Abstract
This paper presents an investigation into the development of functional thinking. Search strategies used for solving a problem reveal different stages towards the discovery of the monotonic property, which correspond to stages of proportional reasoning found by Piaget. The dependence between stage and age is confirmed by the results.
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Andelfinger, B.: 1981, Didaktischer Informationsdienst Mathematik. Thema: Proportion, Landesinstitut für Curriculumentwicklung, Lehrerfortbildung und Weiterbildung, Neuß.
Burton L.: 1984, ‘Mathematical thinking: The struggle for meaning’, Journal for Research in Mathematics Education 15, 35–49.
Case R.: 1979, ‘Intellectual development and instruction: A neo-Piagetian view’, in A.Lawson (ed.), The Psychology of Teaching for Thinking and Creativity, ERIC, Columbus, Ohio.
Droz R. and Potter T. F.: 1969, ‘Search and exploration: Modification of efficiency and systematicity with age and repetition’, Archives de psychologie 40, 25–35.
Freudenthal H.: 1983, Didactical Phenomenology of Mathematical Structures, D. Reidel, Dordrecht.
Gutzmer A.: 1908, Tie Tätigkeit der Unterrichtskommission der Gesellschaft Deutscher Naturforscher und Ärzte, Teubner, Leipzig.
Häussler P.: 1981, Denken und Lernen Jugendlicher beim Erkennen funktionaler Beziehungen, Huber, Bern.
Hart K. M.: 1981, Children's Understanding of Mathematics: 11–16, Murray, London.
Inhelder B. and Piaget J.: 1958, The Growth of Logical Thinking from Childhood to Adolescence, Basic Books, New York.
Kagan J.: 1965, ‘Impulsive and reflective children: Significance of conceptual tempo’, in J. D.Krumboltz (ed.), Learning and the Educational Process, Rand McNally, Chicago.
Karplus R., Pulos S., and Stage E. K.: 1983, ‘Proportional reasoning of early adolescents’, in R.Lesh and M.Landau (eds.), Acquisition of Mathematics Concepts and Processes, Academic Press, New York.
Kirsch A.: 1969, ‘Eine Analyse der sogenannten Schlußrechnung, Mathematisch-Physikalische Semesterberichte 16, 41–55.
Meißner H.: 1985a, ‘Selfdeveloping strategies with a calculator game’, in L.Streefland (ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education, Vol. 1, PME, Utrecht.
Meißner H.: 1985b, ‘Versuchen und Probieren — Beobachtungen zum mathematischen Lernprozeß’, in W.Dörfler and R.Fischer (eds.), Empirische Untersuchungen zum Lehren und Lernen von Mathematik, Hölder-Pichler-Tempsky, Wien.
Piaget J., Grize J. B., Szeminska A., and Bang V.: 1968, Epistémologie et psychologie de la fonction, Presses Universitaires de France, Paris.
Ricco G.: 1982, ‘Les premières acquisitions de la notion de fonction linéaire chez l'enfant de 7 à 11 ans’, Educational Studies in Mathematics 13, 289–327.
Siegler R. S.: 1976, ‘Three aspects of cognitive development’ Cognitive Psychology 8, 481–520.
Suarez A.: 1977, Formales Denken und Funktionsbegriff bei Jugendlichen, Huber, Bern.
Tourniaire F. and Pulos S.: 1985, ‘Proportional reasoning: A review of the literature’, Educational Studies in Mathematics 16, 181–204.
Vollrath H.-J.: 1978, ‘Schülerversuche zum Funktionsbegriff’, Der Mathematikunterricht 24 (4), 90–101.
Vollrath H.-J.: 1984, Methodik des Begriffslehrens im Mathematikunterricht, Klett, Stuttgart.
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Vollrath, HJ. Search strategies as indicators of functional thinking. Educ Stud Math 17, 387–400 (1986). https://doi.org/10.1007/BF00311326
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DOI: https://doi.org/10.1007/BF00311326