메뉴 건너뛰기




Volumn 24, Issue 3-4, 2005, Pages 385-401

The identity of problem solving

Author keywords

Application of knowledge; Conceptualization; Exploration; Problem posing; Problem solving; Proof; Reading mathematical text; Representation

Indexed keywords


EID: 29444454722     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2005.09.011     Document Type: Article
Times cited : (36)

References (53)
  • 1
    • 0003599607 scopus 로고    scopus 로고
    • Theory of didactical situations in mathematics
    • N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds. and Trans.) Dordrecht: Kluwer Academic Publishers
    • Brousseau, G. (1997). Theory of didactical situations in mathematics. In N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds. and Trans.), Didactique des mathématiques 1970-1990. Dordrecht: Kluwer Academic Publishers.
    • (1997) Didactique Des Mathématiques 1970-1990
    • Brousseau, G.1
  • 4
    • 0007328245 scopus 로고    scopus 로고
    • Why is intuition so important to mathematicians but missing from mathematics education?
    • L. Burton Why is intuition so important to mathematicians but missing from mathematics education? For the Learning of Mathematics 19 3 1999 27-32
    • (1999) For the Learning of Mathematics , vol.19 , Issue.3 , pp. 27-32
    • Burton, L.1
  • 6
    • 80052358657 scopus 로고    scopus 로고
    • What research tells us about teaching mathematics through problem solving
    • F. Lester (Ed.) National Council of Teachers of Mathematics Reston, VA
    • J. Cai What research tells us about teaching mathematics through problem solving In: F. Lester (Ed.) Research and issues in teaching mathematics through problem solving 2003 National Council of Teachers of Mathematics Reston, VA
    • (2003) Research and Issues in Teaching Mathematics Through Problem Solving
    • Cai, J.1
  • 7
    • 29444438295 scopus 로고    scopus 로고
    • Abductive inference: Connections between problem posing and solving
    • Haifa, Israel
    • Cifarelli, V. (1999). Abductive inference: Connections between problem posing and solving. Proceedings of PME 23 (Vol. II, pp. 217-224). Haifa, Israel.
    • (1999) Proceedings of PME 23 , vol.2 , pp. 217-224
    • Cifarelli, V.1
  • 8
    • 84888813800 scopus 로고    scopus 로고
    • The proof language as a regulator of rigor in proof, and its effect on student behavior
    • (in press). Group - 14
    • Downs, M. L. N., & Mamona-Downs, J. (in press). The proof language as a regulator of rigor in proof, and its effect on student behavior. Proceedings of CERME 4, Group - 14.
    • Proceedings of CERME 4
    • Downs, M.L.N.1    Mamona-Downs, J.2
  • 9
    • 29444448651 scopus 로고    scopus 로고
    • Eliciting students' dilemmas through activities that involve posing questions or reformulation of problems
    • Cuernavaca, Morelos, Mexico
    • Estrada, J., & Santos, M. (1999). Eliciting students' dilemmas through activities that involve posing questions or reformulation of problems. Proceedings of PME - NA 21 (Vol. 2, pp. 566-571). Cuernavaca, Morelos, Mexico.
    • (1999) Proceedings of PME - NA 21 , vol.2 , pp. 566-571
    • Estrada, J.1    Santos, M.2
  • 11
    • 0010048980 scopus 로고
    • Structures variables in problem solving
    • G.A. Goldin & C.E. McClintock (Eds.) The Franklin Institute Press Philadelphia, PA
    • G.A. Goldin Structures variables in problem solving In: G.A. Goldin & C.E. McClintock (Eds.) Task variables in mathematical problem solving 1984 The Franklin Institute Press Philadelphia, PA 103-164
    • (1984) Task Variables in Mathematical Problem Solving , pp. 103-164
    • Goldin, G.A.1
  • 12
    • 0032324617 scopus 로고    scopus 로고
    • Representational systems, learning and problem solving in mathematics
    • G.A. Goldin Representational systems, learning and problem solving in mathematics The Journal of Mathematical Behavior 17 1998 137-165
    • (1998) The Journal of Mathematical Behavior , vol.17 , pp. 137-165
    • Goldin, G.A.1
