Problem-solving, proving, and learning: The relationship between problem-solving processes and learning opportunities in the activity of proof construction

Journal of Mathematical Behavior

Volumn 24, Issue 3-4, 2005, Pages 351-360

  Weber, Keith ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Learning; Problem solving; Problem solving processes; Proof; Reasoning

Indexed keywords

EID: 29444445929     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2005.09.005     Document Type: Article

References (34)

1. L. Alcock & A. Simpson Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role Educational Studies in Mathematics 57 2004 1-32
2. L. Alcock & A. Simpson Convergence of sequences and series 2: Interactions between non-visual reasoning and the learner's beliefs about their own role Educational Studies in Mathematics 58 1 2005 77-110
3. Alcock, L., & Weber, K. (in press). Referential and syntactic approaches to proving: Case studies from a transition-to-proof course. Research in Collegiate Mathematics Education.
4. D. Alibert M. Thomas Research on mathematical proof In: D. Tall (Ed.) Advanced mathematical thinking 1991 Kluwer Dordrecht 215-230
5. J.R. Anderson Cognitive psychology and its implications 5th ed. 2000 Worth Publishers New York
6. P. Cobb A. Boufi K. McCain & J. Whitenack Reflective discourse and collective reflection Journal for Research in Mathematics Education 28 2 1997 258-277
7. T. Fukawa-Connelly Thoughts on learning advanced mathematics For the Learning of Mathematics 25 2 2005 33-35
8. E. Gray D. Pitta M. Pinto & D. Tall Knowledge construction and divergent thinking in elementary and advanced mathematics Educational Studies in Mathematics 38 1999 111-133
9. G. Hanna Some pedagogical aspects of proof Interchange 21 1990 6-13
10. Harel, G., & Sowder, L. (1998). Students' proof schemes: Results from exploratory studies. CBMS issues in mathematics education, 7: Research in collegiate mathematics education III (pp. 234-283).
11. O. Hazzan Reducing abstraction: The case of constructing an operation table for a group Journal of Mathematical Behavior 20 2001 163-172
12. D.A. Hinsley J.R. Hayes & H.A. Simon From words to equations: Meaning and representation in algebra word problems In: P. Carpenter & M. Just (Eds.) Cognitive processes in comprehension 1978 Lawrence Erlbaum Hillsdale, NJ
13. K.R. Koedinger & J.R. Anderson Reifying implicit planning in geometry: Guidelines for model-based intelligent tutoring system design In: S. Derry & S. Lajoie (Eds.) Computers as cognitive tools 1993 Lawrence Erlbaum Associates Hillsdale, NJ
14. Lester, F. K., & Garafalo, J. (1982). Metacognitive aspects of elementary school students' performance on arithmetic tasks. Paper presented at the annual meeting of the American Educational Research Association, New York.
15. J. Lithner Students' mathematical reasoning in university textbook exercises Educational Studies in Mathematics 52 2003 29-55
16. Maher, C. (2002). How students structure their own investigations and educate us: What we've learned from a fourteen-year case study. In: A. D. Cockburn, & E. Nardi (Eds.) Proceedings of the 26th Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 31-46). Norwich, England.
17. Mamona-Downs, J., & Downs, M. (this issue). The identity of problem solving. Journal of Mathematical Behavior.
18. Nunokawa, K. (this issue). Mathematical problem solving and learning mathematics: What we expect students to obtain. Journal of Mathematical Behavior.
19. Pinto, M. M. F., & Tall, D. (1999). Student constructions of formal theories: Giving and extracting meaning. In Proceedings of the Twenty-third Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 281-288). Haifa, Israel.
20. G. Polya How to solve it 1945 Princeton University Press Princeton
21. M. Raman Key ideas: What are they and how can they help us understand how people view proof? Educational Studies in Mathematics 52 2003 319-325
22. M.M. Rodd On mathematical warrants: Proof does not always a warrant and a warrant may be other than a proof Mathematical Thinking and Learning 2 2000 221-244
23. A. Schoenfeld Mathematical problem solving 1985 Academic Press Orlando
24. A. Schoenfeld Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics In: D.A. Grouws (Ed.) Handbook for research on mathematics teaching and learning 1992 Macmillan New York
25. T.L. Schroeder & F.K. Lester Developing understanding in mathematics via problem solving In: R. Trafton (Eds.) New directions for elementary school mathematics, 1989 yearbook of the National Council of Teachers of Mathematics 1990 NCTM Reston, VA
26. J. Selden & A. Selden Unpacking the logic of mathematical statements Educational Studies in Mathematics 29 2 1995 123-151
27. Stacey, K. (this issue). Directions for research on problem-solving as a fundamental but elusive goal of mathematics teaching. Journal of Mathematical Behavior.
28. K. Stacey & M. McGregor Taking the algebraic thinking out of algebra Mathematics Education Research Journal 11 1 1999 25-38
29. K. Weber Student difficulty in constructing proofs: The need for strategic knowledge Educational Studies in Mathematics 48 1 2001 101-119
30. K. Weber Traditional instruction in advanced mathematics classrooms: A case study of one professor's lectures and proofs in an introductory real analysis course Journal of Mathematical Behavior 23 2004 115-133
31. Weber, K. (in press-a). Investigating and teaching the processes used to construct proofs. Research in Collegiate Mathematics Education.
32. Weber, K. (in press-b). A procedural route toward understanding aspects of proof: Case studies from real analysis. Canadian Journal of Science, Mathematics, and Technology Education.
33. K. Weber & L. Alcock Semantic and syntactic proof productions Educational Studies in Mathematics 56 2004 209-234
34. Weber, K., Alcock, L., & Radu, I. (in press). Undergraduates' use of examples in a transition-to-proof course, Proceedings of the 27th Conference for the North American Chapter of the Psychology of Mathematics Education, Roanoke, VA.