How Hands-On Projects Can Deepen Math Learning for Teens

Students measure pieces of Styrofoam to fit a boat they are building. (Courtesy of Allison Shelley/The Verbatim Agency for American Education: Images of Teachers and Students in Action)

On math worksheets, numbers are usually neat and tidy. In the real world, not so much. Whether it’s polling data, analysis of investment options or calculations for timed traffic lights, real-world math can be messy. “If you give those kinds of numbers in homework you’re a mean teacher,” said teacher Victor Hernández. Fortunately, he doesn’t have to worry about that complaint much. Hernández works at Science Leadership Academy, a public magnet school in Philadelphia, where students gather and apply real data to hands-on projects throughout the curriculum. In January, Hernández and two colleagues shared some of the benefits of project-based learning with math teachers attending EduCon 2020, SLA’s annual school innovation conference.

In addition to incorporating real data, applied projects can bring meaning to the purpose of math. SLA teacher Jonathan Estey said that authenticity is often lacking for students. If you ask a struggling math student how many quarters make 75 cents, he noted, “they’ll know it, because they have to use money.” Similarly, by building a catapult or telling a story with equations, students can see how their calculation and formulas translate to contexts beyond a whiteboard. That authenticity yields stronger engagement, especially when projects allow teenagers to connect to their interests. “Even when students complain about the amount of work, it’s a lot more motivating for them to believe they have something to say at the end of a math project,” said Estey.

Along with authentic applications and higher engagement comes deeper understanding of math concepts. Take interquartile range, for example. In a typical textbook problem, the data set is small enough to simply count to find quartiles. In a polling project this year, Estey’s classes collected data from more than 100 SLA students. Thus, when determining interquartile range, students needed to use computation to identify quartiles. That required a more clear understanding of the concept, and it also resulted in greater accuracy, Estey said.

Another benefit, according to Hernández, is that students gain knowledge that would not be part of a traditional unit. He discussed a project in which students, working in pairs, created personal financial plans for one another’s post-secondary plans. Their predictions required an understanding of exponential functions, but they also learned, for example, the difference between subsidized and unsubsidized loans. As Hernández and Estey shared these and other examples from their classrooms, they offered tips on project-based learning for other math educators.

Tips for Project-Based Learning in Math

1. Know your students. A few years ago, Estey developed a project that required students to compare costs and carbon footprints of conventional and alternative energy sources. He said the project would have worked great when he taught in Hood River, Oregon, but he realized it was a bad fit in Philadelphia after spending more time teaching what a wood stove is than teaching math. By contrast, a project that examines inequality through ratios and proportions works well at SLA because students are passionate about social justice. “They get to tailor it to whichever cause they care about, and because they’re invested in having this message, they’re invested in getting the math right,” said Estey.

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2. Avoid group grades. Many adults and kids can recall working on a class project where some people pulled more of the weight than others. Although project-based learning often involves teamwork, the SLA math teachers said they do not assign group grades. 

They grade students on five domains for each project: design, knowledge, application, presentation and process. While the first three domains relate more to the actual math, the final two relate to how well the student explained the work, how they collaborated with teammates and whether they kept up with the project in and out of class. A student might have strong math skills but wait till the last minute to complete a project, for example. Another might follow all the right steps but commit calculation errors. The first student would receive higher marks in “knowledge,” while the second would earn higher marks in “process.”

3. Prepare students to work outside of class. Project-based learning does not mean that students are always doing hands-on activities in class. “If it’s a project that’s extended over two weeks, no way are we suspending instruction for two weeks,” said Estey. An SLA student at the EduCon session explained that in the “nitty gritty part of a project,” a teacher might start class by addressing questions that have been coming up, but mostly they’re working on projects after school or during free periods. Hernández said he uses nightly checkpoints to ensure projects are progressing, and Estey said that with freshmen he works hard to ensure that they seek additional support when needed because they’re accustomed to getting by on in-class work in middle school.

4. Keep it simple. Hernández and Estey said their biggest challenges with project-based learning have come from making projects too complex. For example, in previous years, Estey’s students chose different topics for the polling project, which meant 30 different surveys were flying around. This year, they all focused on one topic — building issues at the school — and proposed various questions to ask their peers. Estey culled the questions to avoid repetition and ensure they would yield usable data.“Every year I ask myself how I can make this simpler,” he said.

5. Don’t be afraid of what’s unfamiliar. EduCon participants said that some teachers are afraid to try project-based learning because it’s not the way they were taught. Hernández said that need not be a barrier. His job interview at SLA required him to plan a hands-on student project, so he gave it a go. “I would be bored if I taught the way I was taught,” he said.