An open problem in high school geometry.

Like most teachers (I assume) when I start to plan instruction on a topic I begin by turning to the usual suspects: my district adopted textbook, Google, my past attempts to teach it, and the other teachers in my level. Let’s take a closer look at a few of these.

District Adopted Text

There are a number of problems with heavy reliance on a textbook. Ours falls a bit short in a lot of ways. For example, one state standards reads as follows: Translate between the geometric description and the equation for a conic section. Our textbook covers only the parabola, and even then it doesn’t even make a passing reference to conics. Granted this is a “supporting standard” (whatever that means), but it misses the mark.


This is often by far the most useful and most disconcerting part of the planning process. More often than not when looking for activities, the results all come from 6th through 8th grade teachers. Of course, the tasks are perfectly usable in high school classroom, but it begs the question: Why are the same standards being taught then and retaught now? Worse, why are teachers often encouraged to reduce the complexity of the content?

Of course, this ultimately is a minor complaint, and often the lower grades don’t actually cover all of this material, but it still gives me pause. That said I take exception to a lot of the way math is misused and abused from the early grades up.

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