Abstract
This paper offers a critical analysis of Dubinsky et al. (1994) and proposes, as an alternative to the four axioms and the standard definitions, that permutation and symmetry may be regarded as the fundamental concepts of group theory.
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References
Burn, R. P.: 1985, Groups: a Path to Geometry, Cambridge.
Burn, R. P.: forthcoming, ‘Participating in the learning of group theory’, offered to College Mathematics Journal.
Burnside, W.: 1911, The Theory of Groups of Finite Order, Cambridge.
DubinskyE., DautermannJ., LeronU. and ZazkisR.: 1994, ‘On Learning Fundamental Concepts of Group Theory’, Educational Studies in Mathematics 27, 3, 267–305 (FCGT).
DubinskyE. and LeronU.: 1994, Learning Abstract Algebra with ISETL, Springer, New York.
Fraleigh, J. B.: 1967, A First Course in Abstract Algebra, Addison-Wesley (First edition).
FreudenthalH.: 1973, ‘What groups mean in mathematics and what they should mean in mathematical education’, in Developments in Mathematical Education, Proceedings of ICME-2, A. G.Howson (ed.), Cambridge University Press, Cambridge, U.K., 101–114.
JordanC. and JordanD.: 1994, Groups, Arnold, London.
LeronU. and DubinskyE.: 1995, ‘An abstract algebra story’, American Mathematical Monthly 102, 3, 227–242.
Tall, D.: 1992, ‘The transition to advanced mathematical thinking: functions, limits, infinity and proof’, in Handbook of research on Mathematics Teaching and Learning, D. A. Grouws (ed.), Macmillan, 495–511.
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Burn, B. What are the fundamental concepts of group theory?. Educational Studies in Mathematics 31, 371–377 (1996). https://doi.org/10.1007/BF00369154
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DOI: https://doi.org/10.1007/BF00369154