Abstract
Based on the assumptions that (a) addition and subtraction are rule-based cognitive skills, and (b) that the acquisition of cognitive skills is a result of a developmental process in which stages can be distinguished, a “genetic model” was proposed in which emergence of addition and subtraction skills in the domain of the natural numbers 20–100 is described in six stages. The stages were chosen on theoretical and empirical grounds (several studies on addition and subtraction skills conducted at the State University of Leiden). In a longitudinal experiment, 16 second grade elementary school students were followed during 11 months. A diagnostic computer program was used to collect data on their addition and subtraction performance. The strategies appeared to be employed fairly consistently within a stage of development. The proposed genetic model accounted for most of the performance levels displayed by the students. The conclusion seems warranted that instruction should be adapted to the student’s actual stage of development.
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References
Anderson, J.R.: Acquisition of cognitive skill. Psychological Review. 89, 369–406 (1982)
Anderson, R.C.: Some reflections on the acquisition of knowledge. Educational Researcher. 13, 9, 5–10 (1984)
Baroody, A.L., & Ginsburg, H.P.: The relationship between initial meaningful and mechanical knowledge of arithmetic. In: Conceptual and procedural knowledge: The case of mathematics. (J. Hiebert, ed.). pp. 75112. Hillsdale, NJ: Lawrence Erlbaum 1986
Beishuizen, M.: Vervolgonderzoek: Invloeden van leermiddelen op de uitvoering van rekenhandelingen. [Continued research on influences of learning aids on the execution of arithmetic operations]. In: Leerprocessen en instructie. (S. Dijkstra & P. Span, eds.). pp. 131–144. Lisse: Swets & Zeitlinger 1986
Beishuizen, M., & Van Mulken, F.: Twee veelgebruikte oplossingsmanieren bij hoofdrekenen. [Two often employed solution strategies for mental arithmetic]. Panama-post. 6, 3, 32–37 (1988)
Carpenter, Th.P.: Learning to add and subtract: an exercise in problem solving. In: Teaching and learning mathematical problem solving: Multiple research perspectives. (A. Silver, ed.). pp. 17–40. Hillsdale, NJ: Lawrence Erlbaum 1985
Case, R.: Intellectual development: A systematic reinterpretation. New York: Academic Press 1982
Case, R., & Bereiter, C.: From behaviourism to cognitive behaviourism to cognitive development: Steps in the evolution of instructional design. Instructional Science. 13, 141–158 (1984)
Corte, E. de, & Verschaffel, L.: Onderzoek van onderwijsleerprocessen en onderwijspraktijk. [Research on teaching learning processes and educational practice]. Pedagogische Studien. 60, 153–164 (1983)
Fuson, K.C., Richards, J., & Briars, DJ.: The acquisition and elaboration of the number word sequence. In: Children’s logical and mathematical cognition (progress in cognitive development, Vol. 1). (C. Brainerd, ed.). pp. 33–94. Heidelberg: Springer Verlag 1982
Gal’perin, P.J.: Stages in the development of mental acts. In: A handbook of contemporary Soviet psychology. (M. Cole & I. Maltzman, eds.). pp. 249–273. New York: Basic Books 1969
Glaser, R., & Bassok, M.: Learning theory and the study of instruction. Annual Review of Psychology. 40, 631–666 (1989)
Goldstein, I.: The genetic graph: A representation for the evolution of procedural knowledge. In: Intelligent tutoring systems. (D. Sleeman & J.S. Brown, eds.). pp. 51–77. New York: Academic Press 1982
Groen, GJ., & Parkman, J.M.: A chronometers analyses of simple addition. Psychological Review. 79, 4, 329–343 (1972)
Heijden, M. van der, & Beishuizen, M.: Diagnostisering van individuele verschillen in het optellen en aftrekken van basisschoolleerlingen. [Diagnosis of individual differences between elementary school children in addition and subtraction skills]. In: Differentiatie in het onderwijs. (A. Reints, & P. Span, eds.). pp. 155–169. Lisse: Swets & Zeitlinger 1986
Inhelder, B., & Piaget, J.: The growth of logical thinking from childhood to adolescence. New York: Basic Books 1958
Mannaerts, A.A.J.: Een instrument voor de diagnose van rekengedrag. [An instrument for diagnosing arithmetic skills]. Nederlands Tijdschrift voor de Psychologie. 42, 7, 386–391 (1987)
Siegler, R.S., & Klahr, D.: When do children learn? The relationship between existing knowledge and the acquisition of new knowledge. In: Advances in instructional psychology, Vol. 2. (R. Glaser, ed.). pp. 121211. Hillsdale, NJ: Lawrence Erlbaum 1982
Parreren, C.F. van: A building block model of cognitive learning. In: Cognitive psychology and instruction. (A.M. Lesgold, J.W. Pellegrino, S.D. Fokkema, & R. Glaser, eds.). pp. 3–12. New York: Plenum 1978
VanLehn, K.: Toward a theory of impasse-driven learning. In: Learning issues for intelligent tutoring systems (H. Mandl & A. Lesgold, eds.). pp. 19–42. New York: Springer Verlag 1988
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Beishuizen, J., Felix, E. (1992). Adaptive tutoring of arithmetic skills. In: Dijkstra, S., Krammer, H.P.M., van Merriënboer, J.J.G. (eds) Instructional Models in Computer-Based Learning Environments. NATO ASI Series, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02840-7_15
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DOI: https://doi.org/10.1007/978-3-662-02840-7_15
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