Prospectıve Mathematıcs Teachers’ Dıffıcultıes In Doıng Proofs And Causes Of Theır Struggle Wıth Proofs_ERIC

Öz

This research aims to expose prospective mathematics teachers’ difficulties while proving, as well as the reasons behind such difficulties. The research includes 121 second year undergraduate prospective teachers studying at the primary mathematics teaching department of a state university in Turkey. The study has found that prospective teachers had serious deficiencies in doing proof. The primary difficulty experienced
by prospective teachers is expressing definitions. This difficulty is respectively followed by understanding theorem statement, using mathematical language and notations, selecting proper proof strategy and method, distinguishing concepts, creating a proof structure using definitions, and the difficulty of expressing thoughts. In addition, interviews have been conducted with seven prospective teachers representing each difficulty using semi-structured interview form. Interviews with the participants have shown that the major causes of such difficulties stem from prospective teachers having a negative attitude about proofs, and the various shortcomings in learning and teaching proofs.

Anahtar Kelimeler

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PROSPECTIVE MATHEMATICS TEACHERS’ DIFFICULTIES IN DOING PROOFS AND CAUSES OF THEIR STRUGGLE WITH PROOFS

Öz

This research aims to expose prospective mathematics teachers’ difficulties while proving, as well as the reasons behind such difficulties. The research includes 121 second year undergraduate prospective teachers studying at the primary mathematics teaching department of a state university in Turkey. The study has found that prospective teachers had serious deficiencies in doing proof. The primary difficulty experienced by prospective teachers is expressing definitions. This difficulty is respectively followed by understanding theorem statement, using mathematical language and notations, selecting proper proof strategy and method, distinguishing concepts, creating a proof structure using definitions, and the difficulty of expressing thoughts. In addition, interviews have been conducted with seven prospective teachers representing each difficulty using semi-structured interview form. Interviews with the participants
have shown that the major causes of such difficulties stem from prospective teachers having a negative attitude about proofs, and the various shortcomings in learning and teaching proofs. 

Anahtar Kelimeler

• Mathematical proof,difficulties in proof,prospective mathematics teachers,mathematics education

Kaynakça

1. Almeida, D. (2000). A survey of mathematics undergraduates interaction with proof: some implications for mathematics education. International Journal of Mathematical Education in Science and Technology, 31(6), 869-890.
2. Almeida, D. (2003). Engendering proof attitudes: Can the genesis of mathematical knowledge teach us anything? International Journal of Mathematical Education in Science and Education, 34(4), 479-488.
3. Bayazıt, N. (2009). Prospective mathematics teachers’ use of mathematical definitions in doing proof (Unpublished Doctoral Dissertation). Florida State University, Florida.
4. Conradie, J., & Frith, J. (2000). Comprehension tests in mathematics. Educational Studies in Mathematics, 42, 225-235.
5. Coşkun, F. (2009). Reflections from the Experiences of 11th Graders during the Stages of Mathematical Thinking. Education and Science, 35(156), 17-31.
6. De Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17-24.
7. Dickerson, D. S. (2008). High school mathematics teachers’ understandings of the purposes of mathematical proof (Unpublished Doctoral Dissertation). University of Syracuse.
8. Doruk, M., & Kaplan, A. (2013a). Prospective primary mathematics teachers’ views about mathematical proof. Journal of Research in Education and Teaching, 2(1), 241-252.

9. Doruk, M., & Kaplan, A. (2013b). Prospective primary mathematics teachers’ proof evaluation abilties on convergence of sequence concept. Journal of Research in Education and Teaching, 2(1), 231-240.
10. Dreyfus, T. (1999). Why Johnny can’t prove. Educational studies in mathematics 38(1), 85-109.
11. Fawcett, H . P. (1938). The nature of proof: a description and evaluation of certain procedures used in a senior high school to develop an understanding of the nature of proof. (NCTM year book 1938). New York: Teachers’ College, Columbia University.
12. Furinghetti, F. and Morselli, F. (2009). Teachers’ beliefs and the teaching of proof. Proceedings of ICME Study 19: Proof and Proving in Mathematics Education, Taipei, Taiwan.
13. Güler, G. (2013). Investigation of pre-service mathematics teachers’ proof processes in the learning domain of algebra (Unpublished Doctoral Dissertation). Ataturk University Institute of Education Sciences, Erzurum.
14. Hanna, G. (1991). Mathematical proof. In D. Tall (Ed.), Advanced mathematical thinking. Hingham, MA: Kluwer Academic Publishers.
15. Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics 44: 5–23.
16. Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from an exploratory study. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research In College Mathematics Education III (Pp. 234-283). Providence, RI: AMS.
17. Heinze, A., and Reiss, K. (2003). Reasoning and proof: Methodological knowledge as a component of proof competence. In M.A. Mariotti (Ed.), Proceedings of the Third Conference of the European Society for Research in Mathematics Education, Bellaria, Italy.
18. Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24, 389–399.
19. Kitcher, P. (1984). The nature of mathematical knowledge. New York: Oxford university press. Ko, Y. Y. (2010). Mathematics teachers’ conceptions of proof: implications for educational research. International Journal of Science and Mathematics Education, 8, 1109–1129.
20. Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27, 249-266.
21. Moralı, S., Uğurel, I., Türnüklü, E., & Yeşildere, S. (2006). The views of the mathematics teachers on proving. Kastamonu University Journal of Education, 14(1), 147-160.
22. Raman, M. J. (2003). Key ideas: What are they and how can they help us understand how people view proof?. Educational Studies in Mathematics, 52(3), 319-325.
23. Sarı, M., Altun, A., & Aşkar, P. (2007). Undergraduate Students’ Mathematical Proof Processes in a Calculus Course: A Case Study. Ankara University Journal of Faculty of Educational Sciences, 40(2), 295–319.
24. Selden, A., & Selden, J. (2007). Overcoming students’ difficulties in learning to understand and construct proofs. Technical Report, Mathematics Department, Tennesse Technological University retrieved 05.06.2012, from http://www.math.tntech.edu/techreports/TR_2007_1.pdf
25. Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10, 145- 166.
26. Weber, K (2006). Investigating and teaching the processes used to construct proofs. In F.Hitt, G. Harel & A. Selden (Eds), Research in Collegiate Mathematics Education, 6, 197-232.
27. Weber, K. (2001). Student difficulty in constructing proofs: the need for strategic knowledge. Educational Studies in Mathematics, 48, 101-119.
28. Weber, K. (2004). Traditional instruction in advanced mathematics courses: a case study of one professor’s lectures and proofs in an introductory real analysis course. Journal of Mathematical Behaviour, 23, 115–133
29. Yıldırım, A., & Şimşek, H. (2008). Qualitative research methods in social sciences. Ankara: Seçkin Publications.
30. Yıldız, G. (2006). Prepairing and applications of comprehension tests for theorems and proofs in calculus courses and students views (Master’s Thesis). Gazi University Institute of Education Sciences, Ankara.