p>\n\u003cfigure id=\"attachment_49170\" class=\"wp-caption alignnone\" style=\"max-width: 753px\">\u003cimg class=\"size-full wp-image-49170\" src=\"https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2017/09/pixelart-math-1.jpg\" alt=\"\" width=\"753\" height=\"421\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1.jpg 753w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1-160x89.jpg 160w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1-240x134.jpg 240w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1-375x210.jpg 375w, https://ww2.kqed.org/app/uploads/sites/23/2017/09/pixelart-math-1-520x291.jpg 520w\" sizes=\"(max-width: 753px) 100vw, 753px\">\u003cfigcaption class=\"wp-caption-text\">Alice Keeler adapted a YouCubed activity, asking students to visualize the math using pixel art. \u003ccite>(\u003ca href=\"http://alicekeeler.com/2016/07/17/modeling-division-brownies-joboaler/\">Alice Keeler\u003c/a> )\u003c/cite>\u003c/figcaption>\u003c/figure>\n\u003cp>Another popular YouCubed activity asks students to visualize division by divvying up a pan of brownies equally among friends. Keeler does this activity in \u003ca href=\"http://alicekeeler.com/2016/07/17/modeling-division-brownies-joboaler/\" target=\"_blank\" rel=\"noopener noreferrer\">a spreadsheet\u003c/a>, and often asks students to create their own brownie pans -- their own problems -- in the next tab. “It allows them to experiment and play,” she said.\u003c/p>\n\u003cp>Keeler has become something of an \u003ca href=\"http://alicekeeler.com/2016/02/10/teaching-math-with-google-googlemath/\" target=\"_blank\" rel=\"noopener noreferrer\">evangelist for technology in math classrooms\u003c/a>, learning how to set up conditional statements and even simple code in Google Sheets to aid her purposes (she also shares these ideas regularly on \u003ca href=\"http://@alicekeeler\" target=\"_blank\" rel=\"noopener noreferrer\">Twitter\u003c/a>, including activity templates). Over time her teaching evolved and by the time she left the K-12 classroom she had upended some of the practices she once considered fundamental, like assigning \u003ca href=\"https://ww2.kqed.org/mindshift/2012/11/16/parents-wonder-why-so-much-homework/\" target=\"_blank\" rel=\"noopener noreferrer\">homework\u003c/a>.\u003c/p>\n\u003cp>One of the most controversial ideas in math education revolves around \u003ca href=\"https://ww2.kqed.org/mindshift/2013/02/22/can-repetitive-exercises-actually-feed-the-creative-process/\" target=\"_blank\" rel=\"noopener noreferrer\">how, when and how much students should practice\u003c/a>. Many teachers believe it is important for students to do homework so they can practice new concepts learned in class. Boaler agrees that practice is important, but doesn’t think that requires doing the same type of rote problem over and over. Boaler explained this to her daughter’s teacher and was pleasantly surprised at how she used the feedback. After their discussion, the teacher started giving students four problems to practice the calculations and then asked them to represent the concept some other way. They could write a story, make a drawing or come up with something else. The key was showing their knowledge in different ways.\u003c/p>\n\u003cp>Many elementary school educators are willing to consider that homework is not necessary for the young learners they teach, but far fewer high school teachers agree. Keeler taught Algebra and AP Statistics when she was in the classroom. She found that “the only kids who did the homework were the ones who didn’t need to,” so she stopped assigning homework. “It didn’t make a lick of difference” in terms of achievement, she said, but kids started enjoying class more. When she eliminated homework, Keeler found she had much more positive relationships with students and parents, a benefit that far outweighed what she called the “marginal gains of more rote practice.”\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>Ultimately both Keeler and Boaler hope that by making math a subject that’s about \u003ca href=\"https://ww2.kqed.org/mindshift/2016/12/18/what-can-we-learn-from-countries-that-effectively-teach-math/\" target=\"_blank\" rel=\"noopener noreferrer\">ideas, discussion, differing viewpoints \u003c/a>and visual representations, students will learn they can not only do math, but excel at it. Too many students don’t feel that way now, which is why teachers are beginning to see the need for a new approach.\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/49042/how-the-google-suite-can-enhance-open-ended-math-exploration","authors":["234"],"categories":["mindshift_195","mindshift_193"],"tags":["mindshift_20784","mindshift_1040","mindshift_20728","mindshift_20512","mindshift_21114","mindshift_20943","mindshift_392","mindshift_125"],"featImg":"mindshift_49163","label":"mindshift"},"mindshift_47907":{"type":"posts","id":"mindshift_47907","meta":{"index":"posts_1591205157","site":"mindshift","id":"47907","score":null,"sort":[1491395080000]},"guestAuthors":[],"slug":"five-ways-to-shift-teaching-practice-so-students-feel-less-math-anxious","title":"Five Ways To Shift Teaching Practice So Students Feel Less Math Anxious","publishDate":1491395080,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp>Math has been a traditionally thorny subject in many American schools. Lots of children dislike math and many more adults stopped taking mathematics as soon as they are able, even when they were successful in their classes. At the same time, mathematical thinking is a crucial part of many of the most exciting and growing careers in science, technology, engineering and math, not to mention important for a general understanding of the mathematical world around us. So, what can U.S. math educators do to shift this dynamic?\u003c/p>\n\u003cp>Stanford Mathematics Education Professor Jo Boaler is championing a \u003ca href=\"https://ww2.kqed.org/mindshift/2015/11/30/not-a-math-person-how-to-remove-obstacles-to-learning-math/\" target=\"_blank\">dramatic shift\u003c/a> in how many math teachers approach instruction. Rather than focusing on the algorithms and procedures that make mathematics feel like a lock-step process -- with one right way of solving problems -- Boaler encourages teachers to embrace the visual aspects of math. She encourages teachers to ask students to grapple with open-ended problems, to share ideas and to see math as a creative endeavor. She works with students every summer and says that when students are in a math environment that doesn't focus on performance, speed, procedures, and right and wrong answers they thrive. They even begin to change their perceptions of whether they can or can't do math.\u003c/p>\n\u003cp>[vimeo 206159614 w=640 h=360]\u003c/p>\n\u003cp>\u003ca href=\"https://vimeo.com/206159614\">Solving The Math Problem (Subtitles)\u003c/a> from \u003ca href=\"https://vimeo.com/user20989575\">YouCubed\u003c/a> on \u003ca href=\"https://vimeo.com\">Vimeo\u003c/a>.\u003c/p>\n\u003cp>In an \u003ca href=\"http://hechingerreport.org/opinion-time-stop-clock-math-anxiety-heres-latest-research/\" target=\"_blank\">opinion piece for The Hechinger Report\u003c/a>, Boaler lays out five ways teachers can approach instruction differently. She points out that many students experience math anxiety, which is \u003ca href=\"https://hpl.uchicago.edu/sites/hpl.uchicago.edu/files/uploads/The%20Math%20Anxiety%20Performance%20Link,%20Foley%20et%20al.pdf\" target=\"_blank\">negatively related to performance\u003c/a>. While psychology research has pointed to smaller \u003ca href=\"https://ww2.kqed.org/mindshift/2013/02/08/anxious-about-tests-tips-to-ease-angst/\" target=\"_blank\">interventions to lower anxiety\u003c/a> before tests or to help students combat \u003ca href=\"https://ww2.kqed.org/mindshift/2017/01/26/at-age-6-girls-are-less-likely-to-identify-females-as-really-really-smart/\" target=\"_blank\">stereotype threat\u003c/a>, Boaler says those measures fall short. She writes:\u003c/p>\n\u003cblockquote>\u003cp>Widespread, prevalent among women and hugely damaging, math anxiety is prompted in the early years when timed tests are given in classrooms and it snowballs from there. Psychologists’ recommendations — including counseling and words to repeat before a test — severely miss the mark. The only way to turn our nation around is to change the way we teach and view math. The problems that we have now include these:\u003c/p>\n\u003cp>First, math is often taught as a performance subject. Ask your children what their role is in math class, and they are very likely to say it is to get questions correct. They do not say this about other subjects. More than any other subject math is about tests, grades, homework and competitions.\u003c/p>\u003c/blockquote>\n\u003cp>Check out Boaler's recommendations to change the math teaching paradigm in the U.S.