Shading Squares

I recently finished up a unit on sequences and series with my grade 11 pre-calculus students. The unit is somewhat of an enigma because it contains relatively simple ideas bogged down in complex notation. This coupled with the overlapping definitions makes for a fortnight of rather rigorous cognitive exercise. The unit was supported through group tasks as the topics moved along. Arithmetic sequences and series were linked to linear functions through the toothpick problem. Students were asked to arrange toothpicks into boxes and record how many toothpicks it took to make ‘x’ number of boxes. Their results were extrapolated and tied …

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All Factors Considered

I have only been teaching for 2 years, but am already beginning to encounter the recursive nature of the profession. I have had several repeat classes in my 4 semesters of teaching, and they require the achievement of the same outcomes. This does not bother me, in general, because I am excited to see the improvement in my teaching. There is one unit, however, that has already frustrated me. Its ability to sabotage creative exploits is unrivaled throughout the mathematics curriculum; I am speaking of the unit on polynomial factoring. The topic was taught in isolation of numerical factors until this …

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In The Footsteps of Gauss

I like to introduce each topic with a task or activity. These do not necessarily have to be long, but should activate mathematical thinking. The idea has slowly evolved for me throughout my short career. They are the amalgamation of the ideas of a “motivational set” and discovery learning. I felt that both components are positive things to include in a math class, but both had severe implementation problems.The motivational set is far too passive. In my college, a picture, story, or conversation could serve as a motivational set. It was essentially a transition tool that was completely void of …

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Struggling with Infinity

My fascination with infinity began early on in life. I went to a small private school in Prince Edward Island for my entire elementary school career, and it was outside on the playground where I first tasted the enigma of infinity and the power it held. Across the cul-de-sac parking lot stood the swings, slide, and monkey bars; I still remember the first time I encountered infinity under those bars. You see, we had been learning the base-10 number system that day, and my friend Jason and I somehow got into a counting contest of sorts. We began at very small …

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