Abstract
Previous research indicates that children will use either empirical or deductive methods to justify propositions which they consider to be true. The research reported here was designed to discover what type of evidence children find to be convincing: what it is that secures genuine belief.
References
AyerA. J.: 1956, The Problem of Knowledge, Penguin, London.
Baxandall, P. R., Brown W. S., Rose, G. St. C., and Watson, F. R.: 1978, Proof in Mathematics (“If”, “Then” and “Perhaps”), Keele University.
BellA. W.: 1976, A study of pupils' proof-explanations in mathematical situations. Educational Studies in Mathematics 7, 23–40.
Bell, A. W.: 1978, ‘The learning of process aspects of mathematics’, Proceedings of the 2nd Annual Conference of the International Group for the Psychology of Mathematics Education. pp. 48–78, Osnabruck.
Fischbein, E.: 1978, ‘Intuition and mathematical education’, Proceedings of the 2nd Annual Conference of the International Group for the Psychology of Mathematics Education, pp. 148–176, Osnabruck.
FischbeinE., TiroshD., and MelamedU.: 1981, ‘Is it possible to measure the intuitive acceptance of a mathematical statement?’, Educational Studies in Mathematics 12, 491–512.
FischbeinE.: 1982, ‘Intuition and proof’. For the Learning of Mathematics 3, 9–18.
Fischbein, E. and Kedem, I.: 1982, ‘Proof and certitude in the development of mathematical thinking’, Proceedings of the 6th Annual Conference of the International Group for the sychology of Mathematics Education, pp. 128–131, Antwerp.
GalbraithP. L.: 1981, ‘Aspects of proving: A clinical investigation of process’, Educational Studies in Mathematics 12, 1–28.
PiagetJ.: 1928, Judgement and Reasoning in the Child, Routledge and Kegan Paul, London.
Porteous, K.: 1988, Understanding Mathematics: Proof and Children's Autonomous Judgements, PhD thesis, University of Newcastle Upon Tyne.
SchefflerI.: 1965, Conditions of Knowledge, Scott, Foresman and Co., Illinois.
Vinner, S.: 1982, ‘Conflicts between definitions and intuitions-the case of the tangent’. Proceedings of the 6th Annual Conference of the International Group for the Psychology of Mathematics Education, pp. 24–28, Antwerp.
Vinner, S.: 1983, ‘The notion of proof: Some aspects of students’ views at the senior high level’, Proceedings of the 7th Annual Conference of the International Group for the Psychology of Mathematics Education, pp. 289–294, Israel.
WoozleyA. D.: 1949, Theory of Knowledge, Hutchinson, London.
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Porteous, K. What do children really believe?. Educ Stud Math 21, 589–598 (1990). https://doi.org/10.1007/BF00315946
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DOI: https://doi.org/10.1007/BF00315946