Warning: multiple non-sequiturs in this post.

Stumbled across this while wandering through the blogosphere tonight.

First I was stumped.

Then I figured out how to do it with logarithms, but I was pointed to the question by Sue VanHattum, who challenged me to solve it without logarithms, so I kept working.

Then I figured out how to do it without logarithms. I 1) re-learned a really, really awesome property of exponents, and 2) found an awesome new way to think about variables and exponents. I’d challenge you to try to solve it, if you can get through it, it’s enormously gratifying.

Anyway, this made me think about how I want my students to learn from questions like this. One issue, which Grant Wiggins writes articulately about — could a student not show mastery on this question, but have strong skills on the standard I am assessing? Yes. So I don’t want to assess students with it, or send the message that falling short reflects a deficiency in their knowledge.

Second, grit. Kitchentablemath on grit, getting at my basic issue–giving kids hard questions that they then solve can teach them their own efficacy as problem solvers. Giving kids hard questions, refusing to help them, and watching them either fail or get the answer from a classmate teaches them that they don’t have grit. Any time I give students a question like this, looking for a stroke of insight, i worry that I perpetuate a haves/have-nots environment in my classroom where some students are bright and capable, others aren’t, and that won’t change. Hmm.

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Dave MarainThanks for the kind words about my exponent problem. By the way this was based on an actual SAT question. And I totally agree how gratifying it is when we find a way to solve a challenging problem. The issue of students feeling inadequate when someone else succeeds is one we continually face throughout life, but I don’t think we should stop challenging our students. I tried to establish a classroom culture of acceptance and focusing on the problem as our adversary, rather than competing against each other.

Dave

dkane47Post authorThat culture of acceptance is definitely a key. The other question I’ve been thinking about recently is scaffolding, and more specifically which parts of a challenging question to scaffold so that the student is doing valuable thinking while making the task accessible. Too often I tend to under-scaffold and make questions inaccessible, or give my students leading questions that cut out the key insights that the task was useful for in the first place. Struggles.