  • 13
    • 3843146632 scopus 로고    scopus 로고
    • Representation in mathematical learning and problem solving
    • L.D. English (Ed.) Erlbaum Mahwah, NJ
    • G.A. Goldin Representation in mathematical learning and problem solving In: L.D. English (Ed.) Handbook of international research in mathematics education 2002 Erlbaum Mahwah, NJ 197-218
    • (2002) Handbook of International Research in Mathematics Education , pp. 197-218
    • Goldin, G.A.1
  • 16
    • 84888807897 scopus 로고
    • Experimentation and conjecture are not enough
    • D.T. Haimo Experimentation and conjecture are not enough American Mathematical Monthly 102 2 1995 102-112
    • (1995) American Mathematical Monthly , vol.102 , Issue.2 , pp. 102-112
    • Haimo, D.T.1
  • 17
    • 0001099510 scopus 로고    scopus 로고
    • Students' proof schemes: Results from exploratory Studies
    • A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.) Washington DC: Conference Board of the Mathematical Sciences
    • Harel, G., & Sowder, L. (1998). Students' proof schemes: Results from exploratory Studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education: Vol. 3. Issues in mathematical education (No. 7, pp. 234-283). Washington DC: Conference Board of the Mathematical Sciences.
    • (1998) Research in Collegiate Mathematics Education: Vol. 3. Issues in Mathematical Education , Issue.7 , pp. 234-283
    • Harel, G.1    Sowder, L.2
  • 19
    • 29444437583 scopus 로고
    • Research into the construction of mathematical texts
    • J. Konior Research into the construction of mathematical texts Educational Studies in Mathematics 24 3 1993 251-256
    • (1993) Educational Studies in Mathematics , vol.24 , Issue.3 , pp. 251-256
    • Konior, J.1
  • 20
    • 0002363373 scopus 로고    scopus 로고
    • Control processes in remembering
    • E. Tulving & F.I.M. Craik (Eds.) Oxford University Press Oxford
    • A. Koriat Control processes in remembering In: E. Tulving & F.I.M. Craik (Eds.) The Oxford handbook of memory 2000 Oxford University Press Oxford 333-346
    • (2000) The Oxford Handbook of Memory , pp. 333-346
    • Koriat, A.1
  • 22
    • 0001203289 scopus 로고
    • Structuring mathematical proofs
    • U. Leron Structuring mathematical proofs The American Mathematical Monthly 90 3 1983 174-184
    • (1983) The American Mathematical Monthly , vol.90 , Issue.3 , pp. 174-184
    • Leron, U.1
  • 23
    • 0039345889 scopus 로고
    • Musings about mathematical problem solving research: 1970-1994
    • F.K. Lester Jr. Musings about mathematical problem solving research: 1970-1994 Journal for Research in Mathematics Education 25 6 1994 660-675
    • (1994) Journal for Research in Mathematics Education , vol.25 , Issue.6 , pp. 660-675
    • Lester Jr., F.K.1
  • 24
    • 84880648660 scopus 로고    scopus 로고
    • Accessing knowledge for problem solving
    • I. Vakalis, D. Hughes-Hallet, et al. (Compilers) (At the Undergraduate Level), Crete Univ., Iraklion, Greece. New York: John Wiley
    • Mamona-Downs, J. (2002). Accessing knowledge for problem solving [Electronic version]. In I. Vakalis, D. Hughes-Hallet, et al. (Compilers), Proceedings of the 2nd International Conference on the Teaching of Mathematics (At the Undergraduate Level), Crete Univ., Iraklion, Greece. New York: John Wiley.
    • (2002) Proceedings of the 2nd International Conference on the Teaching of Mathematics
    • Mamona-Downs, J.1
  • 25
    • 4544315276 scopus 로고    scopus 로고
    • Realization of techniques in problem solving: The construction of bijections for enumeration tasks
    • J. Mamona-Downs & M.L.N. Downs Realization of techniques in problem solving: The construction of bijections for enumeration tasks Educational Studies in Mathematics 56 2004 235-253
    • (2004) Educational Studies in Mathematics , vol.56 , pp. 235-253
    • Mamona-Downs, J.1    Downs, M.L.N.2
  • 26
    • 29444432933 scopus 로고
