No more students for this year. I’ve spent a full day cleaning up and re-arranging my space for my incoming intern (for whom I’m very excited for).
Amidst the broken calculators and stray linking cubes, I found a note that a student wrote me from my first year of teaching. It served as a brief reminder of why I attempt to curate a community of mathematical action with my students. It isn’t the easiest way to teach, but has a limitless ceiling.
Discussion is one of the organic ways through which human interaction occurs, but not all discussion is created equal in the math classroom. The tone of discussion relies on the mode of listening (Davis, 1996). Most classroom talk focuses on an evaluative mode of listening. Students are expected to share, compare, and contrast solutions to problems.
I do think that justification of their solutions gets at some important points regarding mathematical reasoning, but would like to move the discussion to center around that exact feature–the reasoning.
O Canada!
The debate about best practice in Canadian math education has exploded once again. This time attracting high profile combatants.
This post is not meant to resolve deep-seated values, but rather provide a perspective that gets lost in the partisan arguments. It wouldn’t take a long time to place me in a camp, but that would be assuming that there are two camps that want drastically different things.
A colleague is a religious McDonalds’ coffee drinker. One day she showed up with a medium coffee and a cream on the side. It was in two separate cups:
My department has a set of 10 iPads for mathematics instruction. I use them primarily for the powers of Desmos. When I introduce teachers to the program, they get excited about the possibilities, but are immediately worried about one thing:
I always introduce linear functions with the idea of a growing pattern. Students are asked to describe growth in patterns of coloured squares, predict the values of future stages, and design their own patterns that grow linearly. Fawn’s VisualPatterns is a perfect tool for this.
While stumbling around Visual Patterns with my Grade 9s, we happened upon a pattern that was quadratic. The students asked to give it a try, but we couldn’t quite find a rule that worked at every stage. While I knew this would happen, the students showed a large amount of staying power with the task. The pattern growth was an engaging hook. After a conversation about what made this pattern ugly (the non-constant growth), we looked at the growing square.
I would like to begin with a conjecture:
The mathematical action of a group of learners centred on a particular task gives rise to a unique way of being with the problem, but also reinvents the problem.
In short, what emerges from collectivity is not tidy.
There seems to be three sacred cows in mathematics education:
It is not surprising that these three feed off one another, and make up the bulk of assessment in the typical mathematics classroom (including my own).
Here’s my disclaimer:
While I have been known to slaughter a few of the sacred cows of the instructional process, I have lagged severely behind in my attention to assessment. I value the complexities of learning that occur when student ideas encounter perturbations, curiosities, and other conceptualizations. The type of assessment that comes out of these mathematical encounters is rich, connected, and constantly evolving.
I built this activity for a group of 120 students from grades 7-10 at a provincial math contest. The problems themselves are a mixture of created, adapted, and stolen. I chose them because they fit fairly nicely into a multiple choice format while still eliciting deep thinking.
The puzzle moves forward as follows:
There are 10 stations, and 10 problems. Each problem is responsible for giving a unique letter for the final word scramble. Some of the letters are repeated more than once in the final answer (i.e. have a frequency more than one), but no problem leads to the same letter.