Talking Math With Middle Schoolers

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.

“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 open-ended 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.” 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.

Danielson often brings math into daily life by making a game out of something mundane. When his family dines out or goes grocery shopping, they play their own version of “The Price Is Right,” guessing what the total cost will be. These days, that game may mean inviting kids to look at a grocery list and predict the total before adding items to a virtual shopping cart. Regardless, the same principles apply. “The most useful thing for parents to do is to pay attention to the times in their own lives when they bump up against numbers or patterns, and instead of leaping to telling … think about how to engage their kids in that,” he said.

That process is less predictable than printing out a worksheet and checking a box on a daily schedule. It involves watching for opportunities and seizing the moment. “There’s a lot of trust involved that injecting these conversations into our life over the long-span is going to be productive even if I can’t see it in the 15-minute chunks that school gets doled out in,” Danielson said. He thinks it’s worth it. “If the only reading that kids ever did was the reading that happens in school, we would feel that something was lost,” he said. “I feel the same way about math.”

Allison Green
Boston Tutoring Services