Is a dump truck a vehicle? What about a skateboard? An elevator? A hamster wheel? These are some of the questions math educator Christopher Danielson has asked — or been asked — while playing a reasoning game he calls “Is It or Not?” The game began with a debate between another math educator, Kassia Wedekind, and her six-year-old daughter, but Danielson has played it with children of all ages, including his own. “It was a dinner table conversation. Both kids really joined in on it and enjoyed thinking of interesting, additional cases,” he said. His daughter, who was 12 at the time, raised the hamster wheel question and continued developing the list well after the meal ended.
Definitions are central to mathematics, but children’s concept images — what they picture for a triangle, for example — does not always line up with the concept definition. “Is It or Not?” helps them strengthen their concept images. It’s also a fun way to bring mathematical thinking into everyday conversation, a practice Danielson champions on his blog, Talking Math With Your Kids, and through an ongoing Twitter discussion.
“Our inclination is to think of math as a thing that happens in school,” Danielson said. That leaves parents in the role of homework helper and can lead to anxiety when parents lack math confidence, especially as kids reach middle school and algebra enters the picture. Such stress may be particularly acute as parents try to keep their kids’ education on track during distance learning. But watching over your middle schooler’s shoulder as they complete worksheets is not the only or best way to help them. By asking open-ended questions, developing a shared math language and connecting math to young people’s interests, parents can support pre-teens’ mathematical development in a way that is more fun for everyone involved.
Ask Open-ended Questions
“I think for students and our own kids, we want to rescue them as they’re working on math. We just want to tell them how to do it,” said eighth grade math instructor and former Tennessee teacher of the year Cicely Woodard. She suggested a different starting point for parents: asking questions. That’s a central practice in her inquiry-driven classroom, and she shared a few to try:
- What do you notice about the problem?
- What are you wondering?
- What does this symbol mean?
- What do you see?
These questions can be applied to formal math problems but also during informal conversations, such as noticing patterns in nature. Listening to kids’ answers, said Woodard, can “reveal important information about what they understand and don’t understand.”
Develop a Shared Language
Talking about math takes practice. To give students a structure for engaging in math conversations, Woodard presents sentence stems, such as:
- “I agree/disagree with ____ because …”
- “My solution is like ____’s because …”
- “I don’t understand ____ part of your reasoning, because …”
In her classroom, Woodard’s students use these phrases to compare ideas in small groups, then present different solution paths to the class. At home, young people can use sentence starters like these in family conversations about topics such as screen time or budgets. It’s “amazing” to watch tweens articulate decisions about math when “given the tools and the opportunities to do it,” Woodard said.
Make the Stakes Real
Identity development looms large in middle schoolers’ lives. For this reason, Danielson said, math talk with tweens should focus on “helping them gain leverage or influence in the world.” For example, when Danielson’s son was 13, he hired him to help with the manufacturing process for the tesselating turtle sets he sells. The pair agreed to a per-pound rate, and when payment time arrived, Danielson asked his son to calculate the bill. Similarly, after his daughter and a friend provided leaf-raking services at a per-bag rate, Danielson asked how much he owed. The friend reacted with surprise. His daughter was accustomed to doing real-world math, but for her friend, “the idea that she would be responsible for producing a calculation was foreign,” Danielson said.