Conceptual Mathematics

Grant Wiggins has a very interesting post on "conceptual mathematics".

The list of 9 misconceptions in arithmetic and the challenge test with 13 questions for conceptual understanding both make for very interesting reading.

The first misconception he cites:

1. A number with three digits is always bigger than one with two
. Some children will swear blind that 3.24 is bigger than 4.6 because it’s got more digits. Why? Because for the first few years of learning, they only came across whole numbers, where the ‘digits’ rule does work.

And the first question in the challenge test:

1) “You can’t divide by zero.” Explain why not, (even though, of course, you can multiply by zero.)

Very nice read.