    • (March). Paper presented in honor of David Tall at the Centre for Mathematics Education of the Open University, Milton Keynes, UK
    • Mason, J. (1995, March). Abduction as the heart of mathematical being. Paper presented in honor of David Tall at the Centre for Mathematics Education of the Open University, Milton Keynes, UK.
    • (1995) Abduction As the Heart of Mathematical Being
    • Mason, J.1
  • 27
    • 29444458419 scopus 로고    scopus 로고
    • Structure of attention in the learning of mathematics
    • J. Novotnà (Ed.) Prague: Charles University
    • Mason, J. (2003). Structure of attention in the learning of mathematics. In J. Novotnà (Ed.), Proceedings, International Symposium on Elementary Mathematics Teaching (pp. 9-16). Prague: Charles University.
    • (2003) Proceedings, International Symposium on Elementary Mathematics Teaching , pp. 9-16
    • Mason, J.1
  • 28
    • 84888770833 scopus 로고    scopus 로고
    • An experience of problem solving in mathematical analysis
    • (in press). Group-14
    • Menghini, M., & Bagni, G. (in press). An experience of problem solving in mathematical analysis. Proceedings of CERME 4, Group-14.
    • Proceedings of CERME 4
    • Menghini, M.1    Bagni, G.2
  • 29
    • 29444438018 scopus 로고    scopus 로고
    • Language and assessment issues in mathematics education
    • Valencia, Spain
    • Morgan, C. (1996). Language and assessment issues in mathematics education. Proceedings of PME 20 (Vol. 4, pp. 19-26). Valencia, Spain.
    • (1996) Proceedings of PME 20 , vol.4 , pp. 19-26
    • Morgan, C.1
  • 30
    • 0031521276 scopus 로고    scopus 로고
    • Giving new senses to the existing elements: A characteristic of the solution accompanied by global restructuring
    • K. Nunokawa Giving new senses to the existing elements: A characteristic of the solution accompanied by global restructuring The Journal of Mathematical Behavior 16 1997 365-378
    • (1997) The Journal of Mathematical Behavior , vol.16 , pp. 365-378
    • Nunokawa, K.1
  • 31
    • 29444446553 scopus 로고    scopus 로고
    • Geometry problem solving in a computational environment: Advantages and reservations
    • Paper presented at ICME 10, TSG 18. Copenhagen, Denmark
    • Papadopoulos, I. (2004). Geometry problem solving in a computational environment: Advantages and reservations. Paper presented at ICME 10, TSG 18. Copenhagen, Denmark.
    • (2004)
    • Papadopoulos, I.1
  • 32
    • 8644238718 scopus 로고    scopus 로고
    • Building formal mathematics on visual imagery: A case study and a theory
    • M. Pinto & D. Tall Building formal mathematics on visual imagery: A case study and a theory For the Learning of Mathematics 22 1 2002 2-10
    • (2002) For the Learning of Mathematics , vol.22 , Issue.1 , pp. 2-10
    • Pinto, M.1    Tall, D.2
  • 33
    • 0004235832 scopus 로고
    • 2nd ed. Princeton: Princeton University Press
    • G. Polya How to solve it 2nd ed. 1973 Princeton University Press Princeton
    • (1973) How to Solve It
    • Polya, G.1
  • 34
    • 3543046786 scopus 로고    scopus 로고
    • A Comparison of verbal and written descriptions of students' problem solving processes
    • D.K. Pugalee A Comparison of verbal and written descriptions of students' problem solving processes Educational Studies in Mathematics 55 1-3 2004 27-47
    • (2004) Educational Studies in Mathematics , vol.55 , Issue.1-3 , pp. 27-47
    • Pugalee, D.K.1
  • 35
    • 4544320620 scopus 로고    scopus 로고
    • Key ideas: What are they and how can they help us understanding how people view proof?
    • M. Raman Key ideas: What are they and how can they help us understanding how people view proof? Educational Studies in Mathematics 52 2003 319-325
    • (2003) Educational Studies in Mathematics , vol.52 , pp. 319-325
    • Raman, M.1
  • 38
    • 0002242225 scopus 로고
    • Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics
    • D. Grouws (Eds.) Macmillan New York
    • A. Schoenfeld Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics In: D. Grouws (Eds.) Handbook of research on mathematics teaching and learning 1992 Macmillan New York 334-370