\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>\u003c/p>\n\u003cp>http://hechingerreport.org/opinion-time-stop-clock-math-anxiety-heres-latest-research/\u003c/p>\n\n","blocks":[],"excerpt":"A Stanford professor argues U.S. schools need to fundamentally shift math instruction away from procedural problems to turn the tide on math achievement.","status":"publish","parent":0,"modified":1491395080,"stats":{"hasAudio":false,"hasVideo":true,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":10,"wordCount":439},"headData":{"title":"Five Ways To Shift Teaching Practice So Students Feel Less Math Anxious | KQED","description":"A Stanford professor argues U.S. schools need to fundamentally shift math instruction away from procedural problems to turn the tide on math achievement.","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","schema":{"@context":"http://schema.org","@type":"Article","headline":"Five Ways To Shift Teaching Practice So Students Feel Less Math Anxious","datePublished":"2017-04-05T12:24:40.000Z","dateModified":"2017-04-05T12:24:40.000Z","image":"https://cdn.kqed.org/wp-content/uploads/2020/02/KQED-OG-Image@1x.png"}},"disqusIdentifier":"47907 https://ww2.kqed.org/mindshift/?p=47907","disqusUrl":"https://ww2.kqed.org/mindshift/2017/04/05/five-ways-to-shift-teaching-practice-so-students-feel-less-math-anxious/","disqusTitle":"Five Ways To Shift Teaching Practice So Students Feel Less Math Anxious","path":"/mindshift/47907/five-ways-to-shift-teaching-practice-so-students-feel-less-math-anxious","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>Math has been a traditionally thorny subject in many American schools. Lots of children dislike math and many more adults stopped taking mathematics as soon as they are able, even when they were successful in their classes. At the same time, mathematical thinking is a crucial part of many of the most exciting and growing careers in science, technology, engineering and math, not to mention important for a general understanding of the mathematical world around us. So, what can U.S. math educators do to shift this dynamic?\u003c/p>\n\u003cp>Stanford Mathematics Education Professor Jo Boaler is championing a \u003ca href=\"https://ww2.kqed.org/mindshift/2015/11/30/not-a-math-person-how-to-remove-obstacles-to-learning-math/\" target=\"_blank\">dramatic shift\u003c/a> in how many math teachers approach instruction. Rather than focusing on the algorithms and procedures that make mathematics feel like a lock-step process -- with one right way of solving problems -- Boaler encourages teachers to embrace the visual aspects of math. She encourages teachers to ask students to grapple with open-ended problems, to share ideas and to see math as a creative endeavor. She works with students every summer and says that when students are in a math environment that doesn't focus on performance, speed, procedures, and right and wrong answers they thrive. They even begin to change their perceptions of whether they can or can't do math.\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"vimeo","attributes":{"named":{"w":"640","h":"360","label":"206159614"},"numeric":["206159614"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003ca href=\"https://vimeo.com/206159614\">Solving The Math Problem (Subtitles)\u003c/a> from \u003ca href=\"https://vimeo.com/user20989575\">YouCubed\u003c/a> on \u003ca href=\"https://vimeo.com\">Vimeo\u003c/a>.\u003c/p>\n\u003cp>In an \u003ca href=\"http://hechingerreport.org/opinion-time-stop-clock-math-anxiety-heres-latest-research/\" target=\"_blank\">opinion piece for The Hechinger Report\u003c/a>, Boaler lays out five ways teachers can approach instruction differently. She points out that many students experience math anxiety, which is \u003ca href=\"https://hpl.uchicago.edu/sites/hpl.uchicago.edu/files/uploads/The%20Math%20Anxiety%20Performance%20Link,%20Foley%20et%20al.pdf\" target=\"_blank\">negatively related to performance\u003c/a>. While psychology research has pointed to smaller \u003ca href=\"https://ww2.kqed.org/mindshift/2013/02/08/anxious-about-tests-tips-to-ease-angst/\" target=\"_blank\">interventions to lower anxiety\u003c/a> before tests or to help students combat \u003ca href=\"https://ww2.kqed.org/mindshift/2017/01/26/at-age-6-girls-are-less-likely-to-identify-females-as-really-really-smart/\" target=\"_blank\">stereotype threat\u003c/a>, Boaler says those measures fall short. She writes:\u003c/p>\n\u003cblockquote>\u003cp>Widespread, prevalent among women and hugely damaging, math anxiety is prompted in the early years when timed tests are given in classrooms and it snowballs from there. Psychologists’ recommendations — including counseling and words to repeat before a test — severely miss the mark. The only way to turn our nation around is to change the way we teach and view math. The problems that we have now include these:\u003c/p>\n\u003cp>First, math is often taught as a performance subject. Ask your children what their role is in math class, and they are very likely to say it is to get questions correct. They do not say this about other subjects. More than any other subject math is about tests, grades, homework and competitions.\u003c/p>\u003c/blockquote>\n\u003cp>Check out Boaler's recommendations to change the math teaching paradigm in the U.S.\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003c/p>\n\u003cp>http://hechingerreport.org/opinion-time-stop-clock-math-anxiety-heres-latest-research/\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/47907/five-ways-to-shift-teaching-practice-so-students-feel-less-math-anxious","authors":["234"],"categories":["mindshift_193"],"tags":["mindshift_20784","mindshift_1040","mindshift_20943","mindshift_392","mindshift_20893"],"featImg":"mindshift_47918","label":"mindshift"},"mindshift_42933":{"type":"posts","id":"mindshift_42933","meta":{"index":"posts_1591205157","site":"mindshift","id":"42933","score":null,"sort":[1452154486000]},"guestAuthors":[],"slug":"how-saying-and-showing-kids-i-believe-in-you-can-empower-them-at-school","title":"How Showing and Telling Kids 'I Believe in You' Can Empower Them at School","publishDate":1452154486,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp>\u003cem>The excerpt below is from the book \"\u003ca href=\"http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470894520,descCd-buy.html\">Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching\u003c/a>,\" by Jo Boaler. This excerpt is from the chapter entitled “Teaching Mathematics for a Growth Mindset.”\u003c/em>\u003c/p>\n\u003cp>\u003cstrong>Believe in All of Your Students\u003c/strong>\u003c/p>\n\u003cp>I have always known how important it is that students know their teacher believes in them; I knew this as a teacher and more recently became more acutely aware of it as a parent. When my daughter was five, she realized the teacher of her class in England was giving other students harder math problems, and she came home to me and asked why. When she realized that the teacher did not think she had potential—and sadly, this was true; the teacher had decided she had limited ability—her self-belief was shattered, and she developed a terribly fixed mindset that damaged her learning and confidence for a long time afterward. Now, some years later, after a lot of work from her parents and some wonderful teachers, she is transformed: she has a growth mindset and loves math. Despite the fact that the teacher never said to my daughter that she did not believe in her, she managed to communicate that message loud and clear, and this was understood by my daughter even at the young age of five.\u003c/p>\n\u003cp>The school that my daughter attended in England put students into ability groups in second grade, but they stopped this practice after reading the research evidence and learning about the strategies for teaching heterogeneous groups. After they made this change, the principal wrote to tell me it had transformed math classes and raised achievement across the school. If students are placed into ability groups, even if they have innocuous names such as the red and blue groups, students will know, and their mindsets will become more fixed. When children were put into ability groups in my daughter’s school, children from the lower groups came home saying “All the clever children have gone into another group now.” The messages the students received about their potential as learners in general (not just about math) were devastating for them. One of the first steps we need to take, as a nation, is to move away from outdated methods of fixed mindset grouping and communicate to all students that they can achieve.\u003c/p>\n\u003cfigure id=\"attachment_42983\" class=\"wp-caption alignleft\" style=\"max-width: 250px\">\u003cimg class=\"size-full wp-image-42983\" src=\"http://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2015/12/Boaler-e1449126976155.jpg\" alt=\"Jo Boaler\" width=\"250\" height=\"312\">\u003cfigcaption class=\"wp-caption-text\">Jo Boaler\u003c/figcaption>\u003c/figure>\n\u003cp>The importance of students thinking their teacher believes in them was confirmed in a recent study that had an extremely powerful result (Cohen & Garcia, 2014). Hundreds of students were involved in this experimental study of high school English classes. All of the students wrote essays and received critical diagnostic feedback from their teachers, but half the students received a single extra sentence on the bottom of the feedback. The students who received the extra sentence achieved at significantly higher levels a year later, even though the teachers did not know who received the sentence and there were no other differences between the groups. It may seem incredible that one sentence could change students’ learning trajectories to the extent that they achieve at higher levels a year later, with no other change, but this was the extra sentence:\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>“I am giving you this feedback because I believe in you.”\u003c/p>\n\u003cp>Students who received this sentence scored at higher levels a year later. This effect was particularly significant for students of color, who often feel less valued by their teachers (Cohen & Garcia, 2014). I share this finding with teachers frequently, and they always fully understand its significance. I do not share the result in the hope that teachers will add this same sentence to all of their students’ work. That would lead students to think the sentence was not genuine, which would be counterproductive. I share it to emphasize the power of teachers’ words and the beliefs they hold about students, and to encourage teachers to instill positive belief messages at all times.