Concrete and formal arguments: The case of division by zero

Mathematics Education Research Journal

Volumn 12, Issue 2, 2000, Pages 92-106

  Tsamir, Pessia ^a   Sheffer, Ruth ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749401433     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03217078     Document Type: Article

References (30)

1. Australian Education Council (1991). A national statement on mathematics for Australian schools. Melbourne: Curriculum Corporation.
2. Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21, 132-144.
3. Blake, R., & Verhille, C. (1985). The story of 0. For the Learning o/Mathematics, 5, 35-47.
4. Dreyfus, T. (1999). Why Johnny can't prove? Educational Studies in Mathematics, 38, 85-109.
5. Dreyfus, T. (2000). Some views on proofs by teachers and mathematicians. In A. Gagatsis & G. Makrides (Eds.), Proceedings of the 2nd Mediterranean Conference on Mathematics Education (Vol. 1, pp. 11-25). Nicosia, Cyprus: Cyprus Mathematical Society & Cyprus Pedagogical Institute.
6. Duncan, H. F. (1971). Division by zero. Arithmetic Teacher, 18, 381-382.
7. Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, The Netherlands: Reidel.
8. Fischbein, E. (1999). Intuition and schemata in mathematical reasoning. Education Studies in Mathematics, 38, 11-50.
9. Fischbein, E., Tirosh, D., & Melamed, U. (1981). Is it possible to measure the intuitive acceptance of a mathematical statement? Educational Studies in Mathematics, 12, 491-512.
10. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: Reidel.
11. Grouws, D. A., & Reys, R. E. (1975). Division involving zero: An experimental study and its implications. Arithmetic Teacher, 22, 74-80.
12. Hart, K. M. (1981). Children's understanding of mathematics: 11-16. London: John Murray.
13. Henry, B. (1969). Zero, the troublemaker. Arithmetic Teacher, 16, 365-367.
14. Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive psychology, 3, 430-454.
15. Knifong, J. D., & Burton, G. M. (1980). Intuitive definitions for division with zero. Mathematics Teacher, 73, 179-186.
16. Maor, E. (1991). To infinity and beyond. Princeton, NJ: Princeton University.
17. Ministry of Education (1988). The National Mathematics curriculum. Jerusalem, Israel: Ministry of Education.
18. National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
19. National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author.
20. Orton, A., & Frobisher, L. (1996). Insights into teaching mathematics. London, England: Cassell.
21. Reys, R. E. (1974). Division by zero: An area of needed research. Arithmetic Teacher, 21, 153-157.
22. Reys, R. E., & Grouws, D. A. (1975). Division involving zero: Some revealing thoughts from interviewing children. School Science and Mathematics, 78, 593-605.
23. Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 465-494). New York, NY: Macmillan.
24. Sundar, V. K. (1990). Thou shalt not divide by zero. Arithmetic Teacher, 37, 50-51.
25. Tirosh, D. (1993). Teachers' tmderstanding of undefined mathematical expressions. Substratum, 1, 61-86.
26. Tsarnir, P. (1995). Teaching prospective teachers about division by zero. Unpublished manuscript, Tel Aviv University, Israel.
27. Tsamir, P. (1996). Two problems under one title: The case of division by zero. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th annual conference of the International Group/or the Psychology of Mathematics Education (Vol. 4, pp. 347-354). Valencia, Spain: Program Committee.
28. Vinner, S. (1991). The role of definitions in teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65-78). Dordrecht, The Netherlands: Kluwer.
29. Watson, J. M. (1991). Models to show the impossibility of division by zero. School Science and Mathematics. 91, 373-376.
30. Wheeler, M., M., & Feghali, I. (1983). Much ado about nothing: Preservice elementary school teachers' concept of zero. Journal for Research in Mathematics Education, 14, 147-155.