An investigation of young children's understanding of multiplication
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The issue of how young children learn arithmetic has generated considerable research that focuses upon the child as an active “meaning maker” in the process of learning mathematics. Close observation of the children's actions and utterances have led to formulations that provide a description of children's cognitive development with respect to counting (Gelman, 1972; Schaeffer, Eggleston and Scott, 1974; Steffe, Von Glasserfeld, Richards and Cobb, 1983) and to addition and subtraction (Carpenter, Moser and Romberg, 1982; Fuson, 1984; Baroody, 1984) This paper presents an analysis of children's solution strategies for multiplication tasks. Consideration is also given to the difficulties experienced by unsuccessful children.
This study looks at the development of understanding of multiplication from the early school years, before its formal introduction in school, through to the top primary age group. Concrete tasks based on different aspects of multiplication were presented to 152 children in individual interviews. The children's behaviours were observed and successful solution strategies were analysed to reveal a development from unitary counting, through rhythmic counting in groups to the application of a single multiplication fact. Progressive abstraction in the observed procedures is related to the children's developing understanding of number and to their procedures for addition.
KeywordsUnary Operation Multiplication Task Counting Sequence Number Pattern Unitary Counting
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- AusubelD. P., NovakJ. D. and HanesianH.: 1978, Educational Psychology: A Cognitive View, Holt, Rinehart and Winston, New York.Google Scholar
- BeilinH.: 1975, Studies in the Cognitive Basis of Language Development, Academic Press, New York.Google Scholar
- BrownM.: 1981, ‘Number Operations’, K.Hart (ed.), Children's Understanding of Mathematics: 11–16, John Murray, London.Google Scholar
- CarpenterT., MoserJ. and RombergT.: 1982, Addition and Subtraction: A Cognitive Perspective, Erlbaum, New Jersey.Google Scholar
- GelmanR. and GallistelC. P.: 1978, The Child's Understanding of Number, Harvard University Press, Cambridge, Mass.Google Scholar
- Ginn Mathematics, Level 3, Teachers' Resource Book: 1983, Ginn & Co., London.Google Scholar
- GinsburgH.: 1977, Children's Arithmetic: The Learning Process, Van Nostrand, New York.Google Scholar
- HerveyM.: 1966, ‘Children's responses to two types of multiplication problems’, The Arithmetic Teacher 33, 288–291.Google Scholar
- Mathematics in Schools, Level 11, Teacher's Resource Books 1 & 2: 1979, Addison-Wesley, London.Google Scholar
- Nuffield Mathematics 3, Teachers' Handbook & Pupil's Book: 1979, Longman, London.Google Scholar
- ShuardH. and RotheryA.: 1984, Children Reading Mathematics, Murray, London.Google Scholar
- SteffeL., VonGlaserfeldE., RichardsJ. and CobbP.: 1983, Children's Counting Types: Philosophy, Theory and Applications, Praeger, New York.Google Scholar
- Steffe, L.: 1986, ‘Composite units and their constructive operations’, Paper presented to the pre-session to the Annual Meeting of the N.C.T.M., Washington D.C.Google Scholar
- VergnaudG.: 1983, ‘Multiplicative structures’, in R.Lesh and M.Landau (eds.), Acquisition of Mathematics Concepts and Processes, pp. 127–174, Academic Press, New York.Google Scholar