# Practical Ways to Develop Students’ Mathematical Reasoning

Traditional math class was all about solving problem sets as fast as possible, but increasingly math teachers are slowing down to allow kids the time and space to reason through their answers and explain their thinking to peers. For those who seekĀ a demonstration of that path, take a look at the Teaching Channel video below. Third grade teacher Jen Saul leads a lesson meant to support students’ mathematical problem solving abilities. She works hard to normalize struggle and has students find three different ways to represent the same problem.

“They can assure themselves and don’t have to wait for the teacher to come around and say, ‘yeah, you got it.'” Saul said of the approach. She makes sure students have time to work independently before they share their strategies with one another, a time when they practice using math language and explaining their thinking. Meanwhile, Saul is rotating around the room, supporting students and pushing their thinking along. One of the most important parts, she says, is when she invites students to come to the front and share their solutions. This student-led solution time reinforces the class culture and helps students see one another as experts.

Algebra is another important area of math and is often seen as the gateway subject to higher math. While students may see algebra as a time to memorize equations, strong teachers know this is an incredibly important time to make sure students’ math reasoning is solid. In the video below, math coach Audra McPhillips explains how she leads eighth graders through the process of developing a conjecture about functions. She asks them to look for patterns and has intentionally given them three examples that have something in common (the rate of change) and a point of difference (the y-intercept), meant to push student thinking a little further.

McPhillips does very little telling students how to think, instead she lets them develop a conjecture that they believe to be true beyond the examples in front of them and requires them to explain why. Note, she doesn’t expect all students to write a conjecture by the end of the lesson, but she does have them fill out exit slips to record what they learned and how far they got as a quick reflection before they head to their next class.

Practical Ways to Develop Students’ Mathematical Reasoning 14 January,2016

• Karelien Kriel

Very insightful article. Although in reality I found that we have to finish a certain amount of work in a certain period – so we don’t always have the luxury of time. I think we should strive to let kids think for themselves, suffer a bit and figure things out.

• John Tapper

I understand the rush – there are expectations to finish – but letting the kids work the ideas out IS MATH learning. If you rush this process, and tell them a formula before they understand what they’re doing, you’re creating a hole in understanding. I work with (and have written about) many struggling learners. The vast majority of them learned a formula or algorithm they don’t understand and can’t apply in problem solving. the THINKING is most important. The answer is simply an artifact of the thinking.

Excellent lesson!! Society often judges teachers on their smile and excitement. But what is most important is their lesson design and implementation. This is the art and science of teaching and this is an excellent teacher.

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## Author

### Katrina Schwartz

Katrina Schwartz is a journalist based in San Francisco. She’s worked at KPCC public radio in LA and has reported on air and online for KQED since 2010. She’s a staff writer for KQED’s education blog MindShift.