Linked with only this minor comment: I've been saying this for years. There are people who say that students can learn algebra if you just give them a calculator in place of knowing the multiplication tables. They can't, Sal Khan is right.
Linked with only this minor comment: I've been saying this for years. There are people who say that students can learn algebra if you just give them a calculator in place of knowing the multiplication tables. They can't, Sal Khan is right.
3 comments:
I'm a retired English teacher with three grandchildren. In the summer they practically live here. As each hit 3rd grade, I used M and M candy to drill the tines tables into their brains, just as I did with their mother. Every right answer, they got one, but a wrong answer, they had to return two to the pile. We kept on until they didn't have to think about the answer, and we reviewed every week to keep them sharp. They are all three good at math. When I was teaching, I saw so many hs kids struggling with algebra because they didn't know the basics like the times table.
Rote work builds fluency - you know how to proceed through the steps required to solve the problem, whether it’s the multiplication tables, long division, FOIL, matrix multiplication, integration by parts, or raising and lowering tensor indices.
Once you have fluency, you develop understanding of the concepts. After you’ve differentiated the sine and cosine functions enough times and stared at the graphs of each, you understand why the derivative of sine is cosine; you can see the relationship in the shape of the curves.
Once you have understanding of the concepts, you can apply the concepts to new problems.
Teaching concepts first and expecting the students to intuit the algorithms and then develop fluency is one of the biggest math education malpractices ever unleashed on our kids.
Hear hear.
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