\u003c/p>\n\u003cp>\u003cimg class=\"alignleft size-full wp-image-42982\" src=\"http://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2015/12/Mathematical-Mindsets-cover-image-e1449127016383.jpg\" alt=\"Mathematical Mindsets cover image\" width=\"250\" height=\"311\">\u003c/p>\n\u003cp>Teachers can communicate positive expectations to students by using encouraging words, and it is easy to do this with students who appear motivated, who learn easily, or who are quick. But it is even more important to communicate positive beliefs and expectations to students who are slow, appear unmotivated, or struggle. It is also important to realize that the speed at which students appear to grasp concepts is not indicative of their mathematics potential (Schwartz, 2001). As hard as it is, it is important to not have any preconceptions about who will work well on a math task in advance of their getting the task. We must be open at all times to any student’s working really well. Some students give the impression that math is a constant struggle for them, and they may ask a lot of questions or keep saying they are stuck, but they are just hiding their mathematics potential and are likely to be suffering from a fixed mindset. Some students have had bad math experiences and messages from a young age, or have not received opportunities for brain growth and learning that other students have, so they are at lower levels than other students, but this does not mean they cannot take off with good mathematics teaching, positive messages, and, perhaps most important, high expectations from their teacher. You can be the person who turns things around for them and liberates their learning path. It usually takes just one person—a person whom students will never forget.\u003c/p>\n\u003cp>\u003c/p>\n\u003cp>\u003cem>\u003ca href=\"http://@joboaler\">Jo Boaler\u003c/a> is a Professor of Mathematics Education at Stanford University and co-founder of \u003ca href=\"http://www.youcubed.org/\">www.youcubed.org\u003c/a>. Former roles have included being the Marie Curie Professor of Mathematics Education in England, and a mathematics teacher in London comprehensive schools. She is the author of eight books including \u003ca href=\"http://www.amazon.com/Whats-Math-Got-Do-It/dp/0143115715\">What's Math Got To Do With It?\u003c/a>\u003c/em>\u003c/p>\n\n","blocks":[],"excerpt":"The types of messages students receive can make a difference in how eager they are to learn subjects like math.","status":"publish","parent":0,"modified":1568751198,"stats":{"hasAudio":false,"hasVideo":false,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":12,"wordCount":982},"headData":{"title":"How Showing and Telling Kids 'I Believe in You' Can Empower Them at School | KQED","description":"The types of messages students receive can make a difference in how eager they are to learn subjects like math.","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","schema":{"@context":"http://schema.org","@type":"Article","headline":"How Showing and Telling Kids 'I Believe in You' Can Empower Them at School","datePublished":"2016-01-07T08:14:46.000Z","dateModified":"2019-09-17T20:13:18.000Z","image":"https://cdn.kqed.org/wp-content/uploads/2020/02/KQED-OG-Image@1x.png"}},"disqusIdentifier":"42933 http://ww2.kqed.org/mindshift/?p=42933","disqusUrl":"https://ww2.kqed.org/mindshift/2016/01/07/how-saying-and-showing-kids-i-believe-in-you-can-empower-them-at-school/","disqusTitle":"How Showing and Telling Kids 'I Believe in You' Can Empower Them at School","path":"/mindshift/42933/how-saying-and-showing-kids-i-believe-in-you-can-empower-them-at-school","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>\u003cem>The excerpt below is from the book \"\u003ca href=\"http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470894520,descCd-buy.html\">Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching\u003c/a>,\" by Jo Boaler. This excerpt is from the chapter entitled “Teaching Mathematics for a Growth Mindset.”\u003c/em>\u003c/p>\n\u003cp>\u003cstrong>Believe in All of Your Students\u003c/strong>\u003c/p>\n\u003cp>I have always known how important it is that students know their teacher believes in them; I knew this as a teacher and more recently became more acutely aware of it as a parent. When my daughter was five, she realized the teacher of her class in England was giving other students harder math problems, and she came home to me and asked why. When she realized that the teacher did not think she had potential—and sadly, this was true; the teacher had decided she had limited ability—her self-belief was shattered, and she developed a terribly fixed mindset that damaged her learning and confidence for a long time afterward. Now, some years later, after a lot of work from her parents and some wonderful teachers, she is transformed: she has a growth mindset and loves math. Despite the fact that the teacher never said to my daughter that she did not believe in her, she managed to communicate that message loud and clear, and this was understood by my daughter even at the young age of five.\u003c/p>\n\u003cp>The school that my daughter attended in England put students into ability groups in second grade, but they stopped this practice after reading the research evidence and learning about the strategies for teaching heterogeneous groups. After they made this change, the principal wrote to tell me it had transformed math classes and raised achievement across the school. If students are placed into ability groups, even if they have innocuous names such as the red and blue groups, students will know, and their mindsets will become more fixed. When children were put into ability groups in my daughter’s school, children from the lower groups came home saying “All the clever children have gone into another group now.” The messages the students received about their potential as learners in general (not just about math) were devastating for them. One of the first steps we need to take, as a nation, is to move away from outdated methods of fixed mindset grouping and communicate to all students that they can achieve.\u003c/p>\n\u003cfigure id=\"attachment_42983\" class=\"wp-caption alignleft\" style=\"max-width: 250px\">\u003cimg class=\"size-full wp-image-42983\" src=\"http://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2015/12/Boaler-e1449126976155.jpg\" alt=\"Jo Boaler\" width=\"250\" height=\"312\">\u003cfigcaption class=\"wp-caption-text\">Jo Boaler\u003c/figcaption>\u003c/figure>\n\u003cp>The importance of students thinking their teacher believes in them was confirmed in a recent study that had an extremely powerful result (Cohen & Garcia, 2014). Hundreds of students were involved in this experimental study of high school English classes. All of the students wrote essays and received critical diagnostic feedback from their teachers, but half the students received a single extra sentence on the bottom of the feedback. The students who received the extra sentence achieved at significantly higher levels a year later, even though the teachers did not know who received the sentence and there were no other differences between the groups. It may seem incredible that one sentence could change students’ learning trajectories to the extent that they achieve at higher levels a year later, with no other change, but this was the extra sentence:\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>“I am giving you this feedback because I believe in you.”\u003c/p>\n\u003cp>Students who received this sentence scored at higher levels a year later. This effect was particularly significant for students of color, who often feel less valued by their teachers (Cohen & Garcia, 2014). I share this finding with teachers frequently, and they always fully understand its significance. I do not share the result in the hope that teachers will add this same sentence to all of their students’ work. That would lead students to think the sentence was not genuine, which would be counterproductive. I share it to emphasize the power of teachers’ words and the beliefs they hold about students, and to encourage teachers to instill positive belief messages at all times.\u003c/p>\n\u003cp>\u003cimg class=\"alignleft size-full wp-image-42982\" src=\"http://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2015/12/Mathematical-Mindsets-cover-image-e1449127016383.jpg\" alt=\"Mathematical Mindsets cover image\" width=\"250\" height=\"311\">\u003c/p>\n\u003cp>Teachers can communicate positive expectations to students by using encouraging words, and it is easy to do this with students who appear motivated, who learn easily, or who are quick. But it is even more important to communicate positive beliefs and expectations to students who are slow, appear unmotivated, or struggle. It is also important to realize that the speed at which students appear to grasp concepts is not indicative of their mathematics potential (Schwartz, 2001). As hard as it is, it is important to not have any preconceptions about who will work well on a math task in advance of their getting the task. We must be open at all times to any student’s working really well. Some students give the impression that math is a constant struggle for them, and they may ask a lot of questions or keep saying they are stuck, but they are just hiding their mathematics potential and are likely to be suffering from a fixed mindset. Some students have had bad math experiences and messages from a young age, or have not received opportunities for brain growth and learning that other students have, so they are at lower levels than other students, but this does not mean they cannot take off with good mathematics teaching, positive messages, and, perhaps most important, high expectations from their teacher. You can be the person who turns things around for them and liberates their learning path. It usually takes just one person—a person whom students will never forget.