Annah and Camilla get unstuck… and 5 million points.
ANNAH and Camilla have got themselves unstuck. And they’ve written a couple sentences each on where and why they got stuck… and how they got themselves unstuck.
They’d had trouble tackling an expression with a negative exponent, and writing it as a positive exponent. Their strategy was to look up their notes, find a similar problem and see they could take the reciprocal and change the sign of the exponent.
I can only hope they found in their notes the demonstration and informal proof using the number 2 and meant to show why expressions with negative exponents are, effectively, fractions… rather than just use the bulleted-rule “flip it and change the sign of the exponent”.
The demo takes, say, 23 and divide it by 25. By writing out the three factors and dividing them by the five factors it is clear from cancelling that the answer is 1/22. It is also clear from such demonstrations that the answer can be derived from subtracting the exponent 5 from the exponent 3… 2−2.
Annah and Camilla’s brief note didn’t go in to even this limited level of detail. But at least they wrote some sentences of reflection and, indeed, had reflected on the problem. It’s a welcome start.
Student self-assessment is meant to help students focus on their own work and their own learning… to take responsibility for getting themselves unstuck. At the moment students seem reluctant to reflect, let alone to leisurely reflect and to intellectually wander and to ask what if? Getting the answer, and as quickly as possible, mostly seems preferable.
I’ve tried to break this by simply abandoning traditional assessment approaches that inevitably value the answer, rather than putting the main focus on the mathematical thinking provoked by the problem.
The closest my classes have got to an heuristic approach to questioning and thinking is when we’ve gone completely off-curriculum and thrown up a couple of problems and let the conversation and argument go where it will.
Congratulations to Annah and Camilla for stopping, looking back, thinking and working out how to solve the problem. Five million points!