Thursday, February 17, 2011

What does it mean to do mathematics?

My MTH 329 class just finished the first unit of Teaching and Learning Middle Grades Mathematics. The focus of this unit is on the NCTM Process Standards. Yesterday we spent a considerable amount of our class period reflecting on what we’ve been doing so far.

We start the workshop with a schema activation/connection that asks the learners to review a simile survey taken the first day of class. One part of the survey says, “Choose the simile that best describes doing math and explain your choice.” The similes to choose from are: climbing a mountain, conducting an experiment, cooking a meal, reading a book, working a puzzle, or playing a game. In reviewing their original choices, I want my learners to consider how their view of doing math has changed and why.

The focus/concentration for the workshop is to create an anchor chart representing what they think it means to do mathematics. This chart might hang in their future classroom as a constant reminder to their learners what it means to be a mathematician. (My colleague shares his experience with anchor charts here.)

During the activity/construction phase of the workshop, groups of four work together to develop a rough draft anchor chart. The first group builds on the simile idea and develops a chart showing doing math as working a puzzle. Each piece of the puzzle represents a different aspect of their vision of doing math.

Group two decides that they want to make a chart that would appeal to middle grade learners. They use graffiti as the theme and begin searching Urban Dictionary for terms they could use for the Process Standards. At one point they discuss whether or not the chart is appropriate (culturally sensitive) and decide that it is because it is intended to engage and not to mock.

The final group considers the anchor chart from a graph theory perspective. They had just been discussing a discrete mathematics assignment and it seems to find its way into the representation. That’s the Green Arrow up in the Algebra block. The color of each arrow has some significance, I think. (These are works in progress.)

These are rough drafts that I post on our classroom Blackboard site. The future teachers will make adjustments to whichever one they choose and make it their own for inclusion in the course portfolio. This is the reflection/consolidation portion of the workshop.

So what do I think it means to do mathematics? It involves collaborating with others in an effort to solve problems, making and revising representations for/of our thinking, trying to connect various ideas, and communicating the reasoning behind our thought process to others. In other words, yesterday doing mathematics involved making anchor charts.


  1. Lately I have been spending a lot of time thinking about "doing" math or any subject for that matter. We as teachers often think about what we have to do or what our students have to do but is "doing" enough? Is it enough to have students who can simply "do" math? I think we need to think bigger, see the bigger picture and explore why we teach math in our schools. Is the goal to have students who can do math OR is it to have students we can BE mathematical? This little switch of a word can help teachers see the whole picture, reach for the future and make math more exciting, and relevant for our students. After all one can "do" without thinking but one can not "be" without thinking. Helping our students be is an investment in their future and ours.

  2. Very interesting. The units of study in Teaching and Learning Middle Grades Mathematics are typically "Doing Math," "Learning Math," and "Teaching Math." I wonder what would happen if we changed it to "Being a Mathematician," "Being a Mathematical Learner," and "Being a Mathematics Teacher." Something to think about. Thanks!

  3. With the units you describe the optimal situation would be to have complete alignment between doing-learning-teaching. Probably in this order teaching-doing-learning. We make assumptions that students will learn from what we teach and what they do but quite often that is not the case. We then as teachers deconstruct the learning, isolate the components and settle for teaching and doing. We lose sight of our goal which is to help students be mathematical and learn about mathematics. Thanks for allowing me to explore this line of thought. There is always more to learn but that is what being a teacher is really all about...being a learner.