Download Analysis of Arithmetic for Mathematics Teaching by Gaea Leinhardt, Ralph Putnam, Rosemary A. Hattrup PDF

By Gaea Leinhardt, Ralph Putnam, Rosemary A. Hattrup

This quantity emerges from a partnership among the yankee Federation of academics and the educational learn and improvement middle on the college of Pittsburgh. The partnership introduced jointly researchers and specialist lecturers for extensive discussion classes concentrating on what each one group is familiar with approximately powerful mathematical studying and guideline. The chapters take care of the learn on, and conceptual research of, particular mathematics issues (addition, subtraction, multiplication, department, decimals, and fractions) or with overarching topics that pervade the early curriculum and represent the hyperlinks with the extra complex themes of arithmetic (intuition, quantity experience, and estimation). Serving as a hyperlink among the groups of cognitive researchers and arithmetic educators, the booklet capitalizes at the contemporary examine successes of cognitive technological know-how and studies the literature of the mathematics schooling group as well.

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For her, school arithmetic seemed to be an isolated, self-contained context in which the possibility of doing anything other than attempting to recall prescribed methods did not arise” (p. 98). Resnick and Omanson (1987) had similar results with four children they observed over the period the children were learning to carry in addition. They found that a strong se­ mantic understanding of addition, including the ability to find sums men­ tally, did not carry over to the written addition requiring the carry pro­ cedure.

Adjustments were made both dur­ ing and after calculation to bring an estimate closer to the exact answer. It was pcirticularly interesting to note that these students often ignored the rules they had been taught for rounding, but rounded instead to numbers more suitable for solving the problem presented. Less-skilled students feel bound to round in the manner in which they were taught (Sowder & Wheel­ er, 1989). Sometimes teachers, too, resist rounding that does not follow the rules. B. Reys (in Sowder & Schappelle, 1989) recalled an incident where one teacher was quite dismayed when another teacher rounded 26 to 25 in order to estimate the product of 26 cind 37.

Make up some equations using three of these numbers: 24, 2, 8, 8, 2, 4, 6, 2, 3. And from Grade 3: Give the numbers that must be added to 700,500 to give 900,500. Choose two pairs of numbers whose sum is 1,000: 250, 360, 220, 830, 750, 780, 170, 640. ) Find pairs of numbers whose product is 60; whose quotient is 10. What is 395448 x 9 - 395448 x 8? Summary and Comments. The ability to decompose and recompose numbers is at the heart of flexible mental computation (Greeno, 1989; Resnick, 1989a; Trafton, 1989).

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