Abstract
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.
Similar content being viewed by others
References
AusubelD. P., NovakJ. D. and HanesianH.: 1978, Educational Psychology: A Cognitive View, Holt, Rinehart and Winston, New York.
BaroodyA.: 1984, ‘Children's difficulties in subtration: Some causes and questions’, Journal for Research in Mathematics Education 15(3), 203–213.
BeilinH.: 1975, Studies in the Cognitive Basis of Language Development, Academic Press, New York.
BrownM.: 1981, ‘Number Operations’, K.Hart (ed.), Children's Understanding of Mathematics: 11–16, John Murray, London.
CarpenterT., MoserJ. and RombergT.: 1982, Addition and Subtraction: A Cognitive Perspective, Erlbaum, New Jersey.
CarpenterT. and MoserJ.: 1984, ‘The acquisition of addition and subtraction concepts in grades one through three’, Journal for Research in Mathematics Education 15(3), 179–202.
FusonK.: 1984, ‘More complexities in subtraction’, Journal for Research in Mathematics Education 15(3), 214–226.
GelmanR.: 1972, ‘Logical capacity of very young children: Number invariance rules’, Child Development 43, 75–90.
GelmanR. and GallistelC. P.: 1978, The Child's Understanding of Number, Harvard University Press, Cambridge, Mass.
Ginn Mathematics, Level 3, Teachers' Resource Book: 1983, Ginn & Co., London.
GinsburgH.: 1977, Children's Arithmetic: The Learning Process, Van Nostrand, New York.
HerveyM.: 1966, ‘Children's responses to two types of multiplication problems’, The Arithmetic Teacher 33, 288–291.
HughesM.: 1981, ‘Can pre-school children add and subtract?’, Educational Psychology, 1(3), 207–219.
Mathematics in Schools, Level 11, Teacher's Resource Books 1 & 2: 1979, Addison-Wesley, London.
Nuffield Mathematics 3, Teachers' Handbook & Pupil's Book: 1979, Longman, London.
SchaefferB., EgglestonV. and ScottJ.: 1974, ‘Number development in young children’, Cognitive Psychology, 6, 357–379.
ShuardH. and RotheryA.: 1984, Children Reading Mathematics, Murray, London.
SteffeL., VonGlaserfeldE., RichardsJ. and CobbP.: 1983, Children's Counting Types: Philosophy, Theory and Applications, Praeger, New York.
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.
VergnaudG.: 1983, ‘Multiplicative structures’, in R.Lesh and M.Landau (eds.), Acquisition of Mathematics Concepts and Processes, pp. 127–174, Academic Press, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Anghileri, J. An investigation of young children's understanding of multiplication. Educational Studies in Mathematics 20, 367–385 (1989). https://doi.org/10.1007/BF00315607
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00315607