메뉴 건너뛰기




Volumn 70, Issue 3, 2009, Pages 217-241

The array representation and primary children's understanding and reasoning in multiplication

Author keywords

Array; Multiplication; Reasoning; Representations; Understanding

Indexed keywords


EID: 63349094954     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-008-9145-1     Document Type: Article
Times cited : (80)

References (40)
  • 1
    • 33646549299 scopus 로고    scopus 로고
    • DeFT: A conceptual framework for considering learning with multiple representations
    • S. Ainsworth 2006 DeFT: a conceptual framework for considering learning with multiple representations Learning and Instruction 16 3 183 198
    • (2006) Learning and Instruction , vol.16 , Issue.3 , pp. 183-198
    • Ainsworth, S.1
  • 3
    • 63349096401 scopus 로고    scopus 로고
    • Graphical knowledge display-mind mapping and concept mapping as efficient tools in mathematics education
    • A. Brinkmann 2003 Graphical knowledge display-mind mapping and concept mapping as efficient tools in mathematics education Mathematics Education Review 16 35 48
    • (2003) Mathematics Education Review , vol.16 , pp. 35-48
    • Brinkmann, A.1
  • 5
    • 33847073698 scopus 로고    scopus 로고
    • A framework of mathematics inductive reasoning
    • C. Christou E. Papageorgiou 2007 A framework of mathematics inductive reasoning Learning and Instruction 17 1 55 66
    • (2007) Learning and Instruction , vol.17 , Issue.1 , pp. 55-66
    • Christou, C.1    Papageorgiou, E.2
  • 7
    • 63349097228 scopus 로고    scopus 로고
    • Using an interactive whiteboard to facilitate pupil understanding of quadrilateral definitions
    • I. Davison 2003 Using an interactive whiteboard to facilitate pupil understanding of quadrilateral definitions Proceedings of the British Society for Research into Learning Mathematics 23 1 13 18
    • (2003) Proceedings of the British Society for Research into Learning Mathematics , vol.23 , Issue.1 , pp. 13-18
    • Davison, I.1
  • 13
    • 0001697023 scopus 로고
    • The power of five: The step before the power of ten
    • R. J. Flexer 1986 The power of five: the step before the power of ten The Arithmetic Teacher 34 3 5 9
    • (1986) The Arithmetic Teacher , vol.34 , Issue.3 , pp. 5-9
    • Flexer, R.J.1
  • 14
    • 0032324617 scopus 로고    scopus 로고
    • Representational systems, learning and problem solving in mathematics
    • G. A. Goldin 1998 Representational systems, learning and problem solving in mathematics The Journal of Mathematical Behavior 17 2 137 165
    • (1998) The Journal of Mathematical Behavior , vol.17 , Issue.2 , pp. 137-165
    • Goldin, G.A.1
  • 16
    • 33646068436 scopus 로고    scopus 로고
    • Effects of multiple solution methods in mathematics learning
    • C. S. Groe A. Renkl 2006 Effects of multiple solution methods in mathematics learning Learning and Instruction 16 122 138
    • (2006) Learning and Instruction , vol.16 , pp. 122-138
    • Groe, C.S.1    Renkl, A.2
  • 19
    • 24944464097 scopus 로고    scopus 로고
    • Teaching and learning two-digit multiplication: Coordinating analyses of classroom practice and individual student learning
    • A. Izsák 2004 Teaching and learning two-digit multiplication: coordinating analyses of classroom practice and individual student learning Mathematical Thinking and Learning 6 1 37 79
    • (2004) Mathematical Thinking and Learning , vol.6 , Issue.1 , pp. 37-79
    • Izsák, A.1
  • 20
    • 0002534799 scopus 로고
    • Research on the acquisition of science knowledge: Epistemological foundations of cognition
    • Macmillan New York
    • Lawson, A. E. (1994). Research on the acquisition of science knowledge: epistemological foundations of cognition. In D. Gabel (Ed.), Handbook of research on science teaching and learning (pp. 131-176). New York: Macmillan.
    • (1994) Handbook of Research on Science Teaching and Learning , pp. 131-176
    • Lawson, A.E.1    Gabel, D.2
  • 22
    • 34748817078 scopus 로고    scopus 로고
    • Defining and describing reason
    • Cambridge University Press Cambridge
    • Leighton, J. P. (2004). Defining and describing reason. In J. P. Leighton, & R. J. Sternberg (Eds.), The nature of reasoning (pp. 3-11). Cambridge: Cambridge University Press.
    • (2004) The Nature of Reasoning , pp. 3-11
    • Leighton, J.P.1    Leighton, J.P.2    Sternberg, R.J.3
  • 23
    • 2942593146 scopus 로고    scopus 로고
    • Concept maps and schematic diagrams as devices for the growth of mathematical knowledge
    • In O. Zaslavsky (Ed.) Haifa, Israel, July 1999
    • McGowan, M., & Tall, D. (1999). Concept maps and schematic diagrams as devices for the growth of mathematical knowledge. In O. Zaslavsky (Ed.) Proceedings of the 23rd conference of PME, Haifa, Israel, July 1999 (vol 3), 281-288.
