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 yank Federation of lecturers and the educational examine and improvement heart on the collage of Pittsburgh. The partnership introduced jointly researchers and professional lecturers for extensive discussion periods concentrating on what every one group is familiar with approximately powerful mathematical studying and guideline. The chapters care for the study on, and conceptual research of, particular mathematics themes (addition, subtraction, multiplication, department, decimals, and fractions) or with overarching issues that pervade the early curriculum and represent the hyperlinks with the extra complex themes of arithmetic (intuition, quantity feel, and estimation). Serving as a hyperlink among the groups of cognitive researchers and arithmetic educators, the ebook capitalizes at the contemporary examine successes of cognitive technology and reports the literature of the mathematics schooling group as well.

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This program is referred to here as the Soviet Math Program (SMP). Overview The foundations for the development of whole number sense were dis­ cussed in the first section. The breakdown here reflects the earlier discus^The Soviet texts have been translated by the Resource Development Component of the University of Chicago School Mathematics Project and are available at the University of 1. MAKING SENSE OF NUMBERS 25 sion. The manner in which texts develop number understanding for small numbers and place-value understanding is first discussed.

She considered both to be correct, 15 for the worksheet prob­ lem, 25 when the problem represented 16 cookies plus 9 more. “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.

Fractions also are introduced in CAP2 in Grade 1, but students are expected only to find halves of discrete sets and to estimate halves of some measures (length and volume). The fraction symbol is not introduced until Grade 2, and only after experience with the words and pictures represent­ ing one half and one fourth. There is a series of eight lessons on fractions in Grade 3. ” After lessons on finding fractional parts of sets, students are introduced to equiv­ alent fractions through pictures showing different subdivisions of the same 1.

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