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

*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.

#### Latest posts by Denise Treacy (see all)

- Announcing an Online Community! - August 15, 2018
- What Does It Mean to be a Math Person? - March 26, 2018
- Using Tools in Art and Math - October 30, 2017

I love the parallels you’ve drawn here between art and math toolboxes. In my work with adult math learners I notice that most have internalized math as a set of prescribed procedures. Some enjoy the predictability while others feel lost in the procedures, but in neither case do they (yet!) notice how math can involve flexibility and creativity.

I have just started reading “But Why Does It Work? (Heinemann) and this morning came across this quote: “For students to be drawn to engage in mathematics, it is essential that they encounter the subject as a creative field in which they can play an integral role. They should have image of mathematicians as curious and imaginative people who love doing mathematics but who still make mistakes and get stuck on hard problems.” It made me think of your comment, Beth!

Thank you, Beth! A goal of Investigations is children and adults who understand that math is both flexible and creative. This reminds me of Megan’s post, From “Uh Oh to Aha” (https://investigations.terc.edu/uh-oh-aha/), about her journey as an adult from liking “how tidy [math is], how you get an answer you can put a box around,” to seeing the beauty in creatively solving problems.