Abstract
2493 children aged from 5 to 15 years in 114 classes in 25 primary schools were asked to do a similar set of 22 arithmetic word problems. 1195 of the children were in Grades K through 6 in Victorian schools (Australia) and 1298 were in Grades 4 through 6 in Papua New Guinea (PNG) schools. For both samples the questions were posed in English. This was the first language for most children in the Victorian sample but, for the PNG sample, English was usually the second, third, or even fourth language (even though it is the language of instruction in PNG schools). While the test instrument was based on widely accepted information processing models of how children solve arithmetic word problems, the data obtained were not so much in accord with these models as with psycholinguistic theories on children's acquisition of polarised comparative pairs (like “more” and “less”). The data also indicate that children from the two samples used similar strategies and made similar errors, with the order of relative difficulty being the same for both samples, the main factor determining difficulty being the semantic structure of the questions. Differences in performance between corresponding grades from the two samples can be attributed to differences in the degree of English language competence rather than to numerical facility.
This is a preview of subscription content, log in via an institution to check access.
References
Adetula, L. O.: 1985, The Effects of Language and Schooling on the Solutions of Addition and Subtraction Word Problems by Nigerian Children, unpublished D.Ed dissertation, University of Wisconsin-Madison.
Adetula, L. O.: September 1987, Language Factors: Does it Affect Children's Performance on Word Problem? Paper presented at the Annual National Conference of the Mathematical Association of Nigeria, Zaria.
BrainerdC. J.: 1979, The Origins of the Number Concept, Praeger, New York.
BriarsD. J. and LarkinJ. H.: 1984, ‘An integrated model of skill in solving elementary word problems’, Cognition and Instruction 1, 245–297.
BryantP.: 1974, Perception and Understanding in Young Children, Methuen, London.
CarpenterT. P.: 1983, ‘Learning to add and subtract: An exercise in problem solving’, in E.Silver (ed.), Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, Erlbaum, Hillsdale, N.J.
CarpenterT. P. and MoserJ. M.: 1982, ‘The development of addition and subtraction problem solving skills’, in T. P.Carpenter, J. M.Moser, and T.Romberg (eds.), Addition and Subtraction: A Cognitive Perspective, Erlbaum, Hillsdale, N.J.
CarpenterT. P. and MoserJ. M.: 1983, ‘The acquisition of addition and subtraction concepts’, in R.Lesh and M.Landau (eds.), Acquisition of Mathematics Concepts and Processes, Academic Press, New York.
CarpenterT. P. and MoserJ. M.: 1984, ‘The acquisition of addition and subtraction concepts in grades one through three’, Journal for Research in Mathematics Education 15, 179–202.
CarpenterT. P., MoserJ. M. and BeboutH. C.: 1988, ‘Representation of addition and subtraction word problems’, Journal for Research in Mathematics Education 19, 345–357.
ClarkE. V.: 1972, ‘On the child's acquisition of antonyms in two semantic fields’, Journal of Verbal Learning and Verbal Behaviour 11, 750–758
ClarkE. V.: 1973, ‘What's in a word? On the child's acquisition of semantic structure in his first language’, in T. E.Moore (ed.), Cognitive Development and the Acquisition of Language, Academic Press, New York.
ClementsM. A.: 1981–82, ‘Visual imagery and school mathematics’, For the Learning of Mathematics 1981, 2, 2–9 and 1982, 2, 31–40 (published in two parts).
Clements, M. A. and Del Campo, G.: July 1986, Linguistic and Pedagogical Factors Influencing Elementary Schoolchidren's Processing of Arithmetic Word Problems. Paper presented at the Annual Meeting of the Mathematics Education Research Group of Australiasia, Launceston.
CobbP.: 1987, ‘An analysis of three models of early number development’, Journal for Research in Mathematics Education 18(3), 163–179.
CoombsB. and HarcourtL.: 1986, Explorations 1, Addison-Wesley, Don Mills (Ontario).
DaweL.: 1983, ‘Bilingualism and mathematical reasoning in English as a second language’, Educational Studies in mathematics 14, 325–353.
DeCorteE. and VerschaffelL.: 1985a, ‘Beginning first graders' initial representation of arithmetic word problems’, Journal of Mathematical Behaviour, 4, 3–21.
De Corte, E. and Verschaffel, L.: 1985b, An Empirical Validation of Computer Models of Children's Word Problem Solving. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago.
De Corte, E. and Verschaffel, L.: 1985c, ‘Working with simple problems in early mathematics instruction’, in L. Streefland (ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education, P.M.E., Noordwijkerout (The Netherlands), Vol. 1.
DeCorteE., VerschaffelL., and DeWinL.: 1985, ‘Influence of rewording verbal problems on children's problem representations and solutions’ Journal of Educational Psychology 77 460–470.
Del Campo, G. and Clements, M. A.: 1987, ‘Elementary schoolchildren's processing of “Change” arithmetic word problems’, in J. C. Bergeron, N. Herscovics, and C. Kieran (eds.), Proceedings of the Eleventh International Conference on the Psychology of Mathematics Education, P.M.E., Montreal, Vol. 2, pp. 382–386.
DonaldsonM. and BalfourG.: 1968, ‘Less is more: A study of language comprehension in children’, British Journal of Psychology 59, 461–471.
