메뉴 건너뛰기




Volumn 25, Issue 3, 2006, Pages 196-207

Students' understanding of mathematical objects in the context of transformational geometry: Implications for constructing and understanding proofs

Author keywords

Linear algebra; Mathematical connections; Mathematics teacher education; Proof; Transformational geometry

Indexed keywords


EID: 33751212456     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2006.09.002     Document Type: Article
Times cited : (14)

References (21)
  • 1
    • 0039938094 scopus 로고
    • Teaching mathematics for understanding: What do teachers need to know about subject matter?
    • Kennedy M. (Ed), Teachers College Press, New York
    • Ball D.L. Teaching mathematics for understanding: What do teachers need to know about subject matter?. In: Kennedy M. (Ed). Teaching academic subjects to diverse learners (1991), Teachers College Press, New York 63-83
    • (1991) Teaching academic subjects to diverse learners , pp. 63-83
    • Ball, D.L.1
  • 2
    • 33751244026 scopus 로고    scopus 로고
    • Conference Board of Mathematical Sciences. (2001). The mathematical education of teachers. Issues in mathematics education (Vol. II). Washington, DC: American Mathematical Society and Mathematical Association of America.
  • 3
    • 0002573795 scopus 로고
    • Reflective abstraction in advanced mathematical thinking
    • David O., and Tall (Eds), Kluwer Academic Publishing, Dordrecht
    • Dubinsky E. Reflective abstraction in advanced mathematical thinking. In: David O., and Tall (Eds). Advanced mathematical thinking (1991), Kluwer Academic Publishing, Dordrecht 95-123
    • (1991) Advanced mathematical thinking , pp. 95-123
    • Dubinsky, E.1
  • 4
    • 33751241513 scopus 로고    scopus 로고
    • Ferrini-Mundy, J., & Findell, B. (2001). The mathematical education of prospective teachers of secondary school mathematics: Old assumptions, new challenges. In CUPM discussion papers about mathematics and the mathematical sciences in 2010: What should students know? (pp. 31-41). Washington, DC: Mathematical Association of America.
  • 6
    • 0001099510 scopus 로고    scopus 로고
    • Students' proof schemes
    • Schoenfeld A.H., Kaput J., and Dubinsky E. (Eds), American Mathematical Society, Providence, RI
    • Harel G., and Sowder L. Students' proof schemes. In: Schoenfeld A.H., Kaput J., and Dubinsky E. (Eds). Research in college mathematics education III (1998), American Mathematical Society, Providence, RI 234-283
    • (1998) Research in college mathematics education III , pp. 234-283
    • Harel, G.1    Sowder, L.2
  • 7
    • 8644231607 scopus 로고    scopus 로고
    • Learning mathematics for teaching: Results from California's mathematics professional development institutes
    • Hill H.C., and Ball D.L. Learning mathematics for teaching: Results from California's mathematics professional development institutes. Journal for Research in Mathematics Education 35 5 (2004) 330-351
    • (2004) Journal for Research in Mathematics Education , vol.35 , Issue.5 , pp. 330-351
    • Hill, H.C.1    Ball, D.L.2
  • 8
    • 85061659351 scopus 로고    scopus 로고
    • The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics
    • English L.E. (Ed), Lawrence Erlbaum Associates, Mahwah, NJ
    • Lakoff G., and Núñez R.E. The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics. In: English L.E. (Ed). Mathematical reasoning: Analogies, metaphors, and images (1997), Lawrence Erlbaum Associates, Mahwah, NJ 21-89
    • (1997) Mathematical reasoning: Analogies, metaphors, and images , pp. 21-89
    • Lakoff, G.1    Núñez, R.E.2
  • 9
    • 27544494269 scopus 로고    scopus 로고
    • The interplay of teacher and student actions in the teaching and learning of geometric proof
    • Martin T.S., McCrone S.S., Wallace M., and Dindyal J. The interplay of teacher and student actions in the teaching and learning of geometric proof. Educational Studies in Mathematics 60 1 (2005) 95-124
    • (2005) Educational Studies in Mathematics , vol.60 , Issue.1 , pp. 95-124
    • Martin, T.S.1    McCrone, S.S.2    Wallace, M.3    Dindyal, J.4
  • 13
    • 33751204817 scopus 로고    scopus 로고
    • Plato (360 b.c.). The Republic.
  • 14
    • 84993660881 scopus 로고    scopus 로고
    • What do new views of knowledge and thinking have to say about research on teacher learning?
    • Putnam R.T., and Borko H. What do new views of knowledge and thinking have to say about research on teacher learning?. Educational Researcher 29 1 (2000) 4-15
    • (2000) Educational Researcher , vol.29 , Issue.1 , pp. 4-15
    • Putnam, R.T.1    Borko, H.2
  • 15
    • 0002546637 scopus 로고
    • On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin
    • Sfard A. On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics 22 (1991) 1-36
    • (1991) Educational Studies in Mathematics , vol.22 , pp. 1-36
    • Sfard, A.1
  • 18
    • 33751235967 scopus 로고    scopus 로고
    • Is symmetry an intuitive basis for proof in Euclidean geometry?
    • Vinner S., and Kopelman E. Is symmetry an intuitive basis for proof in Euclidean geometry?. Focus on Learning Problems in Mathematics 20 2-3 (1998) 14-26
    • (1998) Focus on Learning Problems in Mathematics , vol.20 , Issue.2-3 , pp. 14-26
    • Vinner, S.1    Kopelman, E.2
  • 19
    • 2942589599 scopus 로고    scopus 로고
    • Student difficulty in constructing proofs: The need for strategic knowledge
    • Weber K. Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics 48 (2001) 101-119
    • (2001) Educational Studies in Mathematics , vol.48 , pp. 101-119
    • Weber, K.1
  • 21
    • 20444362130 scopus 로고    scopus 로고
    • Using warranted implications to understand and validate proofs
    • Weber K., and Alcock L. Using warranted implications to understand and validate proofs. For the Learning of Mathematics 25 1 (2005) 34-38
    • (2005) For the Learning of Mathematics , vol.25 , Issue.1 , pp. 34-38
    • Weber, K.1    Alcock, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.