Abstract
This article consists of a review of work done by Dutch and Belgian researchers on arithmetical problems, especially word-problems, involving addition and substraction. The purpose of this review is to synthesise the research on the relationship between instruction in the part-whole line diagram and the solution of arithmetical problems. In the discussion part of this paper, these findings are interpreted from a logical (mathematical) as well as from a psychological point of view.
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References
AssinkE. M. H. en VerloopN.: 1977, ‘Het aanleren van deel-geheel relaties in het aanvankelijk rekenonderwijs’, Ped. Stud. 54, 130–142.
CarpenterT. P., HiebertJ. and MoserJ. M.: 1981, ‘Problem structure and first-grade children's initial solution processes for simple addition and substraction problems’, Journal for Research in Mathematics Education 12, 27–39.
DeCorteE. en VerschaffelL.: 1980, ‘Een exploratief onderwijsexperiment met aanvankelijke rekenopgaven bij 6 à 8-jarige kinderen’, Ped. Stud. 57, 433–448.
DeCorteE. and VerschaffelL.: 1981, ‘Children's Solution Processes in Elementary Arithmetic Problems: Analysis and Improvement’, Journal of Educational Psychology 73, 765–780.
Greeno, J. G.: 1978, ‘Some examples of cognitive task analysis with instructional implications'. Paper presented at the ONE/NPRDC Conference, San Diego, March, 1978.
Herscovics, N. et Bergeron, J. C.: 1982, ‘Pourquoi et comment decrire la comprehension de la mathématique’, Bulletin de l'AMQ (Association Mathématique du Quebec) XXII, No. 1.
Heller, J. I. and Greeno, J. G.: 1978, ‘Semantic processing in arithmetic word-problemsolving’, Paper presented at the Midwestern Psychological Association Convention, Chicago, May.
MikulinaG. G.: 1982, ‘Psychologische mogelijkheden voor het oplossen van opgaven met lettergegevens’, Davydov, V. V., ‘Psychologische capaciteiten van de leerlingen van de lagere school bij het leren van wiskunde’, in M. A. D.Wolters (ed.), Vertalingenbundel Russische psychologie, IPAW, Utrecht, 1982.
Nesher, P. and Greeno, J. G.: 1981, ‘Semantic categories of word-problems, reconsidered’, The 5th Conference of the I.G.P.M.E. (International Group for the Psychology of Mathematical Education), Grenoble, pp. 63–68.
Resnick, L. B.: 1981, ‘The development of number representation in children’, The 5th Conference of the I.G.P.M.E., Grenoble, pp. 69–75.
RileyM. S., GreenoJ. G. and HellerJ. I.: 1982, ‘Development of children's problem-solving ability in arithmetic’, in H. P.Ginsburg (ed.), Development of Mathematical Thinking, A.P., New York.
Vergnaud, G. 1981, ‘A classification of cognitive tasks and operations of thought involved in addition and subtraction problems’, in T. P. Carpenter, J. M. Moser and T. Ramberg (eds.), Addition and Subtraction: Developmental Perspective, LEA.
Wolters, M. A. D.: 1978, Van Rekenen naar Algebra, Een ontwikkelingspsychologische analyse, Utrecht.
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Wolters, M.A.D. The part-whole schema and artithmetical problems. Educ Stud Math 14, 127–138 (1983). https://doi.org/10.1007/BF00303682
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DOI: https://doi.org/10.1007/BF00303682