메뉴 건너뛰기




Volumn 31, Issue 1, 2012, Pages 73-90

The role of multiple solution tasks in developing knowledge and creativity in geometry

Author keywords

Geometry knowledge; Mathematical creativity; Multiple solution tasks

Indexed keywords


EID: 84155172312     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2011.11.001     Document Type: Article
Times cited : (83)

References (62)
  • 2
    • 34548472125 scopus 로고    scopus 로고
    • Policy, practices and principles in teaching numeracy: What makes a difference?
    • Routledge Falmer, London, GB, P. Gates (Ed.)
    • Askew M. Policy, practices and principles in teaching numeracy: What makes a difference?. Issues in mathematics teaching 2001, 105-119. Routledge Falmer, London, GB. P. Gates (Ed.).
    • (2001) Issues in mathematics teaching , pp. 105-119
    • Askew, M.1
  • 3
    • 0000693952 scopus 로고
    • High school geometry students' justifications for their views of empirical evidence and mathematical proof
    • Chazan D. High school geometry students' justifications for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics 1993, 24:359-387.
    • (1993) Educational Studies in Mathematics , vol.24 , pp. 359-387
    • Chazan, D.1
  • 8
    • 0346976613 scopus 로고
    • Is one proof enough? Travels with a mathematician of the baroque period
    • Dhombres J. Is one proof enough? Travels with a mathematician of the baroque period. Educational Studies in Mathematics 1993, 24:401-419.
    • (1993) Educational Studies in Mathematics , vol.24 , pp. 401-419
    • Dhombres, J.1
  • 9
    • 77957696093 scopus 로고    scopus 로고
    • Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics
    • Elia I., Van den Heuvel-Panhuizen M., Kolovou A. Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM 2009, 41:605-618.
    • (2009) ZDM , vol.41 , pp. 605-618
    • Elia, I.1    Van den Heuvel-Panhuizen, M.2    Kolovou, A.3
  • 10
    • 13544262696 scopus 로고
    • Mathematical creativity
    • Kluwer, Dordrecht, Netherlands, D. Tall (Ed.)
    • Ervynck G. Mathematical creativity. Advanced mathematical thinking 1991, 42-53. Kluwer, Dordrecht, Netherlands. D. Tall (Ed.).
    • (1991) Advanced mathematical thinking , pp. 42-53
    • Ervynck, G.1
  • 11
    • 84155172002 scopus 로고    scopus 로고
    • The ongoing value of proof
    • Hanna G. The ongoing value of proof. Paper presented at the PME 20 1996, retrieved from: http://fcis.oise.utoronto.ca/ghanna/pme96prf.html.
    • (1996) Paper presented at the PME 20
    • Hanna, G.1
  • 12
    • 84155172003 scopus 로고    scopus 로고
    • General considerations on curricula designs in geometry
    • Kluwer, Dordrecht, Netherlands, C. Mammana, V. Villani (Eds.)
    • Hansen V.L. General considerations on curricula designs in geometry. Perspectives on the teaching of geometry for the 21st century 1998, 235-242. Kluwer, Dordrecht, Netherlands. C. Mammana, V. Villani (Eds.).
    • (1998) Perspectives on the teaching of geometry for the 21st century , pp. 235-242
    • Hansen, V.L.1
  • 13
    • 24944551175 scopus 로고
    • A framework for assessing mathematical creativity in schoolchildren
    • Haylock D.W. A framework for assessing mathematical creativity in schoolchildren. Educational Studies in Mathematics 1987, 18:59-74.
    • (1987) Educational Studies in Mathematics , vol.18 , pp. 59-74
    • Haylock, D.W.1
  • 15
    • 0036016398 scopus 로고    scopus 로고
    • Engaging students in proving: A double bind on the teacher
    • Herbst P. Engaging students in proving: A double bind on the teacher. Journal for Research in Mathematics Education 2002, 33:176-203.
    • (2002) Journal for Research in Mathematics Education , vol.33 , pp. 176-203
    • Herbst, P.1
  • 16
    • 33645055667 scopus 로고    scopus 로고
    • Proving and doing proofs in high school geometry classes: What is it that is going on for students?
    • Herbst P., Brach C. Proving and doing proofs in high school geometry classes: What is it that is going on for students?. Cognition and Instruction 2006, 24:73-122.
    • (2006) Cognition and Instruction , vol.24 , pp. 73-122
    • Herbst, P.1    Brach, C.2
  • 17
    • 0039194780 scopus 로고
    • Psychological aspects of learning geometry
    • Cambridge University Press, Cambridge, MA, J. Kilpatric, P. Nesher (Eds.)
