메뉴 건너뛰기




Volumn 69, Issue 2, 2008, Pages 111-129

Doctoral students' use of examples in evaluating and proving conjectures

Author keywords

Examples; Generic examples; Number theory; Proof; Reasoning; Strategies

Indexed keywords


EID: 51549100977     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-008-9149-x     Document Type: Article
Times cited : (43)

References (39)
  • 1
    • 77957866654 scopus 로고    scopus 로고
    • Mathematicians' perspectives on the teaching and learning of proof
    • F. Hitt, D. A. Holton, & P. Thompson (Eds.) Providence, RI: American Mathematical Society
    • Alcock, L. (2008). Mathematicians' perspectives on the teaching and learning of proof. In F. Hitt, D. A. Holton, & P. Thompson (Eds.), Research in Collegiate Mathematics Education VII (pp. 73-100). Providence, RI: American Mathematical Society.
    • (2008) Research in Collegiate Mathematics Education VII , pp. 73-100
    • Alcock, L.1
  • 2
    • 8644260889 scopus 로고    scopus 로고
    • Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role
    • DOI: 10.1023/B:EDUC.0000047051.07646.92
    • Alcock, L., & Simpson, A. (2004). Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role. Educational Studies in Mathematics, 57, 1-32. doi: 10.1023/B:EDUC.0000047051.07646.92.
    • (2004) Educational Studies in Mathematics , vol.57 , pp. 1-32
    • Alcock, L.1    Simpson, A.2
  • 3
    • 17444365053 scopus 로고    scopus 로고
    • Convergence of sequences and series 2: Interactions between nonvisual reasoning and the learner's beliefs about their own role
    • DOI: 10.1007/s10649-005-2813-5
    • Alcock, L., & Simpson, A. (2005). Convergence of sequences and series 2: Interactions between nonvisual reasoning and the learner's beliefs about their own role. Educational Studies in Mathematics, 58, 77-100. doi: 10.1007/s10649-005-2813-5.
    • (2005) Educational Studies in Mathematics , vol.58 , pp. 77-100
    • Alcock, L.1    Simpson, A.2
  • 4
    • 84878518898 scopus 로고    scopus 로고
    • Referential and syntactic approaches to proving: Case studies from a transition-to-proof course
    • F. Hitt, D. A. Holton, & P. Thompson (Eds.) Providence, RI: American Mathematical Society
    • Alcock, L., & Weber, K. (2008). Referential and syntactic approaches to proving: Case studies from a transition-to-proof course. In F. Hitt, D. A. Holton, & P. Thompson (Eds.), Research in Collegiate Mathematics Education VII (pp. 101-123). Providence, RI: American Mathematical Society.
    • (2008) Research in Collegiate Mathematics Education VII , pp. 101-123
    • Alcock, L.1    Weber, K.2
  • 5
    • 0001268290 scopus 로고
    • Processus de preuves et situations de validation
    • DOI: 10.1007/BF00314724
    • Balacheff, N. (1987). Processus de preuves et situations de validation. Educational Studies in Mathematics, 18, 147-176. doi: 10.1007/BF00314724.
    • (1987) Educational Studies in Mathematics , vol.18 , pp. 147-176
    • Balacheff, N.1
  • 9
    • 37249041941 scopus 로고    scopus 로고
    • Gesturing makes learning last
    • DOI: 10.1016/j.cognition.2007.04.010
    • Cook, S. W., Mitchell, Z., & Goldin-Meadow, S. (2008). Gesturing makes learning last. Cognition, 106, 1047-1058. doi: 10.1016/j.cognition.2007. 04.010.
    • (2008) Cognition , vol.106 , pp. 1047-1058
    • Cook, S.W.1    Mitchell, Z.2    Goldin-Meadow, S.3
  • 10
    • 3843083271 scopus 로고    scopus 로고
    • Facilitating learning events through example generation
    • DOI: 10.1023/A:1002999415887
    • Dahlberg, R. P., & Housman, D. L. (1997). Facilitating learning events through example generation. Educational Studies in Mathematics, 33, 283-299. doi: 10.1023/A:1002999415887.
    • (1997) Educational Studies in Mathematics , vol.33 , pp. 283-299
    • Dahlberg, R.P.1    Housman, D.L.2
  • 11
    • 0002573795 scopus 로고
    • Reflective abstraction in advanced mathematical thinking
    • Kluwer Dordrecht
    • Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-126). Dordrecht: Kluwer.
    • (1991) Advanced Mathematical Thinking , pp. 95-126
    • Dubinsky, E.1    Tall, D.2
  • 12
    • 0040226925 scopus 로고
    • The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques
    • 1
    • Ginsburg, H. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the Learning of Mathematics, 1(1), 4-11.
    • (1981) For the Learning of Mathematics , vol.1 , pp. 4-11
    • Ginsburg, H.1
  • 13
    • 0032324617 scopus 로고    scopus 로고
    • Representational systems, learning, and problem solving in mathematics
    • DOI: 10.1016/S0364-0213(99)80056-1
    • Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. The Journal of Mathematical Behavior, 17, 137-165. doi: 10.1016/S0364-0213(99)80056-1.
    • (1998) The Journal of Mathematical Behavior , vol.17 , pp. 137-165
    • Goldin, G.A.1
  • 18
    • 34547675801 scopus 로고    scopus 로고
    • Modelling mathematical argumentation: The importance of qualification