\u003c/p>\n\u003cp>\u003c/p>\n\u003cp>\u003cem>\u003ca href=\"http://@joboaler\">Jo Boaler\u003c/a> is a Professor of Mathematics Education at Stanford University and co-founder of \u003ca href=\"http://www.youcubed.org/\">www.youcubed.org\u003c/a>. Former roles have included being the Marie Curie Professor of Mathematics Education in England, and a mathematics teacher in London comprehensive schools. She is the author of eight books including \u003ca href=\"http://www.amazon.com/Whats-Math-Got-Do-It/dp/0143115715\">What's Math Got To Do With It?\u003c/a>\u003c/em>\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/42933/how-saying-and-showing-kids-i-believe-in-you-can-empower-them-at-school","authors":["4354"],"categories":["mindshift_192"],"tags":["mindshift_20784","mindshift_1040","mindshift_20512","mindshift_20943","mindshift_392"],"featImg":"mindshift_43333","label":"mindshift"},"mindshift_42825":{"type":"posts","id":"mindshift_42825","meta":{"index":"posts_1591205157","site":"mindshift","id":"42825","score":null,"sort":[1448874470000]},"guestAuthors":[],"slug":"not-a-math-person-how-to-remove-obstacles-to-learning-math","title":"‘Not a Math Person’: How to Remove Obstacles to Learning Math","publishDate":1448874470,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp>Stanford math education professor \u003ca href=\"https://ed.stanford.edu/faculty/joboaler\" target=\"_blank\" rel=\"noopener\">Jo Boaler \u003c/a>spends a lot of time worrying about how math education in the United States traumatizes kids. Recently, a colleague’s 7-year-old came home from school and announced he didn’t like math anymore. His mom asked why and he said, “math is too much answering and not enough learning.”\u003c/p>\n\u003cp>This story demonstrates how clearly kids understand that unlike their other courses, math is a performative subject, where their job is to come up with answers quickly. Boaler says that if this approach doesn’t change, the U.S. will always have weak math education.\u003c/p>\n\u003cp>“There’s a widespread myth that some people are math people and some people are not,” Boaler told a group of parents and educators gathered at the \u003ca href=\"https://www.innovativelearningconference.org/ehome/index.php?eventid=107259&\" target=\"_blank\" rel=\"noopener\">2015 Innovative Learning Conference\u003c/a>. “But it turns out there’s no such thing as a math brain.” Unfortunately, many parents, teachers and students believe this myth and it holds them up every day in their math learning.\u003c/p>\n\u003caside class=\"pullquote alignright\">'There’s no such thing as a math brain.'\u003ccite>Jo Boaler, Stanford professor of math education\u003c/cite>\u003c/aside>\n\u003cp>“We live in a society with lots of kids who don’t believe they are good at math,” Boaler said at an Education Writers Association conference. “They’re put into low groups; they’re given low-level work and their pathway has been set.” But math education doesn’t have to look like this.\u003c/p>\n\u003cp>Neuroscience research is now showing a strong connection between the attitudes and beliefs students hold about themselves and their academic performance. That’s a departure from the long-held traditional view that academic success is based only on the quality of the teacher and curriculum. But researchers like\u003ca href=\"http://ww2.kqed.org/mindshift/2014/07/16/new-research-students-benefit-from-learning-that-intelligence-is-not-fixed/\" target=\"_blank\" rel=\"noopener\"> Carol Dweck\u003c/a>, \u003ca href=\"http://www.hewlett.org/uploads/documents/Academic_Mindsets_as_a_Critical_Component_of_Deeper_Learning_CAMILLE_FARRINGTON_April_20_2013.pdf\" target=\"_blank\" rel=\"noopener\">Camille Farrington\u003c/a> and \u003ca href=\"http://www.utexas.edu/cola/prc/directory/faculty/profile.php?id=yeagerds\">David Yeager\u003c/a> have shown repeatedly that small interventions to change attitudes about learning can have an outsized effect on performance.\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>Neuroscientists now know that the brain has the ability to grow and shrink. This was demonstrated in a \u003ca href=\"http://www.scientificamerican.com/article/london-taxi-memory/\" target=\"_blank\" rel=\"noopener\">study of taxi drivers in London\u003c/a> who must memorize all the streets and landmarks in downtown London to earn a license. On average it takes people 12 tries to pass the test. Researchers found that the hippocampus of drivers studying for the test grew tremendously. But when those drivers retired, the brain shrank. Before this, no one knew the brain could grow and shrink like that.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe src=\"//assets.nationalgeographic.com/modules-video/assets/ngsEmbeddedVideo.html?guid=add25b17-713c-4e97-ad23-01918ae7eb0e\" width=\"640\" height=\"365\" frameborder=\"0\" seamless=\"seamless\" scrolling=\"no\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>“We now know that when you make a mistake in math, your brain grows,” Boaler said. Neuroscientists did MRI scans of students taking math tests and saw that when a student made a mistake a synapse fired, even if the student wasn’t aware of the mistake. “Your brain grows when you make a mistake, even if you’re not aware of it, because it’s a time when your brain is struggling,” Boaler said. “It’s the most important time for our brains.”\u003c/p>\n\u003cp>A second synapse fires if the student recognizes his mistake. If that thought is revisited, the initial synapse firing can become a brain pathway, which is good for learning. If the thought isn’t revisited, that synapse will wash away.\u003c/p>\n\u003cp>A recent \u003ca href=\"http://www.nature.com/ncomms/2015/150930/ncomms9453/abs/ncomms9453.html\" target=\"_blank\" rel=\"noopener\">study of students with math learning disabilities\u003c/a> found in a scan that their brains did behave differently from kids without the disability. “What they saw was the brain lighting up in lots of different areas while working on math,” Boaler said. The children were recruiting parts of the brain not normally involved in math reasoning.\u003c/p>\n\u003cp>The researchers tutored the group of students with math disabilities for eight weeks using the methods Boaler recommends like \u003ca href=\"https://www.youcubed.org/think-it-up/visual-math-improves-math-performance/\" target=\"_blank\" rel=\"noopener\">visualizing math\u003c/a>, discussing problems and writing about math. At the end of the eight weeks, they scanned their brains again and found that the brains of the test group looked just like the kids who did not have math disabilities. This study shows that all kids can learn math when taught effectively. Boaler estimates that only 2 to 3 percent of people have such significant learning disabilities that they can’t learn math at the highest levels.\u003c/p>\n\u003cp>People who learned math the traditional way often push back against visual representations of math. That kind of thinking represents a deep misunderstanding of \u003ca href=\"http://brannonlab.org.s84504.gridserver.com/wp-content/uploads/Park-Brannon-2013.pdf\" target=\"_blank\" rel=\"noopener\">how the brain works\u003c/a>. “When you think visually about anything, different brain pathways light up than when we think numerically,” Boaler said. The more brain pathways a student engages on the same problem, the stronger the learning.\u003c/p>\n\u003cfigure id=\"attachment_42829\" class=\"wp-caption aligncenter\" style=\"max-width: 923px\">\u003ca href=\"https://www.youcubed.org/think-it-up/visual-math-improves-math-performance/\">\u003cimg class=\"wp-image-42829 size-full\" src=\"http://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2015/11/Screen-shot-2015-11-18-at-2.46.29-PM.png\" alt=\"An example of many ways to visually represent 18 x 5. \" width=\"923\" height=\"271\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2015/11/Screen-shot-2015-11-18-at-2.46.29-PM.png 923w, https://ww2.kqed.org/app/uploads/sites/23/2015/11/Screen-shot-2015-11-18-at-2.46.29-PM-400x117.png 400w, https://ww2.kqed.org/app/uploads/sites/23/2015/11/Screen-shot-2015-11-18-at-2.46.29-PM-800x235.png 800w\" sizes=\"(max-width: 923px) 100vw, 923px\">\u003c/a>\u003cfigcaption class=\"wp-caption-text\">An example of many ways to visually represent 18 x 5. \u003ccite>(Jo Boaler/YouCubed)\u003c/cite>\u003c/figcaption>\u003c/figure>\n\u003cp>\u003cstrong>GROWTH MINDSET AND MATH\u003c/strong>\u003c/p>\n\u003cp>Increasingly, educators are buying into the compelling research showing that what students believe about themselves \u003ca href=\"https://www.youcubed.org/think-it-up/believe-brain-operates-differently/\" target=\"_blank\" rel=\"noopener\">affects how their brains approach learning\u003c/a>. Growth mindset is probably the best known aspect of this research, and many school leaders are trying to figure out \u003ca href=\"http://ww2.kqed.org/mindshift/2015/08/24/growth-mindset-how-to-normalize-mistake-making-and-struggle-in-class/\" target=\"_blank\" rel=\"noopener\">how to implement growth mindset\u003c/a> programs in their classrooms.