Secondary school teachers' awareness of numerical examples as proof

Research in Mathematics Education

Volumn 12, Issue 2, 2010, Pages 117-131

  Tabach, Michal ^a   Levenson, Esther ^a   Barkai, Ruthi ^a   Tirosh, Dina ^a   Tsamir, Pessia ^a   Dreyfus, Tommy ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Counterexamples; Justifications; Numerical examples; Practising teachers' knowledge of proofs

Indexed keywords

EID: 79960320845     PISSN: 14794802     EISSN: 17540178     Source Type: Journal    
DOI: 10.1080/14794802.2010.496973     Document Type: Article

References (26)

1. Balacheff, N. 1986. Cognitive versus situational analysis of problem-solving behaviors. For the Learning of Mathematics 6, no. 3: 10-2.
2. Balacheff, N. 1991a. Treatment of refutations: Aspects of the complexity of a constructivist approach to mathematics learning. In Radical constructivism in mathematics education, ed. E. von Glasersfeld, 89-110. Dordrecht, The Netherlands: Kluwer Academic Publishers.
3. Balacheff, N. 1991b. Benefits and limits of social interaction: The case of teaching mathematical proof. In Mathematical knowledge: Its growth through teaching, ed. A. Bishop, S. Mellin-Olsen, and J. van Dormolen, 175-92. Dordrecht, The Netherlands: Kluwer Academic Publishers.
4. Balacheff, N. 2002. The researcher epistemology: A deadlock from educational research on proof. In International Conference on Mathematics Education-Understanding proving and proving understanding, ed. F.L. Lin, 23-44. Taipei, Taiwan: NCS and NUST.
5. Bell, A.W. 1976. A study of pupils' proof-explanations in mathematical situations. Educational Studies in Mathematics 7, nos. 1 and 2: 23-40.
6. Dreyfus, T. 2000. Some views on proofs by teachers and mathematicians. In Proceedings of the 2nd Mediterranean Conference on Mathematics Education, ed. A. Gagatsis, Vol. I 11-25. Nicosia, Cyprus: The University of Cyprus.
7. Fischbein, E., and I. Kedem. 1982. Proof and certitude in the development of mathematical thinking. In Proceedings of the 6th Conference of the International Group for the Psychology of Mathematics Education, ed. A. Vermandel, 128-31. Antwerp, Belgium: Universitaire Instelling.
8. Galbraith, P. 1981. Aspects of proving: A clinical investigation of process. Educational Studies in Mathematics 12, no. 1: 1-28.
9. Harel, G., and L. Sowder. 1998. Students' proof schemes: Results from exploratory studies. In Research in collegiate mathematics education, ed. A.H. Schoenfeld, J. Kaput, and E. Dubinsky, 234-83. Providence, RI: American Mathematical Society.
10. Healy, L., and C. Hoyles. 1998. Justifying and proving in school mathematics. Technical Report. London: Institute of Education, University of London.
11. Healy, L., and C. Hoyles. 2000. A study of proof conceptions in algebra. Journal for Research in Mathematics Education 31, no. 4: 396-428.
12. Knuth, E.J. 2002. Secondary school mathematics teachers' conceptions of proof. Journal for Research in Mathematics Education 33, no. 5: 379-405.
13. Ko, Y.Y., and E. Knuth. 2009. Problems manifested in prospective secondary mathematics teachers' proofs and counterexamples in differentiation. In Proceedings of the ICMI Study 19 Conference: Proof and proving in mathematics education, ed. F.L. Lin, F.J. Hsieh, G. Hanna and M. de Villiers, Vol. 1 262-7. Taipei, Taiwan: National Taiwan Normal University.
14. Moore, R.C. 1994. Making the transition to formal proof. Educational Studies in Mathematics 27, no. 3: 249-66.
15. NCTM (National Council of Teachers of Mathematics). 2000. Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
16. NCTM (National Council of Teachers of Mathematics). 2009. Focus in high school mathematics: Reasoning and sense making. Reston, VA: National Council of Teachers of Mathematics. Retrieved October 10, 2009, from http://www.nctm.org/.
17. Selden, J., and A. Selden. 1995. Unpacking the logic of mathematical statements. Educational Studies in Mathematics 29, no. 7: 123-51.
18. Shulman, L. 1986. Those who understand: Knowledge growth in teaching. Educational Researcher 15, no. 2: 4-14.
19. Silver, E.A., and T.P. Carpenter. 1989. Mathematical methods. In Results from the fourth mathematics assessment of the National Assessment of Educational Progress, ed. M.M. Lindquist, 10-8. Reston, VA: National Council of Teachers of Mathematics.
20. Stylianides, A. 2007. Proof and proving in school mathematics. Journal for Research in Mathematics Education 38, no. 3: 289-321.
21. Tabach, M., E. Levenson, R. Barkai, P. Tsamir, D. Tirosh, and T. Dreyfus. 2009. Teachers' knowledge of students' correct and incorrect proof constructions. In Proceedings of the ICMI Study 19 Conference: Proof and proving in mathematics education, ed. F.L. Lin, F.J. Hsieh, G. Hanna and M. de Villiers, Vol. 2 214-9. Taipei, Taiwan: National Taiwan Normal University.
22. Tirosh, C. 2002. The ability of prospective teachers to prove or to refute arithmetic statements. PhD diss. Jerusalem, Israel: The Hebrew University.
23. Tsamir, P., D. Tirosh, T. Dreyfus, R. Barkai, and M. Tabach. 2008. Inservice teachers' judgment of proofs in ENT. In Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education, ed. O. Figueras, J.L. Cortina, S. Alatorre, T. Rojano, and A. Sépulveda, Vol. 4 345-52. Morélia, México: PME.
24. Tsamir, P., D. Tirosh, T. Dreyfus, R. Barkai, and M. Tabach. 2009. Should proof be minimal? Ms T's evaluation of secondary school students' proofs. Journal for Mathematical Behavior 28, no. 1: 58-67.
25. Zaslavsky, O., and I. Peled. 1996. Inhibiting factors in generating examples by mathematics teachers and student teachers: The case of binary operation. Journal for Research in Mathematics Education 27, no. 1: 67-78.
26. Zaslavsky, O., and G. Ron. 1998. Students' understandings of the role of counterexamples. In Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, ed. A. Olivier and K. Newstead, Vol. 4 225-32. Stellenbosch, South Africa: University of Stellenbosch.