Studying teachers' mathematical argumentation in the context of refuting students' invalid claims

Journal of Mathematical Behavior

Volumn 29, Issue 3, 2010, Pages 160-168

  Giannakoulias, Eusthathios ^a   Mastorides, Eleutherios ^a   Potari, Despina ^a   Zachariades, Theodossios ^a  

^a UNIVERSITY OF ATHENS   (Greece)

Author keywords

Counterexamples; Mathematical argumentation; Teacher knowledge; Toulmin's model

Indexed keywords

EID: 77957881400     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2010.07.001     Document Type: Article

References (33)

1. Balacheff N. Treatment of refutations: Aspects of the complexity of a constructivist approach to mathematics learning. Radical constructivism in mathematics education 1991, 89-110. Kluwer, Hingham. E. von Glaserfeld (Ed.).
2. Ball D.L., Thames M.H., Phelps G. Content knowledge for teaching: What makes it special?. Journal of Teacher Education 2008, 59:389-407.
3. Ball, D., Bass, H., Sleep, L. & Thames, M. (2005). A theory of mathematical knowledge for Teaching. Work-Session presented at the 15th ICMI study conference: The Professional Education and Development of Teachers of Mathematics, Brazil.
4. Barkai R., Tsamir P., Tirosh D., Dreyfus T. Proving or refuting arithmetic claims: The case of elementary school teachers. Proceedings of the 26th conference of the international group for the psychology of mathematics education, vol. 2 2002, 57-64. University of East Anglia, Norwich. A.D. Cockburn, E. Nardi (Eds.).
5. Bazzini L., Tsamir P. Algebraic equations and inequalities: Issues for research and teaching. Proceedings of the 28th conference of the international group for the psychology of mathematics education, vol. 1 2004, 137-139. M.J. Hoines, A.B. Fuglestad (Eds.).
6. Bills L., Dreyfus T., Mason J., Tsamir P., Watson A., Zaslavsky O. Exemplification in mathematics education. Proceedings of the 30th conference of the international group for the psychology of mathematics education, vol. 1 2006, 126-154. Czehia, Prague. J. Novotná, H. Moraová, M. Krátká, N. Stehliková (Eds.).
7. Biza I., Nardi E., Zachariades T. Using tasks to explore teacher knowledge in situation-specific contexts. Journal of Mathematics Teacher Education 2007, 10:301-309.
8. Boero P., Garuti R., Mariotti M.A. Some dynamic mental processes underlying producing and proving conjectures. Proceedings of the 20th conference of the international group for the psychology of mathematics education, vol. 2 1996, 121-1128. A. Gutierrez, L. Puig (Eds.).
9. Harel G., Sowder L. Students' proof schemes: results from exploratory studies. Research in collegiate mathematics education 3 1998, 234-283. AMS, Providence. A. Schoenfeld, J. Kaput, E. Dubinsky (Eds.).
10. Inglis M., Mejia-Ramos J.P. How persuaded are you? A typology of responses. Research in Mathematics Education 2008, 10:119-133.
11. Inglis M., Mejia-Ramos J.P., Simpson A. Modelling mathematical argumentation: the important of qualification. Educational Studies in Mathematics 2007, 66:3-21.
12. Kieran C. The equation/inequality connection in constructing meaning for inequality situations. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, vol. 1 2004, 143-147. M.J. Hoines, A.B. Fuglestad (Eds.).
13. Ko Y.Y., Knuth E. Undergraduate mathematics majors' writing performance producing proofs and counterexamples about continuous functions. Journal of Mathematical Behavior 2009, 28:68-77.
14. Krummheuer G. Argumentation and participation in the primary mathematics classroom. Two episodes and related theoretical abductions. Journal of Mathematical Behavior 2007, 26:60-82.
15. Lakatos I. Proof and Refutation 1976, Cambridge University Press, New York.
16. Larsen S., Zandieh M. Proofs and refutations in the undergraduate mathematics classroom. Educational Studies in Mathematics 2008, 67:205-216.
17. Lin F.L. Modelling students' learning on mathematical proof and refutation. Proceedings of the 29th of the international group for the psychology of mathematics education, vol. 2 2005, 3-18. H.L. Chick, J.L. Vincent (Eds.).
18. Pedemonte B. How can the relationship between argumentation and proof be analysed?. Educational Studies in Mathematics 2007, 66:23-41.
19. Peled I., Zaslavsky O. Counter-example that (only) prove and Counter-example that (also) explain. Focus on Learning Problems in mathematics 1997, 19:49-61.
20. Perrin-Glorian M.J. The absolute value in secondary school: A case study of 'institutionalisation' process. Proceedings of the 19th annual conference of the international group for the psychology of mathematics education, vol. 2 1995, 74-81.
21. Potari D., Zachariades T., Zaslavsky O. Mathematics teachers' reasoning for refuting students' invalid claims. Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education 2009.
22. Rowland T. The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics 2008, 69:149-163.
23. Toulmin S. The uses of argument 2003, Cambridge University Press, Cambridge.
24. Tsamir P., Tirosh D., Dreyfus T., Barkai R., Tabach M. Should proof be minimal? Ms T's evaluation of secondary school students' proofs. The Journal of Mathematical Behavior 2009, 28:58-67.
25. Watson A., Mason J. Mathematics as a constructive activity: learners generating examples 2005, Erlbaum, Mahwah.
26. Weber K. Problem-solving, proving, and learning: The relationship between problem-solving processes and learning opportunities in the activity of proof construction. Journal of Mathematical Behavior 2005, 24:351-360.
27. Weber K, Alcock L. Using warranted implications to understand and validate proofs. For the Learning of Mathematics 2005, 25:34-38.
28. Yackel E. Explanation, justification, and argumentation in the mathematics classroom. Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, vol. 1 2001, 7-21. M. van den Heuvel-Panhuizen (Ed.).
29. Yackel E., Rasmussen C. Beliefs and norms in the mathematics classroom. Beliefs: A hidden variable in mathematics education? 2002, 313-330. Kluwer, Dordrecht. G. Leder, E. Pehkonen, G. Toerner (Eds.).
30. Zaslavsky O., Peled I. Inhibiting factors in generating examples by Mathematics teachers and student teachers: The case of binary operation. Journal for Research in Mathematics Education 1996, 27:67-78.
31. Zaslavsky O., Ron G. Students' understanding of the role of counter-examples. Proceedings of the 22th conference of the international group for the psychology of mathematics education, vol. 4 1998, 225-232. A. Olivier, K. Newstead (Eds.).
32. Zazkis R., Chernoff E.J. What makes a counterexample exemplary?. Educational Studies in Mathematics 2008, 68:195-208.
33. Zodik I., Zaslavsky O. Characteristics of teachers' choice of examples in and for the mathematics classroom. Educational Studies in Mathematics 2008, 69:165-182.