\u003c/p>\n\u003cp>“More kids have a fixed mindset about math than anything else,” Boaler said. And it’s no coincidence that they feel this way. Teachers often believe their students can’t achieve at the highest levels, and in turn, students believe that about themselves. Plus, the tasks themselves communicate a fixed mindset.\u003c/p>\n\u003cp>“It is very difficult to have a growth mindset and to believe that you can grow or learn if you are constantly given short, closed questions with a right or wrong answer,” Boaler said. Instead, she recommends giving visual problems that provoke discussion and have multiple ways they could be solved.\u003c/p>\n\u003cp>She also says kids should not be grouped by ability or tracked into “advanced” or “remedial” groups. That common practice sends fixed mindset messages to students, both the “advanced” ones and the “low-performing” ones. Kids considered to be “gifted” suffer from ability grouping the most because they develop the ultimate fixed mindset. They become terrified that if they struggle they’ll no longer be considered smart.\u003c/p>\n\u003cp>Instead, mixed ability grouping can work if the \u003ca href=\"https://www.youcubed.org/tasks/\" target=\"_blank\" rel=\"noopener\">tasks are open-ended\u003c/a> and what Boaler calls “low-floor/high-ceiling” tasks that allow every student to participate, while allowing lots of space within the task for students to grow in their thinking.\u003c/p>\n\u003cp>Boaler has lots of example tasks on her website, \u003ca href=\"https://www.youcubed.org/\" target=\"_blank\" rel=\"noopener\">YouCubed\u003c/a>, and on the \u003ca href=\"http://nrich.maths.org/frontpage\" target=\"_blank\" rel=\"noopener\">NRICH website\u003c/a>.\u003c/p>\n\u003cp>\u003cstrong>PUTTING IT INTO PRACTICE\u003c/strong>\u003c/p>\n\u003cp>During the summer of 2015, Boaler invited 81 seventh- and eighth-graders from a low-income district near Stanford to come to a summer math camp focused on algebra concepts. She gave the students a pre-test and found that their abilities ranged from very low (getting 0 answers correct) to fairly high. Then, for 18 days she taught them math well.\u003c/p>\n\u003cp>[youtube https://www.youtube.com/watch?v=aDTUb6UWZYs&w=640&h=360]\u003c/p>\n\u003cp>The instructional program focused on mindset messages, was full of inquiry-based, low-floor/high-ceiling tasks, was visual and used mixed achievement groups. At the end of 18 days, when Boaler gave them another test they had improved on average by 50 percent.\u003c/p>\n\u003cp>“They improved because they changed their beliefs that they were not a math person to believing they were a math person,” Boaler said. After the course, students said they looked forward to math and saw math as a creative subject.\u003c/p>\n\u003cp>Administrators from the district came to observe partway through the camp and couldn’t tell who was a low achiever and who was a high achiever in the class. Boaler also makes it clear to the students in the workshop what she expects from them, and speed is not something she’s evaluating. Instead, they do norm building so that everyone knows how to appropriately work in groups, help one another and be supportive.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe src=\"https://player.vimeo.com/video/118763045\" width=\"500\" height=\"281\" frameborder=\"0\" scrolling=\"yes\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>“If we don’t pay attention to those kinds of interactions, and kids are dominating, or thinking they’re smarter, then we’re really in trouble,” Boaler said.\u003c/p>\n\u003cp>Removing the time pressure from math is another important issue for Boaler. Neuroscience research out of \u003ca href=\"https://hpl.uchicago.edu/\" target=\"_blank\" rel=\"noopener\">Sian Beilock’s lab\u003c/a> at the University of Chicago has shown that time pressure often \u003ca href=\"https://hpl.uchicago.edu/sites/hpl.uchicago.edu/files/uploads/Ramirez%20et%20al%2C%202013.pdf\" target=\"_blank\" rel=\"noopener\">blocks the brain’s working memory\u003c/a> from functioning. This is particularly bad for kids with test anxiety.\u003c/p>\n\u003cp>“The irony of this is mathematicians are not fast with numbers,” Boaler said. “We value speed in math classrooms, but I’ve talked with lots of mathematicians who say they’re not fast at all.\" But it is common for math teachers to call on the kids who get the answer quickly, reinforcing the idea for all students that rapidity is what matters.\u003c/p>\n\u003cp>\u003cstrong>COMMON PUSHBACK\u003c/strong>\u003c/p>\n\u003cp>Math education experts have been making the same case as Boaler for decades, and yet math education in the U.S. has not shifted much. Teachers often say they have to cover all the topics in the curriculum to prepare students for the tests they will be expected to pass, leaving them with no time for the kinds of open-ended, discussion-based math that Boaler advocates.\u003c/p>\n\u003caside class=\"pullquote alignright\">'It is very difficult to have a growth mindset and to believe that you can grow or learn if you are constantly given short, closed questions with a right or wrong answer.'\u003c/aside>\n\u003cp>Boaler agrees with teachers that there is way too much to cover in the curriculum, especially because she finds much of it to be obsolete (don't get her started on the textbooks themselves). “The most important thing we can give kids is to think quantitatively about the world and apply a mathematical lens to different situations,” she said.\u003c/p>\n\u003cp>In addition to teaching students, Boaler \u003ca href=\"https://www.youcubed.org/online-teacher-courses/#\" target=\"_blank\" rel=\"noopener\">trains teachers\u003c/a> in her methods. Often they go back to their classrooms and apply these theories, which means they aren’t covering every topic in the textbook, and yet their students do better on the standardized tests anyway. Boaler is not a fan of all the tests American students must take, but she says teaching math the right way deepens kids' understanding of math in real ways that show up on tests, too.\u003c/p>\n\u003cp>Teachers and parents often push back against this kind of math. They wonder where memorization of math facts fits into the model, given the belief that kids must know their times tables to succeed in higher-level math. Boaler says that's unnecessary. She is a math education teacher and has risen to high levels of math learning without ever learning her math facts. She has number fluency, knows how to manipulate numbers and understands concepts, but she doesn’t have her math facts memorized.\u003c/p>\n\u003cp>The Programme for International Student Assessment test (PISA), which is often used to compare achievement across countries, has a section about \u003ca href=\"http://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf\" target=\"_blank\" rel=\"noopener\">attitudes and beliefs\u003c/a>. Those surveys show that kids who approach \u003ca href=\"http://hechingerreport.org/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises/\">math as memorization\u003c/a> are the lowest achievers in the world. “America has more memorizers than almost any country in the world,” Boaler said. The highest achievers are those who think about the big ideas and make connections.\u003c/p>\n\u003cp>Likewise, repetition of math tasks is not helpful to deep learning. The same kind of problem with different numbers does not improve understanding, Boaler said. What students really need is “productive practice,” approaching the problem from different directions, applying the ideas and explaining reasoning.\u003c/p>\n\u003cp>Boaler is on a mission to “revolutionize” how math is taught in the U.S. She has written several books to help teachers learn to teach with her methods, offers a \u003ca href=\"https://www.youcubed.org/how-to-learn-math-for-students/\" target=\"_blank\" rel=\"noopener\">free online course\u003c/a>, and even gives away curriculum for teachers, students and parents on her YouCubed website. During one week at the start of the 2015 school year Boaler gave away \u003ca href=\"https://www.youcubed.org/week-of-inspirational-math/\" target=\"_blank\" rel=\"noopener\">five free math lessons\u003c/a>, encouraging teachers to try this approach. She’s pleased that 100,000 schools tried the lessons, and teachers could see the difference in their students. A survey of students found that after the lessons and the growth mindset videos, 96 percent believed they should keep trying after making a mistake in math.\u003c/p>\n\u003cp>Boaler said a big problem is that math teachers themselves are math-traumatized. They came through a system very similar to the one in which they work. Elementary school teachers in particular often feel insecure about math.\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>“When they try math in these ways they get it, too,” Boaler said. “They can see this is much more valuable and enriching.”