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Volumn 65, Issue 3, 2007, Pages 255-279

When intuition beats logic: Prospective teachers' awareness of their same sides - Same angles solutions

Author keywords

Angles; Intuitve rule; Polygons; Prospective teacher; Same A same B; Sides; SMK

Indexed keywords


EID: 33947712972     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-006-9053-1     Document Type: Article
Times cited : (14)

References (55)
  • 2
    • 0001867944 scopus 로고
    • Research on teaching mathematics: Making subject-matter knowledge part of the equation
    • J. Brophy ed, JAI Press, London, pp
    • Ball, D.L.: 1991, 'Research on teaching mathematics: Making subject-matter knowledge part of the equation', in J. Brophy (ed.), Advances in Research on Teaching, vol. II, JAI Press, London, pp. 1-49.
    • (1991) Advances in Research on Teaching , vol.2 , pp. 1-49
    • Ball, D.L.1
  • 5
    • 33947715351 scopus 로고
    • Brown, S.I. and Walter, M.I, eds, The Franklin Institute Press, Philadelphia, Pennsylvania, pp
    • Brown, S.I. and Walter, M.I. (eds.): 1983, The Art of Problem Posing, The Franklin Institute Press, Philadelphia, Pennsylvania, pp. 31-62.
    • (1983) The Art of Problem Posing , pp. 31-62
  • 7
    • 84983945760 scopus 로고
    • Using bridging analogies and anchoring intuitions to deal with students' preconceptions in physics
    • Clement, J.: 1993, 'Using bridging analogies and anchoring intuitions to deal with students' preconceptions in physics', Journal of Research in Science Teaching 30, 1241-1257.
    • (1993) Journal of Research in Science Teaching , vol.30 , pp. 1241-1257
    • Clement, J.1
  • 8
    • 0007930006 scopus 로고
    • Teacher education as an exercise in adaptation
    • D.B. Aichele and A.F. Coxford eds, NCTM, Reston, VA, pp
    • Cooney, T.J.: 1994, 'Teacher education as an exercise in adaptation', in D.B. Aichele and A.F. Coxford (eds.), Professional Development for Teachers of Mathematics, NCTM, Reston, VA, pp. 9-22.
    • (1994) Professional Development for Teachers of Mathematics , pp. 9-22
    • Cooney, T.J.1
  • 9
    • 0009885178 scopus 로고    scopus 로고
    • Conceptualizing teachers' ways of knowing
    • Cooney, T.J.: 1999, 'Conceptualizing teachers' ways of knowing', Educational Studies in Mathematics 38, 163-187.
    • (1999) Educational Studies in Mathematics , vol.38 , pp. 163-187
    • Cooney, T.J.1
  • 10
    • 33645651099 scopus 로고    scopus 로고
    • Examining the mathematics in mathematics teacher education
    • A. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick and F.K.S. Leung eds, Kluwer, Dordrecht, The Netherlands, pp
    • Cooney, T.J. and Wiegel, H.G.: 2003, 'Examining the mathematics in mathematics teacher education', in A. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick and F.K.S. Leung (eds.), Second International Handbook of Mathematics Education, Kluwer, Dordrecht, The Netherlands, pp. 795-828.
    • (2003) Second International Handbook of Mathematics Education , pp. 795-828
    • Cooney, T.J.1    Wiegel, H.G.2
  • 11
    • 0030641564 scopus 로고    scopus 로고
    • A comparison of the geometric reasoning of students attending Israeli ultra-orthodox and mainstream schools
    • Dembo, Y., Levin, I. and Siegler, R.S.: 1997, 'A comparison of the geometric reasoning of students attending Israeli ultra-orthodox and mainstream schools', Developmental Psychology 33, 92-103.
    • (1997) Developmental Psychology , vol.33 , pp. 92-103
    • Dembo, Y.1    Levin, I.2    Siegler, R.S.3
  • 12
    • 18844381870 scopus 로고    scopus 로고
    • Integrating academic and practical knowledge in a teacher leaders' development program
    • Even, R.: 1999, 'Integrating academic and practical knowledge in a teacher leaders' development program', Educational Studies in Mathematics 38, 235-252.
    • (1999) Educational Studies in Mathematics , vol.38 , pp. 235-252
    • Even, R.1
  • 13
    • 0039043013 scopus 로고
    • Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter
    • Even, R. and Tirosh, D.: 1995, 'Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter', Educational Studies in Mathematics 29,1-20.
    • (1995) Educational Studies in Mathematics , vol.29 , pp. 1-20
    • Even, R.1    Tirosh, D.2
  • 14
    • 33947727595 scopus 로고
