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Recently, I was chatting with a 7-year-old I know pretty well. I asked her about school, and she quickly started telling me about her current math work, complete with eye rolls and boredom. I decided to change the subject a little.

“I know you like to tell me about math because I love math, but what’s your favorite subject?” I asked.

She thought for a moment and then said, “Art.”

Art was never my favorite subject. I’m not even sure I’ve passed stick figure drawing yet. “Why?” I asked.

She thought about it, and once she had organized her thoughts, she came at me with this big thought – “Well, in art, there are techniques and tools for making an art project, but we can make it however we want.”

“Wow,” I thought.

She continued, “In other subjects, like in math, there’s a way we have to solve the problem.”

“Oh no,” I thought. It is great that she has a creative outlet in art, but her belief that math is a set of steps or rules worries me.

I’m sure she quickly forgot about our conversation. I, on the other hand, have been thinking a lot about it. I’m concerned she is being turned off of math like so many other young girls.

The following week, our team began a staff meeting with a number talk. We each mentally solved a few problems and then shared our strategies. This experience made me think about this notion that there’s one way to “do” math. Consider a few of the strategies shared for 126 x 12:

Each of these solutions requires knowledge of different mathematical tools and strategies. For example, knowing you can decompose a factor additively (12 = 10 + 2; 126 = 125 + 1) or multiplicatively (12 = 4 x 3) is helpful. Similarly, it’s useful to know that you can think about 126 groups of 12 or 12 groups of 126 to figure out what to do with the decomposed parts.

Much like a second grade art project, these strategies look very different, and yet are so much alike. I imagine that the thoughts that went through each of our minds as we chose a strategy are similar to those an artist has when deciding how to start a new project.

As I continue to reflect on the differences my young friend perceives in her math and art classes, I find myself thinking about Mathematical Practice 5: Use appropriate tools strategically. What are the features of classrooms and instruction that give students the opportunity to develop a mathematical tool kit and to use those tools in ways that are meaningful to them? And, how do we develop those sorts of math classrooms?

### Denise Treacy

Since joining TERC in 2014, Denise has worked on the development of Investigations 3. Previously a special education teacher, she has experience using Investigations to teach mathematics in inclusive and self-contained settings at grades K-2.

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Tag(s): art | classroom culture | making sense | MP5 | nature of math | using tools |