So here’s a question. What is math? No really, what is it that we want our children to learn in school and be able to take with them into the world? This has been a big question in the world of education over recent years and something I am constantly reflecting on as a teacher.

It’s generally agreed that there’s more to math than being able to answer arithmetic questions on a piece of paper. These are memorized facts and procedures, which have caused widespread math anxiety, shut down, and a negative attitude toward anything labelled as ‘math.’ This is disheartening because the joy and beauty in mathematical thinking isn’t being experienced as widely as it can and deserves to be. Math has been largely misrepresented and in turn, students are closing doors of opportunity out of disinterest, fear, and anxiety.

I believe the issue lies in how the math curriculum is used. Often it is treated like a checklist of topics to cover. I’d argue that more important than checking off all the topics, is how you approach each topic. The seven mathematical processes should be the emphasis and how we define the complexity of a student’s mathematical thinking. How well can they:

* problem solve

* reason and prove

* reflect

* select tools and computational strategies

* connect

* represent

* communicate

After years of pondering, I've come to see mathematical thinking and skills as being able to take something (an input stimulus in our environment) and being empowered to and being able to find meaning in it.

I want my students to be able to ask themselves what sense can be made here? Can I model this problem with a picture? Using a mental or concrete tool?

I do not want them to get lost and revert to asking themselves what step is next? Add? Multiply? Carry the 1? Move the x over here? These are very abstract questions with no meaning behind them.

In order to encourage students to ask the first set of questions, math needs to be presented within a context. That is, there needs to be a familiar situation presented where the student naturally thinks about it. Mathematizing the situation happens gradually and organically from the student’s current thinking. Let me illustrate this with an example.

You want a student to learn about the concept of a half. Through the use of a story you model two snakes, Longy and Shorty with rectangle models displaying their length.

Shorty is half the length of Longy but you refrain from telling this to your students. Instead you ask what do you notice about the length of these snakes? Students as young as Grade 1 have shown to observe that “two of Shorty would make Longy” or similar statements describing a half, all without being taught this concept directly. A vague response such as “this one is longer than the other,” requires probing questions such as “how much longer? Is it an elephant length longer?” or just a pinky length longer?” how can you describe how much longer?

The key is to ask questions you know the student can respond to in a sensical way. This is a simple example, but this idea of guiding students within a context can help a high school student understand the applicability of linear or quadratic models. Students need to know why they are doing what they are doing in math, and sometimes this requires taking a step back, asking the simplest of questions and artfully crafting a path toward deeper thinking.