    • (1999) Proceedings of the 23rd Conference of PME , vol.3 , pp. 281-288
    • McGowan, M.1    Tall, D.2
  • 24
    • 17444398310 scopus 로고    scopus 로고
    • Threshold concepts and troublesome knowledge: Linkages to ways of thinking and practising within the disciplines
    • [Accessed 27th July 2007 at
    • Meyer, J. H. F., & Land, R. (2003) Threshold concepts and troublesome knowledge: linkages to ways of thinking and practising within the disciplines. Enhancing teaching-learning environments in undergraduate courses project, occasional report 4. [Accessed 27th July 2007 at http://www.ed.ac.uk/ etl/publications.html ]
    • (2003) Enhancing Teaching-learning Environments in Undergraduate Courses Project, Occasional Report 4
    • Meyer, J.H.F.1    Land, R.2
  • 25
    • 27544508520 scopus 로고    scopus 로고
    • Students' early mathematical representation knowledge: The effects of emphasising single or multiple perspectives of the rational number domain in problem solving
    • B. Moseley 2005 Students' early mathematical representation knowledge: the effects of emphasising single or multiple perspectives of the rational number domain in problem solving Educational Studies in Mathematics 60 37 69
    • (2005) Educational Studies in Mathematics , vol.60 , pp. 37-69
    • Moseley, B.1
  • 26
    • 0003865799 scopus 로고    scopus 로고
    • NCTM. National Council of Teachers of Mathematics Reston
    • NCTM (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.
    • (2000) Principles and Standards for School Mathematics
  • 28
    • 0010858777 scopus 로고    scopus 로고
    • Assessing conceptual understanding in mathematics: Representations, problem solutions, justifications, and explanations
    • D. Niemi 1996 Assessing conceptual understanding in mathematics: representations, problem solutions, justifications, and explanations The Journal of Educational Research 89 6 351 364
    • (1996) The Journal of Educational Research , vol.89 , Issue.6 , pp. 351-364
    • Niemi, D.1
  • 30
    • 0345375531 scopus 로고    scopus 로고
    • An analytical model for studying the development of learners' mathematical ideas and reasoning using videotape data
    • A. B. Powell J. M. Francisco C. A. Maher 2003 An analytical model for studying the development of learners' mathematical ideas and reasoning using videotape data The Journal of Mathematical Behavior 22 405 435
    • (2003) The Journal of Mathematical Behavior , vol.22 , pp. 405-435
    • Powell, A.B.1    Francisco, J.M.2    Maher, C.A.3
  • 31
    • 0037400330 scopus 로고    scopus 로고
    • Supporting coherence formation in learning from multiple representations
    • T. Seufert 2003 Supporting coherence formation in learning from multiple representations Learning and Instruction 13 227 237
    • (2003) Learning and Instruction , vol.13 , pp. 227-237
    • Seufert, T.1
  • 32
    • 0002546637 scopus 로고
    • On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin
    • A. Sfard 1991 On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin Educational Studies in Mathematics 22 1 1 36
    • (1991) Educational Studies in Mathematics , vol.22 , Issue.1 , pp. 1-36
    • Sfard, A.1
  • 34
    • 55749097286 scopus 로고    scopus 로고
    • Key developmental understandings in mathematics: A direction for investigating and establishing learning goals
    • M. A. Simon 2006 Key developmental understandings in mathematics: a direction for investigating and establishing learning goals Mathematical Thinking and Learning 8 4 359 371
    • (2006) Mathematical Thinking and Learning , vol.8 , Issue.4 , pp. 359-371
    • Simon, M.A.1
  • 35
    • 0002155120 scopus 로고
    • Relational understanding and instrumental understanding
    • R. Skemp 1976 Relational understanding and instrumental understanding Mathematics Teaching 77 20 26
    • (1976) Mathematics Teaching , vol.77 , pp. 20-26
    • Skemp, R.1
  • 36
    • 24044490041 scopus 로고    scopus 로고
    • Epistemological investigation of classroom interaction in elementary mathematics teaching
    • H. Steinbring 1997 Epistemological investigation of classroom interaction in elementary mathematics teaching Educational Studies in Mathematics 32 1 49 92
    • (1997) Educational Studies in Mathematics , vol.32 , Issue.1 , pp. 49-92
    • Steinbring, H.1
  • 39
    • 22044454676 scopus 로고    scopus 로고
    • Using concept maps to assess conceptual knowledge of function
    • C. G. Williams 1998 Using concept maps to assess conceptual knowledge of function Journal for Research in Mathematics Education 29 4 414 421
    • (1998) Journal for Research in Mathematics Education , vol.29 , Issue.4 , pp. 414-421
    • Williams, C.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.