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:

**How is it used in exams?**

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 amount of collective action in a learning system is inversely related to the possible degree of curricular specificity.*

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.

Continue reading On Collective Consciousness and Individual Epiphanies

There seems to be three sacred cows in mathematics education:

- the worksheet / exercise set
- the
*review day* - the exam

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.

Continue reading The Review Day: Unit Analysis and Scale Factor

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.

*“Whiteboards give me more than eight-and-a-half by eleven ideas”*

Sometime after pyjama time and before bedtime, a math conversation broke out. My wife and I were visiting some good friends, when the topic of a recently purchased board game came up. It was bought at a teaching specialty store and designed to teach addition and subtraction of twos. After examination, I didn’t like the overly symbolic structure, and asked their 5-year old if she wanted to play a math game. She ran and got a piece of paper. When she finally got called up to bed (much later than expected) I took the page and folded it into my back pocket.

Here it is:

Continue reading What High School is (Often) Missing: A Conversation with a Kindergartener

Twenty-fifteen will be the fifth year that my little corner of the blogosphere has been dedicated to digitally curating my own thoughts and experiences regarding the teaching and learning of mathematics. It represents a wide array of posts regarding a wide array of topics. Much has changed from new teacher status to graduate student, and the posts reflect that. Still, the heart of its posts and pages is pragmatic: I write about classroom events that seem to matter (for some reason or another, they catch my attention) in hopes that other teachers might find the same phenomenon.

I am going to call these episodes: *bloggable moments*.

Continue reading Bloggable Distributions: Reading #MTBoS Blogs in 2015

My Grade 9 students don’t see an equation for the first two weeks of their unit of solving linear equations. That is because I think students get all bogged down in the notation, and lose their problem solving intuition.

Instead, I play around with a key metaphor for solving linear equations–the *balance scale*.

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