Students’ understandings of logical implication

Educational Studies in Mathematics

Volumn 51, Issue 3, 2002, Pages 193-223

  Hoyles, Celia ^a   Küchemann, Dietmar ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Deduction; Logic; Logical implication; Proof

Indexed keywords

EID: 3543017641     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1023/A:1023629608614     Document Type: Article

References (33)

1. Anderson, R.C., Chinn, C., Chang, J., Waggoner, M. and Yi, H.: 1997, 'On the logical integrity of children's arguments', Cognition and Instruction 15(2), 135-167.
2. Balacheff, N.: 1988, 'Aspects of proof in pupils' practice of school mathematics', in D. Pimm (ed.), Mathematics, Teachers and Children, Hodder and Stoughton, London, pp. 216-235.
3. Bell, A.W.: 1976, 'A study of pupils' proof-explanations in mathematical situations', Educational Studies in Mathematics 7, 23-40.
4. Ceci, Stephen J.: 1990, On Intelligence-More or Less. A Bio-Ecological Treatise of Intellectual Development, Century Psychology Series, Prentice Hall, USA.
5. Cheng, P.W. and Holyoak, K.J.: 1985, 'Pragmatic reasoning schemas', Cognitive Psychology 17, 391-416.
6. Coe, R. and Ruthven, K.: 1994, 'Proof practices and constructs of advanced mathematics students', British Educational Research Journal 20(1), 41-53.
7. Deloustal-Jorrand, V.: 2002, 'Implication and mathematical reasoning', Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education 26(2), Norwich, England, pp. 281-288.
8. De Villiers, M.: 1990, 'The role and function of proof in mathematics', Pythagoras 24, 17-24.
9. Fischbein, E.: 1982, 'Intuition and proof', For the Learning of Mathematics 3(2), 9-18, 24.
10. Godino, J.D. and Recio, A.M.: 1997, 'Meaning of proofs in mathematics education', Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education, 2, Lahti, Finland, pp. 313-320.
11. Hanna, G.: 1989, 'Proofs that prove and proofs that explain', Proceedings of the 13th Conference of the International Group for the Psychology of Mathematics Education, G.R. Didactique CNRS Paris, pp. 45-51.
12. Hanna, G.: 1995, 'Challenges to the importance of proof', For the Learning of Mathematics 15(3), 42-49.
13. Hanna, G.: 2000, 'Proof, explanation and exploration: an overview', Educational Studies in Mathematics 44, 5-23.
14. Healy, L. and Hoyles, C.: 2000, 'A study of proof conceptions in algebra', Journal for Research in Mathematics Education 31(4), 396-428.
15. Hewitt, D.: 1992, 'Train spotters' paradise', Mathematics Teaching 140, 6-8.
16. Hoyles, C.: 1997, 'The curricular shaping of students' approaches to proof', For the Learning of Mathematics 17(1), 7-16.
17. Inhelder, B. and Piaget, J.: 1958, The Growth of Logical Thinking, Routledge and Kegan Paul, London.
18. Krummheuer, G.: 1995, 'The ethnology of argumentation', in P. Cobb and H. Bauersfeld (eds.), The Emergence of Mathematical Meaning: Interaction in Classroom Cultures, Erlbaum, Hillsdale, NJ, pp. 229-269.
19. Mitchell, D.: 1962, An Introduction to Logic, Hutchinson, London.
20. O'Brien, T.C., Shapiro, B.J. and Reali, N.C.: 1971, 'Logical thinking-language and context', Educational Studies in Mathematics 4, 201-219.
21. Quine, W.V.: 1974, Methods of Logic, (Third edition; first edition published in 1950) Routledge & Kegan Paul, London.
22. Reid, D.A.: 2002, 'Conjectures and refutations in Grade 5 mathematics', Journal for Research in Mathematics Education 33(1), 5-29.
23. Rodd, M.: 2000, 'On mathematical warrants', Mathematical Thinking and Learning 3, 22-244.
24. Simon, M.A.: 2000, 'Reconsidering mathematical validation in the classroom', Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education 4, Hiroshima, Japan, pp. 161-168.
25. Sowder, L. and Harel, G.: 1998, 'Types of students' justifications', The Mathematics Teacher 91(8), 670-675.
26. Toulmin, S.: 1958, The Uses of Argument, Cambridge University Press, Cambridge, UK.
27. Van Dormolen, J.: 1977, 'Learning to understand what a proof really means', Educational Studies in Mathematics 8, 27-34.
28. Vinner, S.: 1983, 'The notion of proof-some aspects of students' views at the senior high school level', Proceedings of the 7th Conference of the International Group for the Psychology of Mathematics Education, pp. 289-294.
29. Wason, P.C.: 1960, 'On the failure to eliminate hypotheses in a conceptual task', Quarterly Journal of Experimental Psychology 12, 129-140.
30. Wason, P.C. and Shapiro, D.: 1971, 'Natural and contrived experience in a reasoning task', Quarterly Journal of Experimental Psychology 23, 63-71.
31. Yackel, E.: 2001, 'Explanation, justification and argumentation in mathematics classrooms', Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, 1, Freudenthal Institute, Utrecht, Holland, pp. 9-23.
32. Yackel, E. and Cobb, P.: 1996, 'Sociomathematical norms, argumentation, and autonomy in mathematics', Journal for Research in Mathematics Education 27, 458-477.
33. Zack, V. and Graves, B.: 2001, 'Making mathematical meaning through dialogue: "Once you think of it, the Z minus three seems pretty weird"', Educational Studies in Mathematics 46(1-3), 229-271.