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Think Critically and Creatively in Math
by Debby McLean, Lower School Director

I didn’t always associate creativity or critical thinking with math. Students either arrived at a right or wrong answer and moved on to the next problem. As a student myself, more often than not, it was the wrong answer. I stopped being interested in math early in my educational journey and didn’t return to it until graduate school when I began exploring how to teach it in a way that would help my students understand the subject more than I ever did. I now see math for its incredible beauty and eloquence. And I am not being facetious. 

As part of our deeper dive into mathematics this year, I am enrolled in the Stanford online class, “How to Learn Math for Teachers” taught by Jo Boaler who is the Nomellini and Olivier Professor of Education at Stanford University. She is also the author of 18 books, including her latest: "Limitless Mind: Learn, Lead and Live without Barriers." To say that she is inspiring is an understatement. She speaks frequently about the need for risk taking in mathematics as well as how very important it is for students to grapple with problems. In the last session, she stated clearly that if students can rush through problems, they aren’t learning. The real learning takes place with sharing one’s thinking and trying different approaches. 

This thinking is counter intuitive to the way many of us learned math. Before the holiday break, Kelly Heard ran a professional development workshop with our teachers on making that shift in understanding the goal in math. We played a game called, “How close to 100,” where we worked as partners with dice to build arrays within a blank hundreds chart. The goal of the game was to fill, or come as close as possible, to 100 spaces without surpassing that number. As a group, we discovered there are multiple ways to complete this task effectively. Winning wasn’t the important part—it was sharing our strategies and methods. 

The 3rd Grade Teachers then played this same game with their students as a way to build number sense around arrays, equal groupings, addition, and subtraction. Amazingly, a group of students independently discovered square arrays and square roots and were able to build their own understanding of the concept through this game. According to the standards published by the National Council of Teachers of Mathematics, exploration of these topics should begin in 5th Grade when the students are introduced to exponents and powers of 10. Square roots and square numbers are further explored through middle school yet our 3rd graders were able to construct their own understanding about the topic. This construction of knowledge makes it “stickier” for students and will lay a strong foundation as they move through the grades. 

In the teachers’ professional development with Kelly Heard, we also watched a TedTalk from Dan Finkel, Founder and Director of Operations of Math for Love. He stressed five important components in teaching math for parents and teachers:

  • Start with a problem

  • Students need time to struggle

  • You are not the answer key

  • Say yes to your students ideas

  • Play

I look forward to our journey to ensure that all of our students think critically and creatively in all of their endeavors, especially math.

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