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Volumn 11, Issue 4, 2009, Pages 258-288

Reasoning-and-proving in school mathematics textbooks

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EID: 70449125890     PISSN: 10986065     EISSN: 15327833     Source Type: Journal    
DOI: 10.1080/10986060903253954     Document Type: Article
Times cited : (99)

References (55)
  • 2
    • 50249163558 scopus 로고
    • A study of students' proving processes at the junior high school level
    • In I. Wirszup & R. Streit (Eds.), Reston, VA: National Council of Teachers of Mathematics
    • Balacheff, N. (1988). A study of students' proving processes at the junior high school level. In I. Wirszup & R. Streit (Eds.), Proceedings of the Second UCSMP International Conference on Mathematics Education (pp. 284-297). Reston, VA: National Council of Teachers of Mathematics.
    • (1988) Proceedings of the Second UCSMP International Conference on Mathematics Education , pp. 284-297
    • Balacheff, N.1
  • 3
    • 2442430987 scopus 로고    scopus 로고
    • Making mathematics reasonable in school
    • In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), Reston, VA: National Council of Teachers of Mathematics
    • Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 27-44). Reston, VA: National Council of Teachers of Mathematics.
    • (2003) A research companion to Principles and Standards for School Mathematics , pp. 27-44
    • Ball, D.L.1    Bass, H.2
  • 4
    • 0002122056 scopus 로고
    • A study of pupil's proof-explanations in mathematical situations
    • Bell, A. W. (1976). A study of pupil's proof-explanations in mathematical situations. Educational Studies in Mathematics, 7(1), 23-40.
    • (1976) Educational Studies in Mathematics , vol.7 , Issue.1 , pp. 23-40
    • Bell, A.W.1
  • 9
    • 85070599154 scopus 로고    scopus 로고
    • An alternative approach to proof in dynamic geometry
    • In R. Lehrer & D. Chazan (Eds.), London: Lawrence Erlbaum Associates
    • de Villiers, M. (1998). An alternative approach to proof in dynamic geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 369-393). London: Lawrence Erlbaum Associates.
    • (1998) Designing learning environments for developing understanding of geometry and space , pp. 369-393
    • de Villiers, M.1
  • 10
    • 50249151744 scopus 로고    scopus 로고
    • The role and function of proof
    • In M. de Villiers (Ed.), Key Curriculum Press
    • de Villiers, M. (1999). The role and function of proof. In M. de Villiers (Ed.), Rethinking proof with the Geometer's Sketchpad (pp. 3-10). Key Curriculum Press.
    • (1999) Rethinking proof with the Geometer's Sketchpad , pp. 3-10
    • de Villiers, M.1
  • 11
    • 33645072184 scopus 로고
    • The psychological and the logical in teaching geometry
    • Dewey, J. (1903). The psychological and the logical in teaching geometry. Educational Review, XXV, 387-399.
    • (1903) Educational Review , vol.25 , pp. 387-399
    • Dewey, J.1
  • 15
    • 0002952407 scopus 로고
    • Some pedagogical aspects of proof
    • Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13.
    • (1990) Interchange , vol.21 , Issue.1 , pp. 6-13
    • Hanna, G.1
  • 16
    • 0001099510 scopus 로고    scopus 로고
    • Students' proof schemes: Results from exploratory studies
    • In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Providence, R.I.: American Mathematical Society
    • Harel, G., & Sowder, L. (1998). Students' proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283). Providence, R.I.: American Mathematical Society.
    • (1998) Research in collegiate mathematics education III , pp. 234-283
    • Harel, G.1    Sowder, L.2
  • 17
    • 35348989433 scopus 로고    scopus 로고
    • Toward comprehensive perspectives on the learning and teaching of proof
    • In F. K. Lester (Ed.), Greenwich, CT: Information Age Publishing
    • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805-842). Greenwich, CT: Information Age Publishing.
    • (2007) Second handbook of research on mathematics teaching and learning , pp. 805-842
    • Harel, G.1    Sowder, L.2
  • 19
    • 70449102257 scopus 로고    scopus 로고
    • Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study
    • Washington, D.C.: U.S. Department of Education, Institute of Education Sciences
    • Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., et al.(2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study. NCES 2003-013. Washington, D.C.: U.S. Department of Education, Institute of Education Sciences.
    • (2003) NCES 2003-013
    • Hiebert, J.1    Gallimore, R.2    Garnier, H.3    Givvin, K.B.4    Hollingsworth, H.5    Jacobs, J.6
  • 20
    • 0036862419 scopus 로고    scopus 로고
    • Secondary school mathematics teachers' conceptions of proof
    • Knuth, E. J. (2002). Secondary school mathematics teachers' conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405.
