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

By Gaea Leinhardt, Ralph Putnam, Rosemary A. Hattrup

ISBN-10: 0805809295

ISBN-13: 9780805809299

This quantity emerges from a partnership among the yankee Federation of academics and the training learn and improvement middle on the college of Pittsburgh. The partnership introduced jointly researchers and specialist academics for in depth discussion periods concentrating on what every one group is aware approximately potent mathematical studying and guide. The chapters care for the examine on, and conceptual research of, particular mathematics themes (addition, subtraction, multiplication, department, decimals, and fractions) or with overarching subject matters that pervade the early curriculum and represent the hyperlinks with the extra complex issues of arithmetic (intuition, quantity feel, and estimation). Serving as a hyperlink among the groups of cognitive researchers and arithmetic educators, the publication capitalizes at the fresh study successes of cognitive technology and reports the literature of the maths schooling group as well.

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SMP Grade 1 teachers are provided with a long treatise on the prepara­ tion for learning numbers. Many examples of counting exercises are pro­ vided, and teachers are told that students should be made aware, through their own practical experiences, that counting does not depend on the order in which objects are counted as long as no object is either omitted or counted twice. Emphasis is given to the relations less than, greater than, as many as, and same as. Teachers are told that determining which grouping has fewer, and how many fewer is more difficult than determining which grouping has more and how many more.

It would therefore seem pedagogically sound to allow (and guide) this discovery rather than to give rules. Text-given rules are less likely to be as adaptable to the types of exercises found in the SMP cis are rules that originate from children. Of the two U 5. programs, CAP2 excels in the variety of ways in which children are introduced to number comparison. The types of problems presented in CAP2 and SMP provide good founda­ tions for strengthening number sense. Foundations for Rational Number Sense Rational number sense appears to be somewhat different than whole num­ ber sense.

The changes were quite radical, in that instruction became en­ tirely student-based rather than text- or program-based. Children did not learn algorithmic procedures, but developed a deep understanding of num­ bers in their first year of school. The following protocol of a first grader solving 246 -K 178 typifies the procedures that children invented, based on their knowledge of numbers: 22 SOWDER Well, 2 plus 1 is 3, so 1 know it’s 200 and 100, so now it’s somewhere in the three hundreds. And then you have to add the tens on.

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

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