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References
ArmitageJ. V.: 1969, ‘The relation between abstract and ‘concrete’ mathematics at school,’ Educational Studies in Mathematics 2, 180–188.
Athen, H. and Kunle, H. (eds.): 1977, Proceedings of the Third International Congress on Mathematical Education, Karlsruhe.
BellA. W.: 1976, ‘A study of pupil's proof explanations in mathematical situations,’ Educational Studies in Mathematics, 7, 23–40.
Beth, E. W. and Piaget, J.: 1961, Épistémologie mathématique et psychologie. Etudes d'épistémologie qénétique XIV, Presses Universitaires de France.
ChristiansenB.: 1969, ‘Induction and deduction in the learning of mathematics and in mathematical instruction,’, Educational Studies in Mathematics, 2, 139–159.
DieudonnéJ.: 1976, ‘L'abstraction et l'intuition mathématique,’ NICO, 20, 45–65.
Fischbein, E.: 1973, ‘Intuition, structure and heuristic methods in the teaching of mathematics‘, in Howson (ed.), 1973, pp. 222–232.
FischbeinE.: 1975, The Intuitive Sources of Probabilistic Thinking in Children, D. Reidel, Dordrecht.
FreudenthalH.: 1973, Mathematics as an Educational Task, D. Reidel, Dordrecht.
GilesG.: 1975, ‘Does teaching inhibit learning?’, Mathematics Teaching 65, 33–38.
GriffithsH. B.: 1971, ‘Mathematical insight and mathematical curricula’, Educational Studies in Mathematics 4, 153–165.
Griffiths, H. B.: 1976, Surfaces, Cambridge University Press.
GriffithsH. B.: 1978, ‘Some Comments on MacDonald's Paper’, Educational Studies in Mathematics 9, 421–427.
HilbertD. and Cohn-VossenS.: 1952, Geometry and the Imagination, Chelsea, New York.
HowsonA. G. (ed.): 1973, Developments in Mathematical Education, Proceedings of the Second International Congress on Mathematical Education, Cambridge University Press, London.
LakatosI.: 1976, Proofs and Refutations, Cambridge University Press, London.
MacDonaldI.: 1978, ‘Insight and intuition in mathematics’, Educational Studies in Mathematics 9, 411–420.
ManinYu.: 1976. ‘How convincing is a proof?’, The Mathematical Intelligencer 2, 17–18.
Shibata, T.: 1973, ‘The role of axioms in contemporary mathematics and in mathematical education’, in Howson (ed.), 1973, pp. 262–271.
Thom. R.: 1973, ‘Modern mathematics: Does it exist?’, in Howson (ed.), 1973, pp. 194–209.
Walther, G.: 1979, Illuminating Examples-An Aspect of Simplification in Mathematics Teaching, Inaugural Lecture, University of Dortmund.
Wittmann, E.: 1980a, Grundfragen des Mathematikunterrichts, Braunschweig.
Wittmann, E.: 1980b, ‘Beziehungen zwischen operativen “Programmen” in Mathematik, Psychologie und Mathematikdidaktik’ to appear in Journal für Mathematikdidaktik.
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Universität Dortmund Institut für Didaktik der Mathematlk
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Wittmann, E. The complementary roles of intuitive and reflective thinking in mathematics teaching. Educ Stud Math 12, 389–397 (1981). https://doi.org/10.1007/BF00311068
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DOI: https://doi.org/10.1007/BF00311068