    • (1992) Handbook of Research on Mathematics Teaching and Learning , pp. 334-370
    • Schoenfeld, A.1
  • 40
    • 0013007169 scopus 로고    scopus 로고
    • Why can't calculus students access their knowledge to solve non-routine problems?
    • J. Kaput, A. Schoenfeld, & E. Dubinsky (Eds.) Washington DC: Conference Board of the Mathematical Sciences
    • Selden, A., Selden, J., Hauk, S., & Mason, A. (2000). Why can't calculus students access their knowledge to solve non-routine problems? In J. Kaput, A. Schoenfeld, & E. Dubinsky (Eds.), Research in collegiate mathematics education: Vol. 4. Issues in mathematical education (No. 8, pp. 128-153). Washington DC: Conference Board of the Mathematical Sciences.
    • (2000) Research in Collegiate Mathematics Education: Vol. 4. Issues in Mathematical Education , Issue.8 , pp. 128-153
    • Selden, A.1    Selden, J.2    Hauk, S.3    Mason, A.4
  • 41
    • 0037257290 scopus 로고    scopus 로고
    • Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?
    • A. Selden & J. Selden Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education 34 1 2003 4-36
    • (2003) Journal for Research in Mathematics Education , vol.34 , Issue.1 , pp. 4-36
    • Selden, A.1    Selden, J.2
  • 42
  • 43
    • 21444460055 scopus 로고    scopus 로고
    • An analysis of arithmetic problem posing by middle school students
    • E. Silver & J. Cai An analysis of arithmetic problem posing by middle school students Journal for Research in Mathematics Education 27 5 1996 521-539
    • (1996) Journal for Research in Mathematics Education , vol.27 , Issue.5 , pp. 521-539
    • Silver, E.1    Cai, J.2
  • 44
    • 29444452582 scopus 로고
    • Stimulating problem posing in mathematics instruction
    • G. Blume & M.K. Heid (Eds.) Pennsylvania Council of Teachers of Mathematics University Park, PA
    • E. Silver & J. Mamona Stimulating problem posing in mathematics instruction In: G. Blume & M.K. Heid (Eds.) Implementing new curriculum and evaluation standards 1989 Pennsylvania Council of Teachers of Mathematics University Park, PA 1-7
    • (1989) Implementing New Curriculum and Evaluation Standards , pp. 1-7
    • Silver, E.1    Mamona, J.2
  • 45
    • 29444448064 scopus 로고    scopus 로고
    • Paper presented in ICME 10, TSG 18. Copenhagen, Denmark
    • Southwell, B. (2004). Investigating problem solving. Paper presented in ICME 10, TSG 18. Copenhagen, Denmark.
    • (2004) Investigating Problem Solving
    • Southwell, B.1
  • 46
    • 0004292754 scopus 로고
    • 1st ed. Cambridge: Cambridge University Press
    • I. Stewart D. Tall Complex Analysis 1st ed. 1983 Cambridge University Press Cambridge
    • (1983) Complex Analysis
    • Stewart, I.1    Tall, D.2
  • 47
  • 48
    • 0032324612 scopus 로고    scopus 로고
    • A comprehensive theory of representation for mathematics education
    • G. Vergnaud A comprehensive theory of representation for mathematics education The Journal of Mathematical Behavior 17 2 1998 167-181
    • (1998) The Journal of Mathematical Behavior , vol.17 , Issue.2 , pp. 167-181
    • Vergnaud, G.1
  • 51
    • 2942589599 scopus 로고    scopus 로고
    • Student difficulty in constructing proofs: The need for strategic knowledge
    • K. Weber Student difficulty in constructing proofs: The need for strategic knowledge Educational Studies in Mathematics 48 1 2002 101-119
    • (2002) Educational Studies in Mathematics , vol.48 , Issue.1 , pp. 101-119
    • Weber, K.1
  • 53
    • 29444456255 scopus 로고    scopus 로고
    • Changing attitudes to university mathematics through problem solving
    • Y.M. Yosof& D. Tall Changing attitudes to university mathematics through problem solving Educational Studies in Mathematics 37 1 1999 67-82
    • (1999) Educational Studies in Mathematics , vol.37 , Issue.1 , pp. 67-82
    • Yosof, Y.M.1    Tall, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.