Proof schemes and learning strategies of above-average mathematics students

Educational Studies in Mathematics

Volumn 53, Issue 2, 2003, Pages 139-158

  Housman, David ^a   Porter, Mary ^b  

^a GOSHEN COLLEGE   (United States)

^b SAINT MARY'S COLLEGE   (United States)

Author keywords

Above average; College mathematics; Learning strategies; Proof; Proof schemes

Indexed keywords

EID: 3843121015     PISSN: 00131954     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025541416693     Document Type: Article

References (22)

1. Balacheff, N.: 1991, 'Benefits and limits of social interaction: The case of teaching mathematical proof', in A. Bishop, S. Mellin-Olsen and J. van Dormolen (eds.), Mathematical Knowledge: Its Growth Through Teaching, Kluwer, Dordrecht, pp. 175-192.
2. Bell, A.: 1978, 'The learning of process aspects of mathematics', Proceedings of the 2nd International Conference, Psychology of Mathematics Education, Osnabrück, West Germany, pp. 48-78.
3. Breidenbach, D., Dubinsky, E., Hawks, J. and Nichols D.: 1992, 'Development of the process conception of function', Educational Studies in Mathematics 23, 247-285.
4. Chazan, D.: 1993, 'High school geometry students' justification for their views of empirical evidence and mathematical proof', Educational Studies in Mathematics 24, 359-387.
5. Dahlberg, R.P. and Housman, D.L.: 1997, 'Facilitating learning events through example generation', Educational Studies in Mathematics 33, 283-299.
6. Galbraith, P.L.: 1981, 'Aspects of proving: A clinical investigation of process', Educational Studies in Mathematics 12, 1-28.
7. Goetting, M.: 1995, The College Student's Understanding of Mathematical Proof, Doctoral Dissertation, University of Maryland.
8. Hanna, G. and Jahnke, N.: 1993, 'Proof and application', Educational Studies in Mathematics 24, 421-438.
9. Harel, G. and Sowder, L.: 1998, 'Students' proof schemes: Results from exploratory studies', in E. Dubinsky, A. Schoenfeld and J. Kaput (eds.), Research in Collegiate Mathematics Education, III, American Mathematical Society, Providence, RI, pp. 234-283.
10. Harel, G.: 2002, 'The development of mathematical induction as a proof scheme: A model for DNR-based instruction', in S.R. Campbell and R. Zazkis (eds.), Learning and Teaching Number Theory: Research in Cognition and Instruction, Ablex, Westport, CT, pp. 185-212.
11. Horgan, J.: 1993, 'The death of proof', Scientific American 269(4), 93-103.
12. Hoyles, C.: 1997, 'The curricular shaping of students' approaches to proof', For the Learning of Mathematics 17(1), 7-16.
13. Lewis, S.M.: 1986, 'University mathematics students' perception of proof and its relationship to achievement', Dissertation Abstracts International 47, 3345A.
14. Martin, W.G. and Harel, G.: 1989, 'Proof frames of preservice elementary teachers', Journal for Research in Mathematics Education 20(1), 41-51.
15. Moore, R.C.: 1994, 'Making the transition to formal proof', Educational Studies in Mathematics 27, 249-266.
16. Selden, A. and Selden, J.: 2003, 'Validation of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?', Journal for Research in Mathematics Education 34(1), 4-36.
17. Selden, J. and Selden, A.: 1995, 'Unpacking the logic of mathematical statements', Educational Studies of Mathematics 29, 123-151.
18. Simon, M. and Blume, G.: 1996, 'Justification in the mathematics classroom: A study of prospective elementary teachers', Journal of Mathematical Behavior 15, 3-31.
19. Sowder, L. and Harel, G.: 1998, 'Types of students' justifications', The Mathematics Teacher 91(8), 670-675.
20. Tall, D.O. and Vinner, S.: 1981, 'Concept image and concept definition in mathematics, with particular reference to limits and continuity', Educational Studies in Mathematics 12, 151-169.
21. Tall, D.O.: 1992, 'The transition to advanced mathematical thinking: functions, limits, infinity, and proof', in D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 495-511.
22. Zaslavsky, O. and Peled, I.: 1996, 'Inhibiting factors in generating examples by mathematics teachers and student teachers: The case of binary operation', Journal for Research in Mathematics Education 27(1), 67-78.