    • What-if-not? A technique for involving and motivating students in psychology courses
    • S.I. Brown and M.I. Walter eds, Erlbaum, Hillsdale, New Jersey, pp
    • Feibel, W.: 1993, '"What-if-not?" A technique for involving and motivating students in psychology courses', in S.I. Brown and M.I. Walter (eds.), Problem Posing: Reflection and Applications, Erlbaum, Hillsdale, New Jersey, pp. 52-57.
    • (1993) Problem Posing: Reflection and Applications , pp. 52-57
    • Feibel, W.1
  • 17
    • 0010690529 scopus 로고
    • The interaction between the formal, the algorithmic and the intuitive components in a mathematical activity
    • R. Biehler, R.W. Scholz, R. Straesser and B. Winkelmann eds, Kluwer, Dordrecht, The Netherlands, pp
    • Fischbein, E.: 1993a, 'The interaction between the formal, the algorithmic and the intuitive components in a mathematical activity', in R. Biehler, R.W. Scholz, R. Straesser and B. Winkelmann (eds.), Didactics of Mathematics as a Scientific Discipline, Kluwer, Dordrecht, The Netherlands, pp. 231-245.
    • (1993) Didactics of Mathematics as a Scientific Discipline , pp. 231-245
    • Fischbein, E.1
  • 19
    • 33645637724 scopus 로고    scopus 로고
    • Forms of knowing mathematics: What preservice teachers should learn
    • Graeber, A.O.: 1999, 'Forms of knowing mathematics: What preservice teachers should learn', Educational Studies in Mathematics 38, 189-208.
    • (1999) Educational Studies in Mathematics , vol.38 , pp. 189-208
    • Graeber, A.O.1
  • 20
    • 21344483370 scopus 로고
    • Duality, ambiguity and flexibility: A proceptual view of simple arithmetic
    • Gray, E. and Tkll, D.: 1994, 'Duality, ambiguity and flexibility: A proceptual view of simple arithmetic', The Journal for Research in Mathematics Education 26, 115-141.
    • (1994) The Journal for Research in Mathematics Education , vol.26 , pp. 115-141
    • Gray, E.1    Tkll, D.2
  • 21
    • 33645648030 scopus 로고    scopus 로고
    • Educating new mathematics teachers: Integrating theory and practice, and the roles of practicing teachers
    • A. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick and F.K.S. Leung eds, Kluwer, Dordrecht, The Netherlands, pp
    • Jaworski, B. and Gellert, U.: 2003, 'Educating new mathematics teachers: Integrating theory and practice, and the roles of practicing teachers', in A. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick and F.K.S. Leung (eds.), Second International Handbook of Mathematics Education, Kluwer, Dordrecht, The Netherlands, pp. 829-875.
    • (2003) Second International Handbook of Mathematics Education , pp. 829-875
    • Jaworski, B.1    Gellert, U.2
  • 22
    • 0344944201 scopus 로고    scopus 로고
    • Problom posing via "What if not?" strategy in solid geometry - A case study
    • Lavy, I. and Bershadsky, I.: 2003, 'Problom posing via "What if not?" strategy in solid geometry - A case study', Journal of Mathematical Behavior 22, 369-387.
    • (2003) Journal of Mathematical Behavior , vol.22 , pp. 369-387
    • Lavy, I.1    Bershadsky, I.2
  • 24
    • 33645648408 scopus 로고    scopus 로고
    • Situating research on mathematics teachers' beliefs and on change
    • G.C. Leder and E. Pehkonen eds, Kluwer, Dordrecht, The Netherlands, pp
    • Lerman, S.: 2002, 'Situating research on mathematics teachers' beliefs and on change', in G.C. Leder and E. Pehkonen (eds.), Beliefs: A Hidden Variable in Mathematics Education?, Kluwer, Dordrecht, The Netherlands, pp. 233-246.
    • (2002) Beliefs: A Hidden Variable in Mathematics Education , pp. 233-246
    • Lerman, S.1
  • 26
    • 33947725715 scopus 로고    scopus 로고
    • Beyond mere knowledge of mathematics: The importance of knowing-to-act in the moment
    • Mason, J. and Spence, M.: 1999, 'Beyond mere knowledge of mathematics: The importance of knowing-to-act in the moment', Educational Studies in Mathematics 38, 51-66.
    • (1999) Educational Studies in Mathematics , vol.38 , pp. 51-66
    • Mason, J.1    Spence, M.2
  • 27
    • 0347114412 scopus 로고    scopus 로고
    • Preservice teachers' understanding of perimeter and area
    • Menon, R.: 1998, 'Preservice teachers' understanding of perimeter and area', School Science and Mathematics 98(7), 361-368.
    • (1998) School Science and Mathematics , vol.98 , Issue.7 , pp. 361-368
