LEADER 04607nam 2200661Ia 450 001 9910828117503321 005 20240722182830.0 010 $a979-82-16-97644-8 010 $a1-280-31546-6 010 $a9786610315468 010 $a0-313-01603-8 024 7 $a10.5040/9798216976448 035 $a(CKB)111087028192288 035 $a(EBL)3000390 035 $a(OCoLC)929144461 035 $a(SSID)ssj0000190468 035 $a(PQKBManifestationID)11189214 035 $a(PQKBTitleCode)TC0000190468 035 $a(PQKBWorkID)10179906 035 $a(PQKB)10694175 035 $a(Au-PeEL)EBL3000390 035 $a(CaPaEBR)ebr10002019 035 $a(MiAaPQ)EBC3000390 035 $a(OCoLC)805255198 035 $a(UkLoBP)BP9798216976448BC 035 $a(EXLCZ)99111087028192288 100 $a20240612e20012024 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aLearning and teaching number theory $eresearch in cognition and instruction /$fedited by Stephen R. Campbell and Rina Zazkis 205 $a1st ed. 210 1$aSanta Barbara :$cPraeger,$d2001. 210 2$aNew York :$cBloomsbury Publishing (US),$d2024. 215 $a1 online resource (244 pages) 225 1 $aMathematics, Learning, and Cognition: Monograph Series of the Journal of Mathematics 300 $aDescription based upon print version of record. 311 $a1-56750-652-6 320 $aIncludes bibliographical references and indexes. 327 $aToward Number Theory as a Conceptual Field by Stephen R. Campbell and Rina Zazkis Coming to Terms with Division: Preservice Teachers' Understanding by Stephen R. Campbell Conceptions of Divisibility: Success and Understanding by Anne Brown, Karen Thomas, and Georgia Tolias Language of Number Theory: Metaphor and Rigor by Rina Zazkis Understanding Elementary Number Theory at the Undergraduate Level: A Semiotic Approach by Pier Luigi Ferrari Integrating Content and Process in Classroom Mathematics by Anne R. Teppo Patterns of Thought and Prime Factorization by Anne Brown What Do Students Do with Conjecture? Preservice Teachers' Generalizations on a Number Theory Task by Laurie D. Edwards and Rina Zazkis Generic Proofs in Number Theory by Tim Rowland The Development of Mathematical Induction as a Proof Scheme: A Model for DNR-Based Instruction by Guershon Harel Reflections on Mathematics Education: Research Questions in Elementary Number Theory by Annie Selden and John Selden Indexes 330 $aNumber theory has been a perennial topic of inspiration and importance throughout the history of philosophy and mathematics. Despite this fact, surprisingly little attention has been given to research in learning and teaching number theory per se. This volume is an attempt to redress this matter and to serve as a launch point for further research in this area. Drawing on work from an international group of researchers in mathematics education, this volume is a collection of clinical and classroom-based studies in cognition and instruction on learning and teaching number theory. Although there are differences in emphases in theory, method, and focus area, these studies are bound through similar constructivist orientations and qualitative approaches toward research into undergraduate students' and preservice teachers' subject content and pedagogical content knowledge. Collectively, these studies draw on a variety of cognitive, linguistic, and pedagogical frameworks that focus on various approaches to problem solving, communicating, representing, connecting, and reasoning with topics of elementary number theory, and these in turn have practical implications for the classroom. Learning styles and teaching strategies investigated involve number theoretical vocabulary, concepts, procedures, and proof strategies ranging from divisors, multiples, and divisibility rules, to various theorems involving division, factorization, partitions, and mathematical induction. 410 0$aMathematics, Learning, and Cognition: Monograph Series of the Journal of Mathematics. 606 $aEducation$2bicssc 606 $aNumber theory$xStudy and teaching 615 7$aEducation 615 0$aNumber theory$xStudy and teaching. 676 $a510 s 676 $a512/.7071 702 $aCampbell$b Stephen R. 702 $aZazkis$b Rina 801 0$bUkLoBP 801 1$bUkLoBP 906 $aBOOK 912 $a9910828117503321 996 $aLearning and teaching number theory$94170944 997 $aUNINA