Thursday, March 01, 2007

Teaching fractions

There is more to knowing and teaching fractions than meets the eye. Paper by H. Wu.

1 Definition of a Fraction . . . . . . . . . . . . . . . . . . . . . . 4
2 Equal Division of a Segment by Ruler and Compass . . . . . . 20
3 Equivalent Fractions (Cancellation Law) . . . . . . . . . . . . 22
4 Fraction as Division . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Ordering Fractions (the Cross-Multiplication Algorithm) . . . 38
6 Addition and Subtraction of Fractions . . . . . . . . . . . . . 46
7 Multiplication of Fractions . . . . . . . . . . . . . . . . . . . . 62
7.1 Formula for the product, and first consequences . . . . . . . . 64
7.2 The first alternative approach . . . . . . . . . . . . . . . . . . 74
7.3 The second alternative approach . . . . . . . . . . . . . . . . . 78
8 Division of Fractions . . . . . . . . . . . . . . . . . . . . . . . 80
9 Complex Fractions . . . . . . . . . . . . . . . . . . . . . . . . 88
10 “Of” and Percent . . . . . . . . . . . . . . . . . . . . . . . . . 93
11 Ratio, Rates, and the Fundamental Assumption of School
Mathematics (FASM) . . . . . . . . . . . . . . . . . . . . . . . 99
12 Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 108
13 APPENDIX: Some Remarks on the Teaching of Fractions in
Elementary School . . . . . . . . . . . . . . . . . . . . . . . . 117

2 comments:

Myrtle Hocklemeier said...

Some years ago I printed out everything he had to say about math and read it. This guy is great and don't forget he's only one of two mathematicians on the National Math Panel.

Freudian Slip said...

Interesting stuff. Fractions are tough to explain aren't they?
Matt