Critical Friend Visit

Liz came to watch me teach my Einsteins where fractions fit on the numberline. I asked her to contribute, rather than just sit back and watch.

What a fascinating session. Students were all prepared to state their ideas, and were adamant about their answers. I asked them to draw a numberline from 1 - 10 in their books and show where 1/2 fitted. They pretty much pointed to 5. Interesting already. It took much coercion, the use of folding paper in half, discussion about what '1' meant, whether 1/2 was more or less than 1. Liz suggested that the paper could represent a chocolate bar. What would Paris prefer 1/2 or 1 whole chocolate bar? The penny finally dropped.

I think it would have been easy to tell them where 1/2 was on the numberline, but the deep understanding was gained.

I did the same lesson with my next group up - Archimedes. They grasped the concept much more quickly, but they still started thinking 1/2 was where 5 was.

Even when I did it with my nearly top Fibonacci group, there was still some teaching to do. You can't ever assume kids have that basic conceptual understanding. One girl, who is in the Explorers group was convinced that 1/2 was less than one. Not that it took long to change her mind, but it illustrated that all kids have misconceptions.