    • (2002) Journal for Research in Mathematics Education , vol.33 , Issue.5 , pp. 379-405
    • Knuth, E.J.1
  • 21
    • 3543046440 scopus 로고    scopus 로고
    • Mapping the conceptual terrain of middle school students' competencies in justifying and proving
    • In D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Weigel, R. L. Bryant, & K. Nooney (Eds.), Athens, GA: Clearinghouse for Science, Mathematics, and Environmental Education
    • Knuth, E. J., Choppin, J., Slaughter, M., & Sutherland, J. (2002). Mapping the conceptual terrain of middle school students' competencies in justifying and proving. In D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Weigel, R. L. Bryant, & K. Nooney (Eds.), Proceedings of the 24th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 1693-1670). Athens, GA: Clearinghouse for Science, Mathematics, and Environmental Education.
    • (2002) Proceedings of the 24th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , vol.4 , pp. 1693-1670
    • Knuth, E.J.1    Choppin, J.2    Slaughter, M.3    Sutherland, J.4
  • 23
    • 70449091380 scopus 로고    scopus 로고
    • London: Institute of Education, University of London. Retrieved 3 May, 2009, from
    • Küchemann, D., & Hoyles, C. (2001-03). Longitudinal Proof Project (Technical Reports). London: Institute of Education, University of London. Retrieved 3 May, 2009, from http://www.mathsmed.co.uk/ioe-proof/techreps.html
    • (2001) Longitudinal Proof Project (Technical Reports)
    • Küchemann, D.1    Hoyles, C.2
  • 24
    • 84870806365 scopus 로고    scopus 로고
    • From empirical to structural reasoning in mathematics: Tracking changes over time
    • In D. A. Stylianou, M. L. Blanton & E. J. Knuth E. (Eds.), New York, N.Y.: Routledge
    • Küchemann, D., & Hoyles, C. (2009). From empirical to structural reasoning in mathematics: tracking changes over time. In D. A. Stylianou, M. L. Blanton & E. J. Knuth E. (Eds.), Teaching and learning proofs across the grades: A K-16 perspective. New York, N.Y.: Routledge.
    • (2009) Teaching and learning proofs across the grades: A K-16 perspective
    • Küchemann, D.1    Hoyles, C.2
  • 26
    • 0010220021 scopus 로고
    • Practices and problems in teaching authentic mathematics
    • In F. K. Oser, A. Dick, & J. Patry (Eds.), San Francisco, CA: Jossey-Bass Publishers
    • Lampert, M. (1992). Practices and problems in teaching authentic mathematics. In F. K. Oser, A. Dick, & J. Patry (Eds.), Effective and responsible teaching: The new synthesis (pp. 295-314). San Francisco, CA: Jossey-Bass Publishers.
    • (1992) Effective and responsible teaching: The new synthesis , pp. 295-314
    • Lampert, M.1
  • 28
    • 0032332037 scopus 로고    scopus 로고
    • Some characteristics of eighth grade mathematics classes in the TIMSS videotape study
    • Manaster, A. B. (1998). Some characteristics of eighth grade mathematics classes in the TIMSS videotape study. American Mathematical Monthly, 105(9), 793-805.
    • (1998) American Mathematical Monthly , vol.105 , Issue.9 , pp. 793-805
    • Manaster, A.B.1
  • 30
    • 0004264316 scopus 로고
    • (with Burton, L., & Stacey, K.), London: Addison-Wesley
    • Mason, J. (with Burton, L., & Stacey, K.) (1982). Thinking mathematically. London: Addison-Wesley.
    • (1982) Thinking mathematically
    • Mason, J.1
  • 31
    • 0010050543 scopus 로고
    • Generic examples: Seeing the general in the particular
    • Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277-289.
    • (1984) Educational Studies in Mathematics , vol.15 , pp. 277-289
    • Mason, J.1    Pimm, D.2
  • 32
    • 0042238792 scopus 로고
    • Stimulating presentation of theorems followed by responsive proofs
    • Movshovitz-Hadar, N. (1988). Stimulating presentation of theorems followed by responsive proofs. For the Learning of Mathematics, 8(2), 12-19, 30.
    • (1988) For the Learning of Mathematics , vol.8 , Issue.2
    • Movshovitz-Hadar, N.1
  • 33
    • 0003425267 scopus 로고
    • National Council of Teachers of Mathematics, Reston, VA: National Council of Teachers of Mathematics
    • National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
    • (1989) Curriculum and evaluation standards for school mathematics
  • 34
    • 0003865799 scopus 로고    scopus 로고
    • National Council of Teachers of Mathematics, Reston, VA: National Council of Teachers of Mathematics
    • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
    • (2000) Principles and standards for school mathematics
  • 36
    • 84993734244 scopus 로고    scopus 로고
    • Measuring the content of instruction: Uses in research and practice
    • Porter, A. (2002). Measuring the content of instruction: Uses in research and practice. Educational Researcher, 31(7), 3-14.