    • Menon, R.1
  • 28
    • 33947727256 scopus 로고    scopus 로고
    • National Council of Teachers of Mathematics [NCTM]: 2000, Professional Standards for Teaching Mathematics, NCTM, Reston, VA.
    • National Council of Teachers of Mathematics [NCTM]: 2000, Professional Standards for Teaching Mathematics, NCTM, Reston, VA.
  • 29
    • 12144250163 scopus 로고
    • Professionalization and mathematics teaching
    • D. A. Grouws ed, Macmillan, New York, pp
    • Noddings, N.: 1992, 'Professionalization and mathematics teaching', in D. A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 197-208.
    • (1992) Handbook of Research on Mathematics Teaching and Learning , pp. 197-208
    • Noddings, N.1
  • 31
    • 0345853184 scopus 로고    scopus 로고
    • Area and perimeter: Prospective teachers' confusion
    • Reinke, K.S.: 1997, 'Area and perimeter: Prospective teachers' confusion', School Science and Mathematics 97(2), 75-77.
    • (1997) School Science and Mathematics , vol.97 , Issue.2 , pp. 75-77
    • Reinke, K.S.1
  • 33
    • 33947716236 scopus 로고
    • A brief and biased history of problem solving
    • F.R. Curcio ed, National Council of Teachers of Mathematics. Reston, Virginia, pp
    • Schoenfeld, A.H.: 1987, 'A brief and biased history of problem solving', in F.R. Curcio (ed.), Teaching and Learning: A Problem-Solving Focus, National Council of Teachers of Mathematics. Reston, Virginia, pp. 27-46.
    • (1987) Teaching and Learning: A Problem-Solving Focus , pp. 27-46
    • Schoenfeld, A.H.1
  • 34
    • 0002242225 scopus 로고
    • Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics
    • D. Grouws ed, Macmillan, New York, pp
    • Schoenfeld, A.H.: 1992, 'Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics', in D. Grouws (ed.), Handbook for Research on Mathematics, Macmillan, New York, pp. 334-370.
    • (1992) Handbook for Research on Mathematics , pp. 334-370
    • Schoenfeld, A.H.1
  • 35
    • 84973848880 scopus 로고
    • Those who understand: Knowledge growth with teaching
    • Shulman, L.S.: 1986, 'Those who understand: Knowledge growth with teaching', Educational Researcher 15(2), 4-14.
    • (1986) Educational Researcher , vol.15 , Issue.2 , pp. 4-14
    • Shulman, L.S.1
  • 40
    • 33947715910 scopus 로고    scopus 로고
    • Tall. D.: 2005, 'A theory of mathematical growth through embodiment, symbolism and proof'. Plenary Lecture for the International Colloquium on Mathematical Learning from Early Childhood to Adulthood, 5-7 July, Belgium.
    • Tall. D.: 2005, 'A theory of mathematical growth through embodiment, symbolism and proof'. Plenary Lecture for the International Colloquium on Mathematical Learning from Early Childhood to Adulthood, 5-7 July, Belgium.
  • 41
    • 0000213855 scopus 로고
    • Concept image and concept definition in mathematics, with special reference to limits and continuity
    • Tall, D. and Vinner, S.: 1981, 'Concept image and concept definition in mathematics, with special reference to limits and continuity', Educational Studies in Mathematics 12, 151-169.
    • (1981) Educational Studies in Mathematics , vol.12 , pp. 151-169
    • Tall, D.1    Vinner, S.2
  • 42
    • 22844453632 scopus 로고    scopus 로고
    • Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions
    • Tirosh, D.: 2000, 'Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions', Journal for Research in Mathematics Education 31, 5-25.
    • (2000) Journal for Research in Mathematics Education , vol.31 , pp. 5-25
    • Tirosh, D.1
  • 43
    • 0041579531 scopus 로고    scopus 로고
    • Intuitive rules: A way to explain and predict students' reasoning
    • Tirosh, D. and Stavy, R.: 1999, 'Intuitive rules: A way to explain and predict students' reasoning', Educational Studies in Mathematics 38, 51-66.
    • (1999) Educational Studies in Mathematics , vol.38 , pp. 51-66
    • Tirosh, D.1    Stavy, R.2
  • 45
    • 13844256055 scopus 로고    scopus 로고
    • Using the intuitive rules theory as a basis for educating teachers
    • F.L. Lin and T. Cooney eds, Kluwer, Dordrecht, The Netherlands
    • Tirosh, D., Stavy, R. and Tsamir, P.: 2001, 'Using the intuitive rules theory as a basis for educating teachers', in F.L. Lin and T. Cooney (eds.), Making Sense of Mathematics Education, Kluwer, Dordrecht, The Netherlands.