    • Hershkowitz R. Psychological aspects of learning geometry. Mathematics and cognition 1990, Cambridge University Press, Cambridge, MA. J. Kilpatric, P. Nesher (Eds.).
    • (1990) Mathematics and cognition
    • Hershkowitz, R.1
  • 22
    • 33847138965 scopus 로고    scopus 로고
    • Cultivating divergent thinking in mathematics through an open-ended approach
    • Kwon O.N., Park J.S., Park J.H. Cultivating divergent thinking in mathematics through an open-ended approach. Asia Pacific Education Review 2006, 7:51-61.
    • (2006) Asia Pacific Education Review , vol.7 , pp. 51-61
    • Kwon, O.N.1    Park, J.S.2    Park, J.H.3
  • 25
    • 2942554254 scopus 로고    scopus 로고
    • Problem-solving preferences of mathematics teachers: Focusing on symmetry
    • Leikin R. Problem-solving preferences of mathematics teachers: Focusing on symmetry. Journal of Mathematics Teacher Education 2003, 6:297-329.
    • (2003) Journal of Mathematics Teacher Education , vol.6 , pp. 297-329
    • Leikin, R.1
  • 27
    • 85126373534 scopus 로고    scopus 로고
    • Exploring mathematical creativity using multiple solution tasks
    • Sense Publisher, Rotterdam, the Netherlands, (Chapter 9), R. Leikin, A. Berman, B. Koichu (Eds.)
    • Leikin R. Exploring mathematical creativity using multiple solution tasks. Creativity in mathematics and the education of gifted students 2009, 129-145. Sense Publisher, Rotterdam, the Netherlands, (Chapter 9). R. Leikin, A. Berman, B. Koichu (Eds.).
    • (2009) Creativity in mathematics and the education of gifted students , pp. 129-145
    • Leikin, R.1
  • 28
    • 34548495342 scopus 로고    scopus 로고
    • Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks
    • Leikin R., Levav-Waynberg A. Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics 2007, 66:349-371.
    • (2007) Educational Studies in Mathematics , vol.66 , pp. 349-371
    • Leikin, R.1    Levav-Waynberg, A.2
  • 29
    • 85011452718 scopus 로고    scopus 로고
    • Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers' knowledge
    • Leikin R., Levav-Waynberg A. Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers' knowledge. Canadian Journal of Science, Mathematics and Technology Education 2008, 8(3):233-251.
    • (2008) Canadian Journal of Science, Mathematics and Technology Education , vol.8 , Issue.3 , pp. 233-251
    • Leikin, R.1    Levav-Waynberg, A.2
  • 30
    • 84155172001 scopus 로고    scopus 로고
    • Development of teachers' conceptions through learning and teaching: Meaning and potential of multiple-solution tasks
    • Leikin R., Levav-Waynberg A. Development of teachers' conceptions through learning and teaching: Meaning and potential of multiple-solution tasks. Canadian Journal of Science, Mathematics and Technology Education 2009, 9(4):203-223.
    • (2009) Canadian Journal of Science, Mathematics and Technology Education , vol.9 , Issue.4 , pp. 203-223
    • Leikin, R.1    Levav-Waynberg, A.2
  • 33
    • 84155163773 scopus 로고    scopus 로고
    • Using multiple solution tasks for the evaluation of students' problem-solving performance in geometry. Canadian Journal of Science, Mathematics and Technology Education, accepted.
    • Levav-Waynberg, A., & Leikin, R. Using multiple solution tasks for the evaluation of students' problem-solving performance in geometry. Canadian Journal of Science, Mathematics and Technology Education, accepted.
    • Levav-Waynberg, A.1    Leikin, R.2
  • 35
    • 38549108482 scopus 로고    scopus 로고
    • A research framework for creative and imitative reasoning
    • Lithner J. A research framework for creative and imitative reasoning. Educational Studies in Mathematics 2008, 67:255-276.
    • (2008) Educational Studies in Mathematics , vol.67 , pp. 255-276
    • Lithner, J.1
  • 37
    • 84155162359 scopus 로고    scopus 로고
    • National Council of Teachers of Mathematics (NCTM). Principles and standards for school mathematics. Reston, VA.
    • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA.
    • (2000)
  • 38
    • 84155170658 scopus 로고    scopus 로고
    • General tendencies in the development of geometry teaching in the past two decades
    • Kluwer, Dordrecht, Netherlands, C. Mammana, V. Villani (Eds.)
    • Neubrand M. General tendencies in the development of geometry teaching in the past two decades. Perspectives on the teaching of geometry for the 21st century 1998, 226-228. Kluwer, Dordrecht, Netherlands. C. Mammana, V. Villani (Eds.).
