Abstract
Coinland is a meaning-oriented approach to facilitating the learning of arithmetic principles. Algorithms based on those principles, such as those used to carry out operations like milti-digit subtraction, emerge for the student through a process of guided exploration, rather than inculcation. The visual representation is applicable to topics from counting to elementary division. This paper treats only subtraction. An alternative visual representation, Numberland, facilitates the important transfer of concepts for use outside the computer environment.
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Brown, J.S. and Burton, R.R., Diagnostic models for procedural bugs in basic mathematical skills, Cognitive Science 2 (1978) 155–192.
Brown, J.S. and Van Lehn, K., Repair theory: A generative theory of bugs in procedural skills, Cognitive Science 4 (1982) 379–426.
Carpenter, T.P., Learning to add and subtract: an exercise in problem solving, in: E.A. Silver (Ed.), Teaching and Learning Mathematical Problem-Solving: Multiple Research Perspectives (Erlbaum, Hillsdale, NJ, 1985).
Hamburger, H. and Lodgher, A., Constrained exploration and heuristic guidance, ms submitted to: J. Machine-Mediated Learning.
Malone, T.W., Heuristics for designing enjoyable user interfaces: lessons from computer games, in: Proceedings of the ACM Conference on Human Factors in Computer Systems (1982) 63–68.
Resnick, L.B. and Omanson, S., Learning to understand arithmetic, in: R. Glaser (Ed.), Advances in Instructional Psychology 3, (Erlbaum, Hillsdale, NJ, 1987) 41–95.
Self, J.A., Bypassing the intractable problem of student modelling, in: Proceedings of the Conference on Intelligent Tutoring Systems, Montreal (1988) 18–24.
Wenger, E., Artificial Intelligence and Tutoring Systems (Morgan Kaufmann, Los Altos, CA, 1987).
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© 1989 Springer-Verlag Berlin Heidelberg
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Hamburger, H., Lodgher, A. (1989). Exploration in Coinland. In: Maurer, H. (eds) Computer Assisted Learning. ICCAL 1989. Lecture Notes in Computer Science, vol 360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51142-3_58
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DOI: https://doi.org/10.1007/3-540-51142-3_58
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