## 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 …

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## 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 …

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