As summer wanes, I have started to gear up for school… mostly. I’ve been jumping into SBG (Standards Based Grading)- objective sheets, quizzes, lesson plans, but most of all: alternative assessments. The short definition is that, as much as possible, I like to go outside and have my kids show me math. Whether its finding distances between points and lines, understanding the symmetry of absolute value, or using swingsets to highlight the differences between polar and parametric equations, my students are going to be putting some substance to the math. Its not every day, or every assessment, and I wish it could be more, but we are going to get our hands dirty.

One a side note, SBG has given my assessments an ethos of grading. When a students asks ‘is this what you wanted’, the line I am going to try out is – “Are you showing me mastery of an objective?” Notice not *the *objective – I’m sure my precalculus kids will routinely deviate from the path I expect them to take – and *now that’s okay*. Sure you won’t get a grade for *this *objective today, but more opportunities for that are coming. We’ll see how well this works out.

While working on my lesson plans, I found something mildly offensive: A direct quote from a sidebar in my Precalculus textbook (implied character is all mine):

“Polar coordinates offer a different mathematical prespective on graphing. For instance, in Exercises 1-8 on page 783, you are asked to find multiple representations of polar coordinates.”

A fresh reminder of why I am making these changes in my teaching philosophy and pedagogy. Worst part is, I think I remember thinking this exact thought when teaching precal for the first time. My hopeful new approach:

Polar coordinates are neat. Plus I need them to think about some questions I had.

Its not perfect yet. I’m certainly no utilitarian when it comes to math, but I think I’m headed in the right direction.

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