DonaldsonM. and WalesR. J.: 1970, ‘On the acquisition of some relational terms’, in J. R.Hayes (ed.), Cognition and the Development of Language, Wiley, New York.
FennemaE. and TartreL. A.: 1985, ‘The use of spatial visualization in mathematics by girls and boys’, Journal for Research in Mathematics Education 16, 184–206.
FusonK. C. and HallJ. W.: 1983, ‘The acquisition of early number word meanings: A conceptual analysis and review’, in H. P.Ginsburg (ed.), The Development of Mathematical Thinking, Academic Press, New York.
Graham, B. E.: 1986, Language and Mathematics in the Aboriginal Context: A Study of Classroom Interactions about Addition in the Early Years, unpublished M.Ed. thesis, Deakin University.
HarrisP.: 1988, Measurement in Tribal Aboriginal Communities, Northern Territory Department of Education, Darwin.
Heller, J. I. and Greeno, J. G.: 1978, Semantic Processing of Arithmetic Word Problems. Paper presented at the Annual Meeting of the Midwestern Psychological Association, Chicago.
HiebertJ. CarpenterT. P., and MoserJ. M.: 1982, ‘Cognitive development and children's performance on addition and subtraction problems’, Journal for Research in Mathematics Education 13, 83–98.
HudsonT.: 1983, ‘Correspondences and numerical differences between disjoint sets’, Child Development 54, 84–90.
JonesJ.: 1974, Cognitive Studies with Students in Papua New Guinea (Working Paper No. 10), University of Papua New Guinea, Port Moresby.
JonesP. L.: 1982, ‘Learning mathematics in a second language: A problem with more and less’, Educational Studies in mathematics 13, 269–287.
KintschW. and GreenoJ. F.: 1985, ‘Understanding and solving word arithmetic problems’, Psychological Review 92, 109–129.
LangfordP. E.: 1986, ‘Arithmetic word problems: Thinking in the head versus thinking on the table’, Educational Studies in Mathematics 17, 193–199.
LeanG. A. and ClementsM. A.: 1981, ‘Spatial ability, visual imagery, and mathematical performance’, Educational Studies in Mathematics 12, 267–299.
LewisA. B. and MayerR. E.: 1987, ‘Students' miscomprehension of relational statements in arithmetic word problems’, Journal of Educational Psychology 79(4), 363–371.
MarriottP.: 1978, ‘Fractions: Now you see them, now you don't’, in D.Williams (ed.), Learning and Applying Mathematics, Australian Association of Mathematics Teachers, Melbourne.
NewmanM. A.: 1983, Language of Mathematics Kit, Harcourt, Brace, and Jovanovich, Sydney.
PalermoD. S.: 1973, ‘More about less: A study of language comprehension of “less”’, Developmental Psychology 10, 827–829.
Quinn, M. J.: 1984, Visualization in Learning Mathematics, unpublished Ph.D. thesis, Monash University, Melbourne.
RichardsM. R.: 1979, ‘Sorting out what's in a word from what's not: Evaluating Clark's semantic features acquisition theory’ Journal of Experimental Child Psychology 27, 1–47.
RileyM. S., GreenoJ. G. and HellerJ. I.: 1983, ‘Development of children's problem-solving ability in arithmetic’, in H. P.Ginsburg (ed.), The Development of Mathematical Thinking, Academic Press, New York.
SiegelL. S.: 1978, ‘The relationship of language and thought in the preoperational child: A reconsideration of nonverbal alternatives to Piagetian tasks’, in L. S.Siegel and C. J.Brainerd (eds.), Alternatives to Piaget: Critical Essays on the Theory, Academic Press, New York.
Suwasono, S.: 1982, Visual Imagery in the Mathematical Thinking of Seventh Grade Students, unpublished Ph.D. thesis, Monash University Melbourne.
VergnaudG. A.: 1982, ‘Classification of cognitive tasks and operations of thought involved in addition and subtraction problems’, in T. P.Carpenter, J. M.Moser and T.Romberg (eds.), Addition and Subtraction: A Cognitive Perspective, Erlbaum, Hillsdale, N.J.
WeinerS. L.: 1978, ‘On the development of more and less’, Journal of Experimental Child Psychology 26, 271–287.
WhiteR. T.: 1985, ‘Interview protocols and dimensions of cognitive structure’, in L. H. T.West and A. L.Pines (eds.), Cognitive Structure and Conceptual Change, Academic Press, New York.
WhiteR. T.: 1986, ‘Origins of PEEL’, in J. R.Baird and I. J.Mitchell (eds.), Improving the Quality of Teaching and Learning, Monash University, Melbourne.
WillisG. B. and FusonK. C.: 1988, ‘Teaching children to use schematic drawings to solve addition and subtraction word problems’, Journal of Educational Psychology, 80(2), 192–201.
WishartL.: 1977, ‘Language as a factor in the teaching of mathematics in primary school infant departments: The acquisition and use of polarised comparative terms’, in M. A.Clements and J.Foyster (eds.), Research in Mathematics Education in Australia, 1977, Vol. 2, Swinburne College Press, Melbourne.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lean, G.A., Clements, M.A. & Del Campo, G. Linguistic and pedagogical factors affecting children's understanding of arithmetic word problems: A comparative study. Educ Stud Math 21, 165–191 (1990). https://doi.org/10.1007/BF00304900
Issue Date:
DOI: https://doi.org/10.1007/BF00304900