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Visual Patterns + Error Analysis


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Most of the work my students do with Visual Patterns occurs in small groups, where collaboration not only is encouraged, but often required. Today I steered things in a slightly different direction. I wanted to see what students were capable of on their own. No peer discussion. No Desmos. I was particularly interested to see whether they could write an equation to describe the relationship they see …


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Embracing Mistakes with a New Weekly Routine


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Over the last 11 years in the classroom, I’ve had the same teaching schedule exactly zero times. Every time August rolls around, it’s a different ballgame. Some years the shifts are subtle. In other years they’re quite dramatic. Within each year, I’ve never taught more than two sections of the same course. In fact, one year I taught seven different courses. (Assuming, of course, that you’ll …


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Two Wrongs and a Right


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Thoughtful analysis of mistakes is a great way to develop and deepen mathematical understanding. Ever since I stumbled across Michael’s Pershan’s Math Mistakes website, I’ve been looking for ways to incorporate more error analysis into my classroom and department. One practice I’ve been using for years is Assessment Corrections, where students identify, correct, and reflect on recent assessment mistakes. (Here’s the form I use to …

Where’s the emphasis? Right where it belongs.


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One of the things I love about Desmos is that it allows students and teachers to keep the focus where it should be. Working on a linear approximation problem in Calculus? It’s easy to get caught up in algebraic and numerical details and lose sight of the big (somewhat amazing) picture: We can approximate a crazy curve with a simple line! (Provided …


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All Mistakes Are Created Equal?


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Preamble I’m a big fan of Michael Pershan’s project Math Mistakes. If you’ve never checked it out, it’s worth exploring. And while I’m meddling with your life, here’s a tip for your entire department: Start each meeting by spending five minutes exploring one of the mistakes posted on Michael’s site. On a rotating basis, have one member of the department share a “provocative” math mistake from the …

Mistakes, Radicals, Rational Exponents, and Partitioning?


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A strange thing happened a few days ago. One of my Algebra 1 students stopped by Thursday afternoon to receive extra help on a topic. (That in itself is not the strange part.) He pulled up a chair, we discussed what he had been struggling with, and from that I typed out a review handout for him to work on while …