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? While this may be a tad short-sighted, it is a legitimate concern. Teachers simply don’t have the resources to constantly be monitoring a class of students to be sure that they are not accessing the internet or communicating with each other (which is fairly easily fixed in settings). The greatest part of iPad technology is …

Continue reading »## Connecting Quadratic Representations

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 …

Continue reading »## On Collective Consciousness and Individual Epiphanies

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. How can I justify curating a collective of learners, when school is so interested in individuals?Learners commerce on a central path of mathematical learning while acting on a problem, but each take away personal, enacted knowings from …

Continue reading »## The Review Day: Unit Analysis and Scale Factor

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 …

Continue reading »## Math Challenge Activity

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. Each …

Continue reading »## Large Whiteboard Project

Group whiteboarding has changed how I teach mathematics. It has also changed how students operate as a community of mathematicians. Since ordering my first set of large whiteboards, our department has ordered four times again, and given workshops to the division’s mathematics teachers. (For a tour through my whiteboarding history, start here: mini whiteboards) My running motto has become, “Whiteboards give me more than eight-and-a-half by eleven ideas” This, coupled with the assertion that you can’t expect limitless ideas with limited innovation space, caused me to think bigger. This is the result. Whiteboard paint from the HomeDepot coupled with ebay’d …

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

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 …

Continue reading »## Bloggable Distributions: Reading #MTBoS Blogs in 2015

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 …

Continue reading »## Visualizing Linear Systems

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. I’ve used the metaphor before, but only verbally alongside an algebraic representation. I would say things like, “What you do to one side, you must do to the other”, or “What would we have to do to keep the scales balanced?” The whole time, I only referenced the metaphor; …

Continue reading »## Polynomial Personal Ads

Every year, my students study the general characteristics of polynomial functions. We investigate the various shapes of various functions and slowly shift parameters to watch changes in the graphs. Eventually, we deduce the roles of the constant term, leading coefficient, and degree. It should be noted that Desmos makes this process much easier than years previous. Just set up the generic polynomial, add sliders, set specific ones to play (depending on what you want to investigate), and have students discuss in groups. See sample here. (Sliding “a” to “0” invites an excellent conversation; same with “b” etc.)After we work with …

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