    • (2002) Educational Researcher , vol.31 , Issue.7 , pp. 3-14
    • Porter, A.1
  • 37
    • 10144261271 scopus 로고    scopus 로고
    • Epistemological messages conveyed by three high-school and college mathematics textbooks
    • Raman, M. (2004). Epistemological messages conveyed by three high-school and college mathematics textbooks. Journal of Mathematical Behavior, 23(4), 389-404.
    • (2004) Journal of Mathematical Behavior , vol.23 , Issue.4 , pp. 389-404
    • Raman, M.1
  • 38
    • 0036001504 scopus 로고    scopus 로고
    • Conjectures and refutations in grade 5 mathematics
    • Reid, D. (2002). Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education, 33(1), 5-29.
    • (2002) Journal for Research in Mathematics Education , vol.33 , Issue.1 , pp. 5-29
    • Reid, D.1
  • 39
    • 3843137709 scopus 로고    scopus 로고
    • Mathematics worth teaching, mathematics worth understanding
    • In E. Fennema & T. Romberg (Eds.), Mahwah, N.J.: Lawrence Erlbaum Associates
    • Romberg, T., & Kaput, J. (1999). Mathematics worth teaching, mathematics worth understanding. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 3-18). Mahwah, N.J.: Lawrence Erlbaum Associates.
    • (1999) Mathematics classrooms that promote understanding , pp. 3-18
    • Romberg, T.1    Kaput, J.2
  • 40
    • 38149144617 scopus 로고
    • What do we know about mathematics curricula?
    • Schoenfeld, A. H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13, 55-80.
    • (1994) Journal of Mathematical Behavior , vol.13 , pp. 55-80
    • Schoenfeld, A.H.1
  • 41
    • 0002207869 scopus 로고
    • Education and the structure of the disciplines
    • In J. Westbury & N. J. Wilkof (Eds.), Chicago & London: The University of Chicago Press
    • Schwab, J. J. (1978). Education and the structure of the disciplines. In J. Westbury & N. J. Wilkof (Eds.), Science, curriculum, and liberal education: Selected essays (pp. 229-272). Chicago & London: The University of Chicago Press.
    • (1978) Science, curriculum, and liberal education: Selected essays , pp. 229-272
    • Schwab, J.J.1
  • 46
    • 33846794805 scopus 로고    scopus 로고
    • The notion of proof in the context of elementary school mathematics
    • Stylianides, A. J. (2007b). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65(1), 1-20.
    • (2007) Educational Studies in Mathematics , vol.65 , Issue.1 , pp. 1-20
    • Stylianides, A.J.1
  • 47
    • 36749028348 scopus 로고    scopus 로고
    • Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics
    • Stylianides, G. J. (2007c). Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics. International Journal of Science and Mathematics Education, 6, 191-215.
    • (2007) International Journal of Science and Mathematics Education , vol.6 , pp. 191-215
    • Stylianides, G.J.1
  • 48
    • 50249180981 scopus 로고    scopus 로고
    • An analytic framework of reasoning-and-proving
    • Stylianides, G. J. (2008a). An analytic framework of reasoning-and-proving. For the Learning of Mathematics, 28(1), 9-16.
    • (2008) For the Learning of Mathematics , vol.28 , Issue.1 , pp. 9-16
    • Stylianides, G.J.1
  • 50
    • 70350351736 scopus 로고    scopus 로고
    • Proof in school mathematics: Insights from psychological research into students' ability for deductive reasoning
    • Stylianides, G. J., & Stylianides, A. J. (2008). Proof in school mathematics: Insights from psychological research into students' ability for deductive reasoning. Mathematical Thinking and Learning, 10(2), 103-133.
    • (2008) Mathematical Thinking and Learning , vol.10 , Issue.2 , pp. 103-133
    • Stylianides, G.J.1    Stylianides, A.J.2
  • 52
    • 33846394053 scopus 로고    scopus 로고
    • From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students' opportunity to learn
    • Tarr, J. E., Chávez, Ó., Reys, R. E., & Reys, B. J. (2006). From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students' opportunity to learn. School Science and Mathematics, 106(4), 191-201.
    • (2006) School Science and Mathematics , vol.106 , Issue.4 , pp. 191-201
    • Tarr, J.E.1    Chávez, Ó.2    Reys, R.E.3    Reys, B.J.4
  • 55
    • 3543018811 scopus 로고    scopus 로고
    • Reasoning and proof
    • In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), Reston, VA: National Council of Teachers of Mathematics
    • Yackel, E., & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 22-44). Reston, VA: National Council of Teachers of Mathematics.
    • (2003) A research companion to Principles and Standards for School Mathematics , pp. 22-44
    • Yackel, E.1    Hanna, G.2


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