LEADER 04295nam 2200577 a 450 001 9910973345703321 005 20251117115844.0 010 $a1-4384-0580-4 035 $a(CKB)1000000000002098 035 $a(EBL)3406959 035 $a(OCoLC)923397449 035 $a(MiAaPQ)EBC3406959 035 $a(BIP)76147657 035 $a(BIP)406339 035 $a(EXLCZ)991000000000002098 100 $a19930401d1994 ub 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 04$aThe Development of multiplicative reasoning in the learning of mathematics /$fedited by Guershon Harel and Jere Confrey 205 $a1st ed. 210 $aAlbany $cState University of New York Press$dc1994 215 $a1 online resource (197 p.) 225 1 $aSUNY series, reform in mathematics education 300 $aDescription based upon print version of record. 311 08$a0-7914-1764-6 320 $aIncludes bibliographical references and indexes. 327 $aCONTENTS; INTRODUCTION; I: THEORETICAL APPROACHES; 1. Children's Multiplying Schemes by Leslie P. Steffe; 2. Multiplicative Conceptual Field: What and Why? by Gerard Vergnaud; 3. Extending the Meaning of Multiplication and Division by Brian Greer; II: THE ROLE OF THE UNIT; 4. Ratio and Proportion: Cognitive Foundations in Unitizing and Norming by Susan J. Lamon; 5. Units of Quantity: A Conceptual Basis Common to Additive and Multiplicative Structures by Merlyn J. Behr, Guershon Harel, Thomas Post, and Richard Lesh; III: RATIO AND RATE 327 $a6. The Development of the Concept of Speed and Its Relationship to Concepts of Rate by Patrick W. Thompson7. Missing-Value Proportional Reasoning Problems: Factors Affecting Informal Reasoning Patterns by James J. Kaput and Mary Maxwell West; IV: MULTIPLICATIVE WORLDS; 8. Splitting, Similarity, and Rate of Change: A New Approach to Multiplication and Exponential Functions by Jere Confrey; 9. Multiplicative Structures and the Development of Logarithms: What Was Lost by the Invention of Function? by Erick Smith and Jere Confrey; V: INTUITIVE MODELS 327 $a10. The Impact of the Number Type on the Solution of Multiplication and Division Problems: Further Considerations by Guershon Harel, Merlyn Behr, Thomas Post, and Richard LeshVI: SUMMARY; 11. Multiple Views of Multiplicative Structure by Thomas E. Kieren; Index; NAME INDEX; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; R; S; T; V; W; SUBJECT INDEX; A; B; C; D; E; F; G; H; I; L; M; N; O; P; Q; R; S; T; U; V; W 330 $aTwo of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework. Guershon Harel is Associate Professor of Mathematics at Purdue University Jere Confrey is Associate Professor of Education at Cornell University. 410 0$aSUNY series, reform in mathematics education. 517 3 $aMultiplicative reasoning in the learning of mathematics 606 $aMathematics$xStudy and teaching (Elementary) 606 $aMultiplication 606 $aDivision 615 0$aMathematics$xStudy and teaching (Elementary) 615 0$aMultiplication. 615 0$aDivision. 676 $a372.7/2044 701 $aHarel$b Guershon$f1952-$01869056 701 $aConfrey$b Jere$01807128 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910973345703321 996 $aThe Development of multiplicative reasoning in the learning of mathematics$94477233 997 $aUNINA