    • DOI: 10.1007/s10649-006-9059-8
    • Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66, 3-21. doi: 10.1007/s10649-006-9059-8.
    • (2007) Educational Studies in Mathematics , vol.66 , pp. 3-21
    • Inglis, M.1    Mejia-Ramos, J.P.2    Simpson, A.3
  • 19
    • 34547714697 scopus 로고
    • An investigation of the behaviour of mathematicians engaged in testing a conjecture
    • May Presented at , Detroit, MI
    • Markowitz, L. M., and Tweney, R. D. (1981, May). An investigation of the behaviour of mathematicians engaged in testing a conjecture. Presented at Midwestern Psychological Association, Detroit, MI.
    • (1981) Midwestern Psychological Association
    • Markowitz, L.M.1    Tweney, R.D.2
  • 20
    • 0010050543 scopus 로고
    • Generic examples: Seeing the general in the particular
    • DOI: 10.1007/BF00312078
    • Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277-289. doi: 10.1007/BF00312078.
    • (1984) Educational Studies in Mathematics , vol.15 , pp. 277-289
    • Mason, J.1    Pimm, D.2
  • 21
    • 51549116296 scopus 로고    scopus 로고
    • Stimulating students to construct boundary examples
    • Mason, J., & Watson, A. (2001). Stimulating students to construct boundary examples. Questiones Mathematicae, Suppl. 1, Supplement, 123-132.
    • (2001) Questiones Mathematicae , Issue.SUPPL. 1 , pp. 123-132
    • Mason, J.1    Watson, A.2
  • 22
    • 0018217861 scopus 로고
    • Understanding understanding mathematics
    • Michener, E. R. (1978). Understanding understanding mathematics. Cognitive Science, 2, 361-383.
    • (1978) Cognitive Science , vol.2 , pp. 361-383
    • Michener, E.R.1
  • 24
    • 8644238718 scopus 로고    scopus 로고
    • Building formal mathematics on visual imagery: A case study and a theory
    • Pinto, M., & Tall, D. O. (2002). Building formal mathematics on visual imagery: A case study and a theory. For the Learning of Mathematics, 22, 2-10.
    • (2002) For the Learning of Mathematics , vol.22 , pp. 2-10
    • Pinto, M.1    Tall, D.O.2
  • 27
    • 0013002317 scopus 로고
    • Unpacking the logic of mathematical statements
    • DOI: 10.1007/BF01274210
    • Selden, J., & Selden, A. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29, 123-151. doi: 10.1007/BF01274210.
    • (1995) Educational Studies in Mathematics , vol.29 , pp. 123-151
    • Selden, J.1    Selden, A.2
  • 29
    • 0037257290 scopus 로고    scopus 로고
    • Validation of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?
    • Selden, J., & Selden, A. (2003). Validation of proofs considered as texts: can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34, 4-36.
    • (2003) Journal for Research in Mathematics Education , vol.34 , pp. 4-36
    • Selden, J.1    Selden, A.2
  • 30
    • 0036403502 scopus 로고    scopus 로고
    • Interaction of visualization and analysis - The negotiation of a visual representation in problem solving
    • DOI: 10.1016/S0732-3123(02)00131-1
    • Stylianou, D. A. (2002). Interaction of visualization and analysis - the negotiation of a visual representation in problem solving. The Journal of Mathematical Behavior, 21, 303-317. doi: 10.1016/S0732-3123(02)00131-1.
    • (2002) The Journal of Mathematical Behavior , vol.21 , pp. 303-317
    • Stylianou, D.A.1
  • 31
    • 0001940478 scopus 로고
    • The role of definitions in teaching and learning mathematics
    • Kluwer Dordrecht
    • Vinner, S. (1991). The role of definitions in teaching and learning mathematics. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Dordrecht: Kluwer.
    • (1991) Advanced Mathematical Thinking , pp. 65-81
    • Vinner, S.1    Tall, D.O.2
  • 34
    • 47949097185 scopus 로고    scopus 로고
    • How mathematicians determine if an argument is a valid proof
    • Weber, K. (2008). How mathematicians determine if an argument is a valid proof. Journal for Research in Mathematics Education, 39, 431-459.
    • (2008) Journal for Research in Mathematics Education , vol.39 , pp. 431-459
    • Weber, K.1
  • 35
    • 51549100837 scopus 로고    scopus 로고
    • Syntactic and semantic reasoning processes in advanced mathematics
    • M. Blanton, D. Stylianou, and E. Knuth (Eds.)
    • Weber, K., & Alcock, L. (2008). Syntactic and semantic reasoning processes in advanced mathematics. In M. Blanton, D. Stylianou, and E. Knuth (Eds.) A proof story across the grades (in press).
    • (2008) A Proof Story Across the Grades (In Press)
    • Weber, K.1    Alcock, L.2
  • 36
    • 4544338745 scopus 로고    scopus 로고
    • Semantic and syntactic proof productions
    • DOI: 10.1023/B:EDUC.0000040410.57253.a1
    • Weber, K., & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56, 209-234. doi: 10.1023/B:EDUC.0000040410.57253.a1.
    • (2004) Educational Studies in Mathematics , vol.56 , pp. 209-234
    • Weber, K.1    Alcock, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.