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Volumn 58, Issue 1, 2005, Pages 77-100

Convergence of sequences and series 2: Interactions between nonvisual reasoning and the learner's beliefs about their own role

(2)  Alcock, Lara a   Simpson, Adrian a  

a NONE

Author keywords

Advanced mathematical thinking; Beliefs; Convergence; Definitions; Proof; Real analysis; Representations; Sequences; Series; Symbolic reasoning

Indexed keywords


EID: 17444365053     PISSN: 00131954     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10649-005-2813-5     Document Type: Article
Times cited : (34)

References (36)
  • 3
    • 4544248650 scopus 로고    scopus 로고
    • Definitions: Dealing with categories mathematically
    • Alcock, L.J. and Simpson, A.P.: 2002, 'Definitions: Dealing with categories mathematically', For the Learning of Mathematics, 22(2), 28-34.
    • (2002) For the Learning of Mathematics , vol.22 , Issue.2 , pp. 28-34
    • Alcock, L.J.1    Simpson, A.P.2
  • 4
    • 8644260889 scopus 로고    scopus 로고
    • Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role
    • In press
    • Alcock, L.J. and Simpson, A.P.: In press, 'Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role', Educational Studies in Mathematics.
    • Educational Studies in Mathematics
    • Alcock, L.J.1    Simpson, A.P.2
  • 9
    • 8644236408 scopus 로고
    • The Perry development scheme: A metaphor for learning and teaching mathematics
    • Copes, L.: 1982, 'The Perry development scheme: a metaphor for learning and teaching mathematics', For the Learning of Mathematics, 3(1), 38-44.
    • (1982) For the Learning of Mathematics , vol.3 , Issue.1 , pp. 38-44
    • Copes, L.1
  • 10
    • 0347681495 scopus 로고
    • Limits
    • D.O. Tall (ed.), Kluwer, Dordrecht
    • Cornu, B.: 1991, 'Limits', in D.O. Tall (ed.), Advanced Mathematical Thinking, Kluwer, Dordrecht, pp. 153-166.
    • (1991) Advanced Mathematical Thinking , pp. 153-166
    • Cornu, B.1
  • 11
    • 0010789409 scopus 로고
    • The interplay of algebra, geometry and logic
    • Davis, R. B.: 1988, 'The interplay of algebra, geometry and logic', Journal of Mathematical Behavior, 7(1), 9-28.
    • (1988) Journal of Mathematical Behavior , vol.7 , Issue.1 , pp. 9-28
    • Davis, R.B.1
  • 12
    • 0000014423 scopus 로고
    • The notion of limit: Some seemingly unavoidable misconception stages
    • Davis, R.B. and Vinner, S.: 1986, 'The notion of limit: Some seemingly unavoidable misconception stages', Journal of Mathematical Behaviour, 5(3), 281-303.
    • (1986) Journal of Mathematical Behaviour , vol.5 , Issue.3 , pp. 281-303
    • Davis, R.B.1    Vinner, S.2
  • 13
    • 0344130972 scopus 로고    scopus 로고
    • APOS: A constructivist theory of learning in undergraduate mathematics education research
    • D. Holton (Ed.), Kluwer, Dordrecht
    • Dubinsky, E. and McDonald, M.A.: 2001, 'APOS: A constructivist theory of learning in undergraduate mathematics education research', in D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study, Kluwer, Dordrecht, pp. 275-282.
    • (2001) The Teaching and Learning of Mathematics at University Level: An ICMI Study , pp. 275-282
    • Dubinsky, E.1    McDonald, M.A.2
  • 17
    • 2142848937 scopus 로고    scopus 로고
    • Understanding elementary number theory at the undergraduate level: A semiotic approach
    • S.R. Campbell and R. Zazkis (Eds.), Ablex Publishing, Westport, Conneticut
    • Ferrari, P.L.: 2002, 'Understanding elementary number theory at the undergraduate level: A semiotic approach', in S.R. Campbell and R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction, Ablex Publishing, Westport, Conneticut, pp. 97-115.
    • (2002) Learning and Teaching Number Theory: Research in Cognition and Instruction , pp. 97-115
    • Ferrari, P.L.1
  • 19
    • 17444404993 scopus 로고    scopus 로고
    • Knowledge Construction and diverging thinking in elementary and advanced mathematics
    • Gray, E.M. Pinto, M., Pitta, D. and Tall, D.O.: 1999 'Knowledge Construction and diverging thinking in elementary and advanced mathematics', Educational Studies in Mathematics, 38(1-3), 111-133.
    • (1999) Educational Studies in Mathematics , vol.38 , Issue.1-3 , pp. 111-133
    • Gray, E.M.1    Pinto, M.2    Pitta, D.3    Tall, D.O.4
  • 20
    • 0002549333 scopus 로고
    • The role of conceptual entities and their symbols in building mathematical concepts
