Problem solving is central to learning mathematics. It is considered an essential process through which students are able to achieve the expectations in mathematics, and is an integral part of the mathematics curriculum in Ontario (Ontario Math Curriculum, 2005, page 12)
Sometimes, the best problems are those that occur spontaneously.
Yesterday, I gave students a bit of a “check-in” formative assessment of our measurement unit. We’ve moved into measuring length in standard units, and so I asked them to draw a few items of various lengths (for example, a 5 cm-long pencil, a feather that was 16 cm long). They were to first draw an estimate, then actually measure and draw.
In my efforts to conserve paper, I distributed GOOS papers which I had cut in half. But in so doing, I inadvertently created a problem: Two of the items of my list of demands were longer than the length and width of the paper I had provided! (Ironically, I had just told them the story of my mother’s German saying “zweimal messen, einmal schneiden”.)
What began as Ms. Teschow’s mistake, however, soon turned into an authentic problem solving assessment opportunity as I watched while various students
- Gave up, and simply did not include the “too long” items on their page
- Made an attempt by turning the page diagonally to try and fit in the longer items
- Drew a 23 cm candy bar in two pieces that added up to 23 cm
- Drew the 38 cm caterpillar going around the perimeter of the page or in accordion fashion to fit more into a smaller space (I did give them one clue by reminding them that caterpillars are "bendy"!)