\u003c/p>\n\n","blocks":[],"excerpt":"Negative experiences such as timed tests, tracking and personal attitudes have hurt how some people feel about math. Stanford professor Jo Boaler wants to change all of that.","status":"publish","parent":0,"modified":1563214775,"stats":{"hasAudio":false,"hasVideo":true,"hasChartOrMap":true,"iframeSrcs":["//assets.nationalgeographic.com/modules-video/assets/ngsEmbeddedVideo.html","https://player.vimeo.com/video/118763045"],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":41,"wordCount":2111},"headData":{"title":"‘Not a Math Person’: How to Remove Obstacles to Learning Math | KQED","description":"Negative experiences such as timed tests, tracking and personal attitudes have hurt how some people feel about math. Stanford professor Jo Boaler wants to change all of that.","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","schema":{"@context":"http://schema.org","@type":"Article","headline":"‘Not a Math Person’: How to Remove Obstacles to Learning Math","datePublished":"2015-11-30T09:07:50.000Z","dateModified":"2019-07-15T18:19:35.000Z","image":"https://cdn.kqed.org/wp-content/uploads/2020/02/KQED-OG-Image@1x.png"}},"disqusIdentifier":"42825 http://ww2.kqed.org/mindshift/?p=42825","disqusUrl":"https://ww2.kqed.org/mindshift/2015/11/30/not-a-math-person-how-to-remove-obstacles-to-learning-math/","disqusTitle":"‘Not a Math Person’: How to Remove Obstacles to Learning Math","path":"/mindshift/42825/not-a-math-person-how-to-remove-obstacles-to-learning-math","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>Stanford math education professor \u003ca href=\"https://ed.stanford.edu/faculty/joboaler\" target=\"_blank\" rel=\"noopener\">Jo Boaler \u003c/a>spends a lot of time worrying about how math education in the United States traumatizes kids. Recently, a colleague’s 7-year-old came home from school and announced he didn’t like math anymore. His mom asked why and he said, “math is too much answering and not enough learning.”\u003c/p>\n\u003cp>This story demonstrates how clearly kids understand that unlike their other courses, math is a performative subject, where their job is to come up with answers quickly. Boaler says that if this approach doesn’t change, the U.S. will always have weak math education.\u003c/p>\n\u003cp>“There’s a widespread myth that some people are math people and some people are not,” Boaler told a group of parents and educators gathered at the \u003ca href=\"https://www.innovativelearningconference.org/ehome/index.php?eventid=107259&\" target=\"_blank\" rel=\"noopener\">2015 Innovative Learning Conference\u003c/a>. “But it turns out there’s no such thing as a math brain.” Unfortunately, many parents, teachers and students believe this myth and it holds them up every day in their math learning.\u003c/p>\n\u003caside class=\"pullquote alignright\">'There’s no such thing as a math brain.'\u003ccite>Jo Boaler, Stanford professor of math education\u003c/cite>\u003c/aside>\n\u003cp>“We live in a society with lots of kids who don’t believe they are good at math,” Boaler said at an Education Writers Association conference. “They’re put into low groups; they’re given low-level work and their pathway has been set.” But math education doesn’t have to look like this.\u003c/p>\n\u003cp>Neuroscience research is now showing a strong connection between the attitudes and beliefs students hold about themselves and their academic performance. That’s a departure from the long-held traditional view that academic success is based only on the quality of the teacher and curriculum. But researchers like\u003ca href=\"http://ww2.kqed.org/mindshift/2014/07/16/new-research-students-benefit-from-learning-that-intelligence-is-not-fixed/\" target=\"_blank\" rel=\"noopener\"> Carol Dweck\u003c/a>, \u003ca href=\"http://www.hewlett.org/uploads/documents/Academic_Mindsets_as_a_Critical_Component_of_Deeper_Learning_CAMILLE_FARRINGTON_April_20_2013.pdf\" target=\"_blank\" rel=\"noopener\">Camille Farrington\u003c/a> and \u003ca href=\"http://www.utexas.edu/cola/prc/directory/faculty/profile.php?id=yeagerds\">David Yeager\u003c/a> have shown repeatedly that small interventions to change attitudes about learning can have an outsized effect on performance.\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>Neuroscientists now know that the brain has the ability to grow and shrink. This was demonstrated in a \u003ca href=\"http://www.scientificamerican.com/article/london-taxi-memory/\" target=\"_blank\" rel=\"noopener\">study of taxi drivers in London\u003c/a> who must memorize all the streets and landmarks in downtown London to earn a license. On average it takes people 12 tries to pass the test. Researchers found that the hippocampus of drivers studying for the test grew tremendously. But when those drivers retired, the brain shrank. Before this, no one knew the brain could grow and shrink like that.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe src=\"//assets.nationalgeographic.com/modules-video/assets/ngsEmbeddedVideo.html?guid=add25b17-713c-4e97-ad23-01918ae7eb0e\" width=\"640\" height=\"365\" frameborder=\"0\" seamless=\"seamless\" scrolling=\"no\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>“We now know that when you make a mistake in math, your brain grows,” Boaler said. Neuroscientists did MRI scans of students taking math tests and saw that when a student made a mistake a synapse fired, even if the student wasn’t aware of the mistake. “Your brain grows when you make a mistake, even if you’re not aware of it, because it’s a time when your brain is struggling,” Boaler said. “It’s the most important time for our brains.”\u003c/p>\n\u003cp>A second synapse fires if the student recognizes his mistake. If that thought is revisited, the initial synapse firing can become a brain pathway, which is good for learning. If the thought isn’t revisited, that synapse will wash away.\u003c/p>\n\u003cp>A recent \u003ca href=\"http://www.nature.com/ncomms/2015/150930/ncomms9453/abs/ncomms9453.html\" target=\"_blank\" rel=\"noopener\">study of students with math learning disabilities\u003c/a> found in a scan that their brains did behave differently from kids without the disability. “What they saw was the brain lighting up in lots of different areas while working on math,” Boaler said. The children were recruiting parts of the brain not normally involved in math reasoning.\u003c/p>\n\u003cp>The researchers tutored the group of students with math disabilities for eight weeks using the methods Boaler recommends like \u003ca href=\"https://www.youcubed.org/think-it-up/visual-math-improves-math-performance/\" target=\"_blank\" rel=\"noopener\">visualizing math\u003c/a>, discussing problems and writing about math. At the end of the eight weeks, they scanned their brains again and found that the brains of the test group looked just like the kids who did not have math disabilities. This study shows that all kids can learn math when taught effectively. Boaler estimates that only 2 to 3 percent of people have such significant learning disabilities that they can’t learn math at the highest levels.\u003c/p>\n\u003cp>People who learned math the traditional way often push back against visual representations of math. That kind of thinking represents a deep misunderstanding of \u003ca href=\"http://brannonlab.org.s84504.gridserver.com/wp-content/uploads/Park-Brannon-2013.pdf\" target=\"_blank\" rel=\"noopener\">how the brain works\u003c/a>. “When you think visually about anything, different brain pathways light up than when we think numerically,” Boaler said. The more brain pathways a student engages on the same problem, the stronger the learning.\u003c/p>\n\u003cfigure id=\"attachment_42829\" class=\"wp-caption aligncenter\" style=\"max-width: 923px\">\u003ca href=\"https://www.youcubed.org/think-it-up/visual-math-improves-math-performance/\">\u003cimg class=\"wp-image-42829 size-full\" src=\"http://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2015/11/Screen-shot-2015-11-18-at-2.46.29-PM.png\" alt=\"An example of many ways to visually represent 18 x 5. \" width=\"923\" height=\"271\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2015/11/Screen-shot-2015-11-18-at-2.46.29-PM.png 923w, https://ww2.kqed.org/app/uploads/sites/23/2015/11/Screen-shot-2015-11-18-at-2.46.29-PM-400x117.png 400w, https://ww2.kqed.org/app/uploads/sites/23/2015/11/Screen-shot-2015-11-18-at-2.46.29-PM-800x235.png 800w\" sizes=\"(max-width: 923px) 100vw, 923px\">\u003c/a>\u003cfigcaption class=\"wp-caption-text\">An example of many ways to visually represent 18 x 5. \u003ccite>(Jo Boaler/YouCubed)\u003c/cite>\u003c/figcaption>\u003c/figure>\n\u003cp>\u003cstrong>GROWTH MINDSET AND MATH\u003c/strong>\u003c/p>\n\u003cp>Increasingly, educators are buying into the compelling research showing that what students believe about themselves \u003ca href=\"https://www.youcubed.org/think-it-up/believe-brain-operates-differently/\" target=\"_blank\" rel=\"noopener\">affects how their brains approach learning\u003c/a>. Growth mindset is probably the best known aspect of this research, and many school leaders are trying to figure out \u003ca href=\"http://ww2.kqed.org/mindshift/2015/08/24/growth-mindset-how-to-normalize-mistake-making-and-struggle-in-class/\" target=\"_blank\" rel=\"noopener\">how to implement growth mindset\u003c/a> programs in their classrooms.\u003c/p>\n\u003cp>“More kids have a fixed mindset about math than anything else,” Boaler said. And it’s no coincidence that they feel this way. Teachers often believe their students can’t achieve at the highest levels, and in turn, students believe that about themselves. Plus, the tasks themselves communicate a fixed mindset.\u003c/p>\n\u003cp>“It is very difficult to have a growth mindset and to believe that you can grow or learn if you are constantly given short, closed questions with a right or wrong answer,” Boaler said. Instead, she recommends giving visual problems that provoke discussion and have multiple ways they could be solved.\u003c/p>\n\u003cp>She also says kids should not be grouped by ability or tracked into “advanced” or “remedial” groups. That common practice sends fixed mindset messages to students, both the “advanced” ones and the “low-performing” ones. Kids considered to be “gifted” suffer from ability grouping the most because they develop the ultimate fixed mindset. They become terrified that if they struggle they’ll no longer be considered smart.