About Teaching Mathematics, Marilyn Burns

Marilyn Burns is vague about specific math learning objectives. But she’s clear that children shouldn’t learn standard arithmetic. Here are **quotes **from Teaching Arithmetic, Part III of in About Teaching Mathematics: A K–8 Resource.

- “Facility with standard paper-and-pencil arithmetic is no longer the measure of arithmetic understanding and competence.” Page 139
- “Because of the present availability of calculators, having children spend more than six years of their schooling mastering paper-and-pencil arithmetic is as absurd as teaching them to ride and care for a horse in case the family car breaks down.” Page 142
- “There is no way for all students to do arithmetic calculations in the same way any more than it is essential for all children to develop identical handwriting or writing styles.” Page 153
- “the emphasis of arithmetic instruction should be on having students invent their own ways to compute, rather than learning and practicing procedures introduced by teacher or textbook.” Page 154
- “The change from teaching time-honored algorithms to having children invent their own methods requires a major shift for most teachers. It requires, foremost, that teachers value and trust children’s ability and inventiveness in making sense of numerical situations, rather than on their diligence in following procedures.” Page 156
- “In all activities, the emphases are on having children invent their own methods for adding and subtracting . . . the standard algorithms are not taught.” Page 183
- “Also, rather than teaching the standard computational algorithm for multiplying, the activities give students the challenge of creating their own procedures for computing.” Page 194
- “A great deal of emphasis traditionally has been put on paper-and-pencil algorithms for addition, subtraction, multiplication, and division of
**fractions**. Too much focus is often on ‘how to do the problem’ rather than on ‘what makes sense’. The following suggestions offer ways to have students calculate mentally with**fractions**. The emphasis shifts from pencil-and-paper computation with the goal of arriving at exact answers to mental calculations with the goal of arriving at estimates and being able to explain why they’re reasonable.” Page 232 [Bold emphasis added].- Comment: Mastery of exact computations with fractions is the number one predictor of later success in algebra.

- On page 241 we have a statement that is almost identical to quote #8, the quote just given for fractions. The difference? Two occurrences of “
**decimals**” replace the two occurrences of “fractions.”

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