I've been teaching the same concept with each of my groups - always starting with my Einsteins and moving up the groups. This has illustrated to me the misconceptions in all topics I'm teaching, as well as making me think the concepts through more carefully. Not that I'm spending longer in the planning stage - actually less time, probably.
I've also found that the ARBs have really good conceptual explanations as well as analytical tests, which I will look into further.
Sunday, September 6, 2009
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.
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.
Conceptualising Maths
I've decided to redirect my Maths Inquiry. More and more I've been thinking about how kids will learn and retain their skills and understandings only if the basic concepts are grasped firmly. These are the basis for all further learning - and not just in Maths. I've been finding my bottom (Einstein) group to be excellent teachers. I'm working very deliberately, and with plenty of materials, and little book recording to give them basic fractions understanding. It's really enjoyable to watch the lights slowly switch on. They've taught me that I need to proceed slowly, but with plenty of activity and sound questioning.
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