\u003c/p>\n\u003cp>Instead, mixed ability grouping can work if the \u003ca href=\"https://www.youcubed.org/tasks/\" target=\"_blank\" rel=\"noopener\">tasks are open-ended\u003c/a> and what Boaler calls “low-floor/high-ceiling” tasks that allow every student to participate, while allowing lots of space within the task for students to grow in their thinking.\u003c/p>\n\u003cp>Boaler has lots of example tasks on her website, \u003ca href=\"https://www.youcubed.org/\" target=\"_blank\" rel=\"noopener\">YouCubed\u003c/a>, and on the \u003ca href=\"http://nrich.maths.org/frontpage\" target=\"_blank\" rel=\"noopener\">NRICH website\u003c/a>.\u003c/p>\n\u003cp>\u003cstrong>PUTTING IT INTO PRACTICE\u003c/strong>\u003c/p>\n\u003cp>During the summer of 2015, Boaler invited 81 seventh- and eighth-graders from a low-income district near Stanford to come to a summer math camp focused on algebra concepts. She gave the students a pre-test and found that their abilities ranged from very low (getting 0 answers correct) to fairly high. Then, for 18 days she taught them math well.\u003c/p>\n\u003cp>\u003c/p>\u003cp>\u003cspan class='utils-parseShortcode-shortcodes-__youtubeShortcode__embedYoutube'>\n \u003cspan class='utils-parseShortcode-shortcodes-__youtubeShortcode__embedYoutubeInside'>\n \u003ciframe\n loading='lazy'\n class='utils-parseShortcode-shortcodes-__youtubeShortcode__youtubePlayer'\n type='text/html'\n src='//www.youtube.com/embed/aDTUb6UWZYs'\n title='//www.youtube.com/embed/aDTUb6UWZYs'\n allowfullscreen='true'\n style='border:0;'>\u003c/iframe>\n \u003c/span>\n \u003c/span>\u003c/p>\u003cp>\u003c/p>\n\u003cp>The instructional program focused on mindset messages, was full of inquiry-based, low-floor/high-ceiling tasks, was visual and used mixed achievement groups. At the end of 18 days, when Boaler gave them another test they had improved on average by 50 percent.\u003c/p>\n\u003cp>“They improved because they changed their beliefs that they were not a math person to believing they were a math person,” Boaler said. After the course, students said they looked forward to math and saw math as a creative subject.\u003c/p>\n\u003cp>Administrators from the district came to observe partway through the camp and couldn’t tell who was a low achiever and who was a high achiever in the class. Boaler also makes it clear to the students in the workshop what she expects from them, and speed is not something she’s evaluating. Instead, they do norm building so that everyone knows how to appropriately work in groups, help one another and be supportive.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe src=\"https://player.vimeo.com/video/118763045\" width=\"500\" height=\"281\" frameborder=\"0\" scrolling=\"yes\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>“If we don’t pay attention to those kinds of interactions, and kids are dominating, or thinking they’re smarter, then we’re really in trouble,” Boaler said.\u003c/p>\n\u003cp>Removing the time pressure from math is another important issue for Boaler. Neuroscience research out of \u003ca href=\"https://hpl.uchicago.edu/\" target=\"_blank\" rel=\"noopener\">Sian Beilock’s lab\u003c/a> at the University of Chicago has shown that time pressure often \u003ca href=\"https://hpl.uchicago.edu/sites/hpl.uchicago.edu/files/uploads/Ramirez%20et%20al%2C%202013.pdf\" target=\"_blank\" rel=\"noopener\">blocks the brain’s working memory\u003c/a> from functioning. This is particularly bad for kids with test anxiety.\u003c/p>\n\u003cp>“The irony of this is mathematicians are not fast with numbers,” Boaler said. “We value speed in math classrooms, but I’ve talked with lots of mathematicians who say they’re not fast at all.\" But it is common for math teachers to call on the kids who get the answer quickly, reinforcing the idea for all students that rapidity is what matters.\u003c/p>\n\u003cp>\u003cstrong>COMMON PUSHBACK\u003c/strong>\u003c/p>\n\u003cp>Math education experts have been making the same case as Boaler for decades, and yet math education in the U.S. has not shifted much. Teachers often say they have to cover all the topics in the curriculum to prepare students for the tests they will be expected to pass, leaving them with no time for the kinds of open-ended, discussion-based math that Boaler advocates.\u003c/p>\n\u003caside class=\"pullquote alignright\">'It is very difficult to have a growth mindset and to believe that you can grow or learn if you are constantly given short, closed questions with a right or wrong answer.'\u003c/aside>\n\u003cp>Boaler agrees with teachers that there is way too much to cover in the curriculum, especially because she finds much of it to be obsolete (don't get her started on the textbooks themselves). “The most important thing we can give kids is to think quantitatively about the world and apply a mathematical lens to different situations,” she said.\u003c/p>\n\u003cp>In addition to teaching students, Boaler \u003ca href=\"https://www.youcubed.org/online-teacher-courses/#\" target=\"_blank\" rel=\"noopener\">trains teachers\u003c/a> in her methods. Often they go back to their classrooms and apply these theories, which means they aren’t covering every topic in the textbook, and yet their students do better on the standardized tests anyway. Boaler is not a fan of all the tests American students must take, but she says teaching math the right way deepens kids' understanding of math in real ways that show up on tests, too.\u003c/p>\n\u003cp>Teachers and parents often push back against this kind of math. They wonder where memorization of math facts fits into the model, given the belief that kids must know their times tables to succeed in higher-level math. Boaler says that's unnecessary. She is a math education teacher and has risen to high levels of math learning without ever learning her math facts. She has number fluency, knows how to manipulate numbers and understands concepts, but she doesn’t have her math facts memorized.\u003c/p>\n\u003cp>The Programme for International Student Assessment test (PISA), which is often used to compare achievement across countries, has a section about \u003ca href=\"http://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf\" target=\"_blank\" rel=\"noopener\">attitudes and beliefs\u003c/a>. Those surveys show that kids who approach \u003ca href=\"http://hechingerreport.org/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises/\">math as memorization\u003c/a> are the lowest achievers in the world. “America has more memorizers than almost any country in the world,” Boaler said. The highest achievers are those who think about the big ideas and make connections.\u003c/p>\n\u003cp>Likewise, repetition of math tasks is not helpful to deep learning. The same kind of problem with different numbers does not improve understanding, Boaler said. What students really need is “productive practice,” approaching the problem from different directions, applying the ideas and explaining reasoning.\u003c/p>\n\u003cp>Boaler is on a mission to “revolutionize” how math is taught in the U.S. She has written several books to help teachers learn to teach with her methods, offers a \u003ca href=\"https://www.youcubed.org/how-to-learn-math-for-students/\" target=\"_blank\" rel=\"noopener\">free online course\u003c/a>, and even gives away curriculum for teachers, students and parents on her YouCubed website. During one week at the start of the 2015 school year Boaler gave away \u003ca href=\"https://www.youcubed.org/week-of-inspirational-math/\" target=\"_blank\" rel=\"noopener\">five free math lessons\u003c/a>, encouraging teachers to try this approach. She’s pleased that 100,000 schools tried the lessons, and teachers could see the difference in their students. A survey of students found that after the lessons and the growth mindset videos, 96 percent believed they should keep trying after making a mistake in math.\u003c/p>\n\u003cp>Boaler said a big problem is that math teachers themselves are math-traumatized. They came through a system very similar to the one in which they work. Elementary school teachers in particular often feel insecure about math.\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>“When they try math in these ways they get it, too,” Boaler said. “They can see this is much more valuable and enriching.”\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/42825/not-a-math-person-how-to-remove-obstacles-to-learning-math","authors":["234"],"categories":["mindshift_193"],"tags":["mindshift_20784","mindshift_1040","mindshift_20512","mindshift_797","mindshift_20943","mindshift_392","mindshift_20893"],"featImg":"mindshift_42928","label":"mindshift"}},"programsReducer":{"possible":{"id":"possible","title":"Possible","info":"Possible is hosted by entrepreneur Reid Hoffman and writer Aria Finger. Together in Possible, Hoffman and Finger lead enlightening discussions about building a brighter collective future. The show features interviews with visionary guests like Trevor Noah, Sam Altman and Janette Sadik-Khan. Possible paints an optimistic portrait of the world we can create through science, policy, business, art and our shared humanity. It asks: What if everything goes right for once? How can we get there? Each episode also includes a short fiction story generated by advanced AI GPT-4, serving as a thought-provoking springboard to speculate how humanity could leverage technology for good.","airtime":"SUN 2pm","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/Possible-Podcast-Tile-360x360-1.jpg","officialWebsiteLink":"https://www.possible.fm/","meta":{"site":"news","source":"Possible"},"link":"/radio/program/possible","subscribe":{"apple":"https://podcasts.apple.com/us/podcast/possible/id1677184070","spotify":"https://open.spotify.com/show/730YpdUSNlMyPQwNnyjp4k"}},"1a":{"id":"1a","title":"1A","info":"1A is home to the national conversation. 