Abstract
An essential procedural aim in secondary education is the learning to solve problems. Problem solving its to be seen as the most complex form of learning, it can include concept learning and rule learning. We hope and believe that the abilities and skills developed through problem solving in secondary schools can be transfered to extra school activities. In geometry teaching we can differentiate between the following typical kinds or ideal types of problems: construction problems, calculation problems, theorem finding problems, proving problems...
“As designers, it is our duty to develop systems and instructional materials aid users to develop more coherent, usable mental models. As teachers, it is our duty to develop conceptual models that will aid the learner to develop adequate and appropriate mental models...” (Donald A. Norman 1983)
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References
Aebli, H. (1985): Das operative Prinzip (The operational principle). Mathematik lernen, 1, 5–6.
Andelfinger, B. (1988). Geometrie (Geometry). Soest.
Anderson, J.A. et al. (1986). The Geometry Tutor. Journal of Mathematical Behavior, 5, 5–19.
Baulac, Y.; Bellemain, F.; Laborde, J.-M. (1988). Cabri-Géomètre, version 1.0/2.0. -Grenoble 1988/89
Becker, G. (1987). Über den Beitrag des Geometrieunterrichts zum Erwerb heuristischer Strategien (On the contribution of teaching geometry for the acquisition of heuristic strategies). Mathematica didáctica, 2, 123 – 144.
Bender, P. (1987). Anschauliches Beweisen im Geometrieunterricht - unter besonderer Berücksichtigung von (stetigen) Bewegungen bzw. Verformungen. (Illustrative proving in teaching geometry - under special consideration of (continuous) movement or deformations respectively). Preprint no. 1, Kassel.
Chazan, D.; Houde, R. (1989). How to use conjecturing and microcomputers to teach geometry. Reston.
Coffey, M. et al. (1986). Geometry. San Rafael.
Holland, G. (1973). Die Bedeutung von Konstruktionsaufgaben für den Geometrieunterricht (The significance of construction problems for teaching geometry). Beitrage zum Mathematikunterricht, 11 – 24.
Holland, G. (1989). GEOCON, Eine lernfähige Lernumgebung für geometrische Konstruktionen (GEOCON, a learning environment conducive to learning for geometric constructions). Beiträge zum Mathematikunterricht 203 – 206.
Moore, O.K.; Anderson, A.R. (1969). Some principles for the design of clarifying educational environments. In: Goslin, A. (ed. ): Handbook of Socialization Theory and Research. Chicago.
Schumann, H . (1988). Der Computer als Werkzeug zum Konstruieren im Geometrieunterricht (The computer as tool for construction in geometric education). Zentralblatt fur Didaktik der Mathematik, 6, 248 – 263.
Schumann, H. (1990). Interaktives Erzeugen von Ortslinien - ein Beitrag zum computerunterstützten Geometrieunterricht (Interactive production of local lines - a contribution to computer support geometric education). Mathematik lernen, 1.
Schumann, H . (1989). Neue Möglichkeiten des Geometrielernens durch interaktives Konstruieren (New possibilities of learning geometry through interactive construction). In: Research Report 74, University of Helsinki “Conference on the Teaching of Geometry” Helsinki 1.4. 8pp. 265 – 272.
Schumann, H. (1989). Satzfindung durch kontinuierliches Variieren geometrischer Konfigurationen mit dem Computer als interaktivem Werkzeug (Theorem finding through continuous variation of geometric configurations with the computer interactive tool). Der Mathematikunterricht, 4, 22 – 37.
Schumann, H. (1989). The computer as a tool for geometric constructions. Micromath, 3, 53 – 56.
Schwartz, J.L., Yerushalmy, M. (1985): The Geometric Supposer: Triangles. Pleasantville.
Winter, H . (1981). Entdeckendes Lernen im Mathematikunterricht (Discovering learning in mathematical education), Braunschweig.
Wittmann, E . (1981). Grundfragen des Mathematikunterrichts (Basic questions of teaching mathematics). Braunschweig.
Yerushalmy, M . (1986). Induction and generalization: an experiment in teaching and learning high school geometry. Ann Arbor, MI.
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© 1996 Springer-Verlag Berlin Heidelberg
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Schumann, H. (1996). The Influence of Interactive Tools in Geometry Learning. In: Laborde, JM. (eds) Intelligent Learning Environments: The Case of Geometry. NATO ASI Series, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60927-5_10
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DOI: https://doi.org/10.1007/978-3-642-60927-5_10
Publisher Name: Springer, Berlin, Heidelberg
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