    • (2001) Making Sense of Mathematics Education
    • Tirosh, D.1    Stavy, R.2    Tsamir, P.3
  • 46
    • 33645651407 scopus 로고    scopus 로고
    • The intuitive rule "same A-same B": The case of triangles and quadrilaterals
    • Tsamir, P.: 2002, 'The intuitive rule "same A-same B": The case of triangles and quadrilaterals', Focus on Learning Problems in Mathematics 24(4), 54-70.
    • (2002) Focus on Learning Problems in Mathematics , vol.24 , Issue.4 , pp. 54-70
    • Tsamir, P.1
  • 47
    • 33645640922 scopus 로고    scopus 로고
    • Different representations in instruction of vertical angles
    • Tsamir, P.: 2003a, 'Different representations in instruction of vertical angles', Focus on Learning Problems in Mathematics 25(1), 1-13.
    • (2003) Focus on Learning Problems in Mathematics , vol.25 , Issue.1 , pp. 1-13
    • Tsamir, P.1
  • 48
    • 33751335094 scopus 로고    scopus 로고
    • From "easy" to "difficult" or vice versa: The case of infinite sets
    • Tsamir, P.: 2003b, 'From "easy" to "difficult" or vice versa: The case of infinite sets', Focus on Learning Problems in Mathematics 25(2), 1-16.
    • (2003) Focus on Learning Problems in Mathematics , vol.25 , Issue.2 , pp. 1-16
    • Tsamir, P.1
  • 49
    • 33751322198 scopus 로고    scopus 로고
    • Basing instruction on theory and research: What is the impact of an extreme case?
    • Tsamir, P.: 2003c, 'Basing instruction on theory and research: What is the impact of an extreme case?', Focus on Learning Problems in Mathematics 25(4), 4-21.
    • (2003) Focus on Learning Problems in Mathematics , vol.25 , Issue.4 , pp. 4-21
    • Tsamir, P.1
  • 50
    • 33645637414 scopus 로고    scopus 로고
    • The intuitive rule same A - same B: The case of area and perimeter
    • T. Nakahara and M. Koyama eds, Hiroshima, Japan, pp
    • Tsamir, P. and Mandel, N.: 2000, 'The intuitive rule same A - same B: The case of area and perimeter", in T. Nakahara and M. Koyama (eds.), Proceedings of the 24th Annual Meeting for the Psychology of Mathematics Education, Vol. IV, Hiroshima, Japan, pp. 225-232.
    • (2000) Proceedings of the 24th Annual Meeting for the Psychology of Mathematics Education , vol.4 , pp. 225-232
    • Tsamir, P.1    Mandel, N.2
  • 51
    • 33646458558 scopus 로고    scopus 로고
    • Intuitive rules: A theory and its implications to mathematics and science teacher education
    • H. Behrendt, H. Dahncke, R. Duit, W. Gruber, M. Komorek, A. Kross and P. Reiska eds, Kluwer, Dordrecht, The Netherlands, pp
    • Tsamir, P., Tirosh, D., Stavy, R. and Ronen, I.: 2001, 'Intuitive rules: A theory and its implications to mathematics and science teacher education', in H. Behrendt, H. Dahncke, R. Duit, W. Gruber, M. Komorek, A. Kross and P. Reiska (eds.), Research in Science Education - Past, Present and Future, Kluwer, Dordrecht, The Netherlands, pp.167-176.
    • (2001) Research in Science Education - Past, Present and Future , pp. 167-176
    • Tsamir, P.1    Tirosh, D.2    Stavy, R.3    Ronen, I.4
  • 52
    • 0011938298 scopus 로고    scopus 로고
    • The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning
    • Vinner, S.: 1997, The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning', Educational Studies in Mathematics 34, 97-129.
    • (1997) Educational Studies in Mathematics , vol.34 , pp. 97-129
    • Vinner, S.1
  • 54
    • 2442610121 scopus 로고    scopus 로고
    • Exploring the relationships between conceptual change and intentional learning
    • G.M. Sinatra and PR. Pintrich eds, Lawrence Erlbaum, Mahwah, NJ
    • Vosniadou, S.: 2002, 'Exploring the relationships between conceptual change and intentional learning", in G.M. Sinatra and PR. Pintrich (eds.), Intentional Conceptual Change. Lawrence Erlbaum, Mahwah, NJ.
    • (2002) Intentional Conceptual Change
    • Vosniadou, S.1
  • 55
    • 2142669691 scopus 로고    scopus 로고
    • Intuitive rules in number theory: Example of The more of A, the more of B' rule implementation
    • Zazkis, R.: 1999, 'Intuitive rules in number theory: Example of "The more of A, the more of B' rule implementation'", Educational Studies in Mathematics 40(2), 197-209.
    • (1999) Educational Studies in Mathematics , vol.40 , Issue.2 , pp. 197-209
    • Zazkis, R.1


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