1A brings on great guests and frames the best debate in ways that make you think, share and engage.","airtime":"MON-THU 11pm-12am","imageSrc":"https://ww2.kqed.org/radio/wp-content/uploads/sites/50/2018/04/1a.jpg","officialWebsiteLink":"https://the1a.org/","meta":{"site":"news","source":"npr"},"link":"/radio/program/1a","subscribe":{"npr":"https://rpb3r.app.goo.gl/RBrW","apple":"https://itunes.apple.com/WebObjects/MZStore.woa/wa/viewPodcast?s=143441&mt=2&id=1188724250&at=11l79Y&ct=nprdirectory","tuneIn":"https://tunein.com/radio/1A-p947376/","rss":"https://feeds.npr.org/510316/podcast.xml"}},"all-things-considered":{"id":"all-things-considered","title":"All Things Considered","info":"Every weekday, \u003cem>All Things Considered\u003c/em> hosts Robert Siegel, Audie Cornish, Ari Shapiro, and Kelly McEvers present the program's trademark mix of news, interviews, commentaries, reviews, and offbeat features. Michel Martin hosts on the weekends.","airtime":"MON-FRI 1pm-2pm, 4:30pm-6:30pm\u003cbr />SAT-SUN 5pm-6pm","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/All-Things-Considered-Podcast-Tile-360x360-1.jpg","officialWebsiteLink":"https://www.npr.org/programs/all-things-considered/","meta":{"site":"news","source":"npr"},"link":"/radio/program/all-things-considered"},"american-suburb-podcast":{"id":"american-suburb-podcast","title":"American Suburb: The Podcast","tagline":"The flip side of gentrification, told through one town","info":"Gentrification is changing cities across America, forcing people from neighborhoods they have long called home. Call them the displaced. Now those priced out of the Bay Area are looking for a better life in an unlikely place. American Suburb follows this migration to one California town along the Delta, 45 miles from San Francisco. But is this once sleepy suburb ready for them?","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/American-Suburb-Podcast-Tile-703x703-1.jpg","officialWebsiteLink":"/news/series/american-suburb-podcast","meta":{"site":"news","source":"kqed","order":"13"},"link":"/news/series/american-suburb-podcast/","subscribe":{"npr":"https://rpb3r.app.goo.gl/RBrW","apple":"https://itunes.apple.com/WebObjects/MZStore.woa/wa/viewPodcast?mt=2&id=1287748328","tuneIn":"https://tunein.com/radio/American-Suburb-p1086805/","rss":"https://ww2.kqed.org/news/series/american-suburb-podcast/feed/podcast","google":"https://podcasts.google.com/feed/aHR0cHM6Ly9mZWVkcy5tZWdhcGhvbmUuZm0vS1FJTkMzMDExODgxNjA5"}},"baycurious":{"id":"baycurious","title":"Bay Curious","tagline":"Exploring the Bay Area, one question at a time","info":"KQED’s new podcast, Bay Curious, gets to the bottom of the mysteries — both profound and peculiar — that give the Bay Area its unique identity. And we’ll do it with your help! You ask the questions. You decide what Bay Curious investigates. And you join us on the journey to find the answers.","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/Bay-Curious-Podcast-Tile-703x703-1.jpg","imageAlt":"\"KQED Bay Curious","officialWebsiteLink":"/news/series/baycurious","meta":{"site":"news","source":"kqed","order":"4"},"link":"/podcasts/baycurious","subscribe":{"apple":"https://podcasts.apple.com/us/podcast/bay-curious/id1172473406","npr":"https://www.npr.org/podcasts/500557090/bay-curious","rss":"https://ww2.kqed.org/news/category/bay-curious-podcast/feed/podcast","google":"https://podcasts.google.com/feed/aHR0cHM6Ly93dzIua3FlZC5vcmcvbmV3cy9jYXRlZ29yeS9iYXktY3VyaW91cy1wb2RjYXN0L2ZlZWQvcG9kY2FzdA","stitcher":"https://www.stitcher.com/podcast/kqed/bay-curious","spotify":"https://open.spotify.com/show/6O76IdmhixfijmhTZLIJ8k"}},"bbc-world-service":{"id":"bbc-world-service","title":"BBC World Service","info":"The day's top stories from BBC News compiled twice daily in the week, once at weekends.","airtime":"MON-FRI 9pm-10pm, TUE-FRI 1am-2am","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/BBC-World-Service-Podcast-Tile-360x360-1.jpg","officialWebsiteLink":"https://www.bbc.co.uk/sounds/play/live:bbc_world_service","meta":{"site":"news","source":"BBC World Service"},"link":"/radio/program/bbc-world-service","subscribe":{"apple":"https://itunes.apple.com/us/podcast/global-news-podcast/id135067274?mt=2","tuneIn":"https://tunein.com/radio/BBC-World-Service-p455581/","rss":"https://podcasts.files.bbci.co.uk/p02nq0gn.rss"}},"code-switch-life-kit":{"id":"code-switch-life-kit","title":"Code Switch / Life Kit","info":"\u003cem>Code Switch\u003c/em>, which listeners will hear in the first part of the hour, has fearless and much-needed conversations about race. Hosted by journalists of color, the show tackles the subject of race head-on, exploring how it impacts every part of society — from politics and pop culture to history, sports and more.\u003cbr />\u003cbr />\u003cem>Life Kit\u003c/em>, which will be in the second part of the hour, guides you through spaces and feelings no one prepares you for — from finances to mental health, from workplace microaggressions to imposter syndrome, from relationships to parenting. The show features experts with real world experience and shares their knowledge. Because everyone needs a little help being human.\u003cbr />\u003cbr />\u003ca href=\"https://www.npr.org/podcasts/510312/codeswitch\">\u003cem>Code Switch\u003c/em> offical site and podcast\u003c/a>\u003cbr />\u003ca href=\"https://www.npr.org/lifekit\">\u003cem>Life Kit\u003c/em> offical site and podcast\u003c/a>\u003cbr />","airtime":"SUN 9pm-10pm","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/Code-Switch-Life-Kit-Podcast-Tile-360x360-1.jpg","meta":{"site":"radio","source":"npr"},"link":"/radio/program/code-switch-life-kit","subscribe":{"apple":"https://podcasts.apple.com/podcast/1112190608?mt=2&at=11l79Y&ct=nprdirectory","google":"https://podcasts.google.com/feed/aHR0cHM6Ly93d3cubnByLm9yZy9yc3MvcG9kY2FzdC5waHA_aWQ9NTEwMzEy","spotify":"https://open.spotify.com/show/3bExJ9JQpkwNhoHvaIIuyV","rss":"https://feeds.npr.org/510312/podcast.xml"}},"commonwealth-club":{"id":"commonwealth-club","title":"Commonwealth Club of California Podcast","info":"The Commonwealth Club of California is the nation's oldest and largest public affairs forum. As a non-partisan forum, The Club brings to the public airwaves diverse viewpoints on important topics. The Club's weekly radio broadcast - the oldest in the U.S., dating back to 1924 - is carried across the nation on public radio stations and is now podcasting. Our website archive features audio of our recent programs, as well as selected speeches from our long and distinguished history. This podcast feed is usually updated twice a week and is always un-edited.","airtime":"THU 10pm, FRI 1am","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/Commonwealth-Club-Podcast-Tile-360x360-1.jpg","officialWebsiteLink":"https://www.commonwealthclub.org/podcasts","meta":{"site":"news","source":"Commonwealth Club of California"},"link":"/radio/program/commonwealth-club","subscribe":{"apple":"https://itunes.apple.com/us/podcast/commonwealth-club-of-california-podcast/id976334034?mt=2","google":"https://podcasts.google.com/feed/aHR0cDovL3d3dy5jb21tb253ZWFsdGhjbHViLm9yZy9hdWRpby9wb2RjYXN0L3dlZWtseS54bWw","tuneIn":"https://tunein.com/radio/Commonwealth-Club-of-California-p1060/"}},"considerthis":{"id":"considerthis","title":"Consider This","tagline":"Make sense of the day","info":"Make sense of the day. Every weekday afternoon, Consider This helps you consider the major stories of the day in less than 15 minutes, featuring the reporting and storytelling resources of NPR. Plus, KQED’s Bianca Taylor brings you the local KQED news you need to know.","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/Consider-This-Podcast-Tile-703x703-1.jpg","imageAlt":"Consider This from NPR and KQED","officialWebsiteLink":"/podcasts/considerthis","meta":{"site":"news","source":"kqed","order":"7"},"link":"/podcasts/considerthis","subscribe":{"apple":"https://podcasts.apple.com/podcast/id1503226625?mt=2&at=11l79Y&ct=nprdirectory","npr":"https://rpb3r.app.goo.gl/coronavirusdaily","google":"https://podcasts.google.com/feed/aHR0cHM6Ly9mZWVkcy5ucHIub3JnLzUxMDM1NS9wb2RjYXN0LnhtbA","spotify":"https://open.spotify.com/show/3Z6JdCS2d0eFEpXHKI6WqH"}},"forum":{"id":"forum","title":"Forum","tagline":"The conversation starts here","info":"KQED’s live call-in program discussing local, state, national and international issues, as well as in-depth interviews.","airtime":"MON-FRI 9am-11am, 10pm-11pm","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2024/04/Forum-Podcast-Tile-703x703-1.jpg","imageAlt":"KQED Forum with Mina Kim and Alexis Madrigal","officialWebsiteLink":"/forum","meta":{"site":"news","source":"kqed","order":"8"},"link":"/forum","subscribe":{"apple":"https://podcasts.apple.com/us/podcast/kqeds-forum/id73329719","google":"https://podcasts.google.com/feed/aHR0cHM6Ly9mZWVkcy5tZWdhcGhvbmUuZm0vS1FJTkM5NTU3MzgxNjMz","npr":"https://www.npr.org/podcasts/432307980/forum","stitcher":"https://www.stitcher.com/podcast/kqedfm-kqeds-forum-podcast","rss":"https://feeds.megaphone.fm/KQINC9557381633"}},"freakonomics-radio":{"id":"freakonomics-radio","title":"Freakonomics Radio","info":"Freakonomics Radio is a one-hour award-winning podcast and public-radio project hosted by Stephen Dubner, with co-author Steve Levitt as a regular guest. 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