    • D.O. Tall (ed.), Kluwer, Dordrecht
    • Harel, G. and Kaput, J.: 1991, "The role of conceptual entities and their symbols in building mathematical concepts', in D.O. Tall (ed.), Advanced Mathematical Thinking, Kluwer, Dordrecht, pp. 82-94.
    • (1991) Advanced Mathematical Thinking , pp. 82-94
    • Harel, G.1    Kaput, J.2
  • 21
    • 0001099510 scopus 로고    scopus 로고
    • 'Students' proof schemes: Results from exploratory studies
    • A.H. Schoenfeld, J. Kaput and E. Dubinsky (eds.)
    • Harel, G. and Sowder, L.: 1998, 'Students' proof schemes: results from exploratory studies', in A.H. Schoenfeld, J. Kaput and E. Dubinsky (eds.), CBMS Issues in Mathematics Education, 7, 234-283.
    • (1998) CBMS Issues in Mathematics Education , vol.7 , pp. 234-283
    • Harel, G.1    Sowder, L.2
  • 22
    • 0040226850 scopus 로고
    • Heuristic presentations: The role of structuring
    • Leron, U.: 1985, 'Heuristic presentations: The role of structuring', For the Learning of Mathematics, 5(3), 7-13.
    • (1985) For the Learning of Mathematics , vol.5 , Issue.3 , pp. 7-13
    • Leron, U.1
  • 24
    • 0347050790 scopus 로고
    • Problems with the language of limits
    • Monaghan, J.: 1991, 'Problems with the language of limits', For the Learning of Mathematics, 11(3), 20-24.
    • (1991) For the Learning of Mathematics , vol.11 , Issue.3 , pp. 20-24
    • Monaghan, J.1
  • 25
    • 0000682797 scopus 로고
    • Making the transition to formal proof
    • Moore, R.C.: 1994, 'Making the transition to formal proof', Educational Studies in Mathematics, 27, 249-266.
    • (1994) Educational Studies in Mathematics , vol.27 , pp. 249-266
    • Moore, R.C.1
  • 26
    • 0001714584 scopus 로고
    • Different worlds in the same classroom
    • P. Ramsden (ed.), Kogan Page, London
    • Perry, W.G.: 1988, 'Different worlds in the same classroom', in P. Ramsden (ed.), Improving learning: New perspectives, Kogan Page, London.
    • (1988) Improving Learning: New Perspectives
    • Perry, W.G.1
  • 28
    • 0037860124 scopus 로고
    • Visualisation and mathematical giftedness
    • Presmeg, N.C.: 1986, 'Visualisation and mathematical giftedness', Educational Studies in Mathematics, 17, 297-311.
    • (1986) Educational Studies in Mathematics , vol.17 , pp. 297-311
    • Presmeg, N.C.1
  • 29
    • 0042173905 scopus 로고    scopus 로고
    • Signs and meanings in students' emergent algebraic thinking: A semiotic analysis
    • Radford, L.: 2000, 'Signs and meanings in students' emergent algebraic thinking: a semiotic analysis', Educational Studies in Mathematics, 42, 237-268.
    • (2000) Educational Studies in Mathematics , vol.42 , pp. 237-268
    • Radford, L.1
  • 30
    • 85068071049 scopus 로고
    • What's all the fuss about metacognition?
    • A.H. Schoenfeld, (Ed.), Lawrence Erlbaum Associates, Hillsdale, NJ
    • Schoenfeld, A.H.: 1987, 'What's all the fuss about metacognition?', in A.H. Schoenfeld, (Ed.), Cognitive science and mathematics education, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 189-215.
    • (1987) Cognitive Science and Mathematics Education , pp. 189-215
    • Schoenfeld, A.H.1
  • 31
    • 24944477378 scopus 로고
    • The gains and pitfalls of reification - The case of algebra
    • Sfard, A. and Linchevsky, L.: 1994, 'The gains and pitfalls of reification - the case of algebra', Educational Studies in Mathematics, 26, 191-228.
    • (1994) Educational Studies in Mathematics , vol.26 , pp. 191-228
    • Sfard, A.1    Linchevsky, L.2
  • 32
    • 0000935350 scopus 로고
    • Humanities students and epistemological obstacles related to limits
    • Sierpinska, A.: 1987, 'Humanities students and epistemological obstacles related to limits'. Educational Studies in Mathematics, 18, 371-397.
    • (1987) Educational Studies in Mathematics , vol.18 , pp. 371-397
    • Sierpinska, A.1
  • 33
    • 0002155120 scopus 로고
    • Relational understanding and instrumental understanding
    • Skemp, R.R.: 1976, 'Relational understanding and instrumental understanding', Mathematics Teaching, 77, 20-26.
    • (1976) Mathematics Teaching , vol.77 , pp. 20-26
    • Skemp, R.R.1
  • 36
    • 17444392166 scopus 로고
    • The mathematical way of thinking
    • Weyl, H.: 1940, "The mathematical way of thinking', Science, 92, 437-446.
    • (1940) Science , vol.92 , pp. 437-446
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.