The Development of multiplicative reasoning in the learning of mathematics
- 其他作者: Harel, Guershon, , Confrey, Jere.
- 出版: Albany : State University of New York Press ©1994.
- 稽核項: 1 online resource (xxviii, 407 pages) :illustrations.
- 叢書名: SUNY series, reform in mathematics education
- 標題: Multiplication. , Teaching Methods & MaterialsMathematics. , Elementary Mathematics & Arithmetic. , Physical Sciences & Mathematics. , Study and teaching (Elementary) , Mathematics. , EDUCATION Teaching Methods & Materials -- Mathematics. , Electronic books. , Mathematics , EDUCATION , Division. , Mathematics Study and teaching (Elementary)
- ISBN: 0791417646 , 9780791417645
- ISBN: 0791417638 , 0791417646
- 試查全文@TNUA:
- 附註: Includes bibliographical references and indexes. Theoretical approaches -- Children's multiplying schemes / Leslie Steffe -- Multiplicative conceptual field : what and why? / Gerard Vergnaud -- Extending the meaning of multiplication and division / Brian Greer -- The role of the unit -- Ratio and proportion : cognitive foundations in unitizing and norming / Susan Lamon -- Units of quantity : a conceptual basis common to additive and multiplicative structures / Merlyn Behr [and others] -- Ratio and rate -- The development of the concept of speed and its relationship to concepts of rate / Patrick Thompson -- Missing-value proportional reasoning problems, factors affecting informal reasoning patterns / James Kaput and Mary Maxwell West -- Multiplicative worlds -- Splitting, similarity, and rate of change : a new approach to multiplication and exponential functions / Jere Confrey -- Multiplicative structures and the development of logarithms : what was lost by the invention of function? / Erick Smith and Jere Confrey -- Intuitive models -- The impact of the number type on the solution of multiplication and division problems : further investigations / Guershon Harel [and others] -- Summary -- Multiple views of multiplicative structures / Thomas Kieren.
- 摘要: Annotation
- 電子資源: https://dbs.tnua.edu.tw/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=6004
- 系統號: 005282569
- 資料類型: 電子書
- 讀者標籤: 需登入
- 引用網址: 複製連結
Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.
來源: Google Book
來源: Google Book
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