    • (1998) Perspectives on the teaching of geometry for the 21st century , pp. 226-228
    • Neubrand, M.1
  • 40
    • 33751564002 scopus 로고
    • On learning, teaching, and learning teaching
    • Polya G. On learning, teaching, and learning teaching. American Mathematical Monthly 1963, 70:605-619.
    • (1963) American Mathematical Monthly , vol.70 , pp. 605-619
    • Polya, G.1
  • 45
    • 78651241383 scopus 로고
    • When good teaching leads to bad results: The disasters of well-taught mathematics courses
    • Schoenfeld A.H. When good teaching leads to bad results: The disasters of well-taught mathematics courses. Educational Psychologist 1988, 23:145-166.
    • (1988) Educational Psychologist , vol.23 , pp. 145-166
    • Schoenfeld, A.H.1
  • 47
    • 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 1991, 22:1-36.
    • (1991) Educational Studies in Mathematics , vol.22 , pp. 1-36
    • Sfard, A.1
  • 49
    • 34250900300 scopus 로고    scopus 로고
    • Fostering creativity through instruction rich in mathematical problem solving and problem posing
    • Silver E.A. Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM-Zentralblatt fuer Didaktik der Mathematik 1997, 3:75-80.
    • (1997) ZDM-Zentralblatt fuer Didaktik der Mathematik , vol.3 , pp. 75-80
    • Silver, E.A.1
  • 51
    • 77951879522 scopus 로고    scopus 로고
    • Are giftedness and creativity synonyms in mathematics?
    • Sriraman B. Are giftedness and creativity synonyms in mathematics?. The Journal of Secondary Gifted Education 2005, 1:20-36.
    • (2005) The Journal of Secondary Gifted Education , vol.1 , pp. 20-36
    • Sriraman, B.1
  • 52
    • 77951878701 scopus 로고    scopus 로고
    • The characteristics of mathematical creativity
    • Sriraman B. The characteristics of mathematical creativity. ZDM 2009, 41:13-27.
    • (2009) ZDM , vol.41 , pp. 13-27
    • Sriraman, B.1
  • 53
    • 77957875217 scopus 로고    scopus 로고
    • The nature and development of experts' strategy flexibility for solving equations
    • Star J.R., Newton J.K. The nature and development of experts' strategy flexibility for solving equations. ZDM 2009, 41:557-567.
    • (2009) ZDM , vol.41 , pp. 557-567
    • Star, J.R.1    Newton, J.K.2
  • 54
    • 53049092693 scopus 로고    scopus 로고
    • Flexibility in problem solving: The case of equation solving
    • Star J.R., Rittle-Johnson B. Flexibility in problem solving: The case of equation solving. Learning and Instruction 2008, 18:565-579.
    • (2008) Learning and Instruction , vol.18 , pp. 565-579
    • Star, J.R.1    Rittle-Johnson, B.2
  • 55
  • 57
    • 84155163772 scopus 로고    scopus 로고
    • Jump or compensate? Strategy flexibility in the number domain up to 100
    • Torbeyns J., De Smedt B., Ghesquière P., Verschaffel L. Jump or compensate? Strategy flexibility in the number domain up to 100. ZDM 2009, 41:581-590.
    • (2009) ZDM , vol.41 , pp. 581-590
    • Torbeyns, J.1    De Smedt, B.2    Ghesquière, P.3    Verschaffel, L.4
  • 59
    • 0010853702 scopus 로고
    • Avoidance of visual considerations in calculus students
    • Vinner S. Avoidance of visual considerations in calculus students. Focus on Learning Problems in Mathematics 1989, 11:149-156.
    • (1989) Focus on Learning Problems in Mathematics , vol.11 , pp. 149-156
    • Vinner, S.1
  • 61
    • 84155163770 scopus 로고    scopus 로고
    • Using comparison to develop flexibility for teaching algebra
    • Yakes C., Star J.R. Using comparison to develop flexibility for teaching algebra. Journal of Mathematics Teacher Education 2009, retrieved from: http://www.springerlink.com/content/v21k817n9168x842/fulltext.pdf.
    • (2009) Journal of Mathematics Teacher Education
    • Yakes, C.1    Star, J.R.2
  • 62
    • 51549113561 scopus 로고    scopus 로고
    • Exemplifying definitions: Example generation for the analysis of mathematics knowledge
    • Zazkis R., Leikin R. Exemplifying definitions: Example generation for the analysis of mathematics knowledge. Educational Studies in Mathematics 2008, 69:131-148.
    • (2008) Educational Studies in Mathematics , vol.69 , pp. 131-148
    • Zazkis, R.1    Leikin, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.