Counting Ability Of Moderately And Mildly Handicapped Children 1 2

Abstract

This study examined what basic counting competencies, difficulties, skill progressions, and variation could be expected in school children classified as mentally handicapped. A total of 13 elementary and 23 intermediate children classified as moderately mentally handicapped and 37 elementary and 27 intermediate children classified as mildly mentally handicapped were individually administered structured interviews. Quantitative and qualitative analyses indicated deficiencies in basic counting competencies and systematic oral- and object-counting errors. Moreover, object-counting competence preceded automatic pattern recognition. Finally, there were striking individual differences in ability, even within “homogeneous” groups of children. Basic counting knowledge, which is acquired by most typical children before formal schooling, cannot be taken for granted in mentally handicapped children of school age. Error analyses provide clues to oral- and object-counting difficulties and direction for remedial efforts. Accurate and ample object-counting experience is essential for the development of more advanced skills, such as automatic pattern recognition. Instructional planning should be based on diagnoses of specific strengths and weaknesses, not generic labels.

Get full access to this article

View all access options for this article.

References

Baroody

A. J.

(in press-a). Children's mathematical thinking: A developmental framework for preschool, primary, and special education teachers. New York: Teachers College.

Baroody

A. J.

(in press-b). A guide to teaching basic mathematics in the primary grades. Boston: Allyn and Bacon.

Baroody

A. J.

, & Ginsburg

H. P.

(1982). Preschoolers’ informal mathematical skills: Research and diagnosis. American Journal of Diseases of Children, 136, 195–197.

Baroody

A. J.

, & Snyder

(1983). A cognitive analysis of basic arithmetic abilities of TMR children. Education and Training of the Mentally Retarded, 18, 253–259.

Beckmann

(1924). Die Entwicklung der Zahlleistung bei 2-6 jahrigen Kindern. Zietschrift fur Angewandte Psychologie, 22, 1–72.

Bjonerud

C. E.

(1960). Arithmetic concepts possessed by the preschool child. Arithmetic Teacher, 8, 347–350.

Darlington

R. B.

(1974). Radicals and squares. Ithaca, NY: Logan Hill.

Denny

M. R.

(1964). Research in learning and performance. In Stevens

H. A.

& Heber

(Eds.), Mental Retardation (pp. 100–142). Chicago: University of Chicago.

Freeman

(1965). Elementary applied statistics: for students of behavioral science. New York: Wiley & Sons.

10.

Fuson

K. C.

, & Hall

J. W.

(1983). The acquisition of early number word meanings: A conceptual analysis and review. In Ginsburg

H. P.

(Ed.), The development of mathematical thinking (pp. 50–102). New York: Academic.

11.

Fuson

K. C.

, & Mierkiewicz

D. B.

(1980, April). A detailed analysis of the act of counting. Paper presented at the annual meeting of the American Educational Research Association, Boston.

12.

Fuson

K. C.

, Pergament

G. G.

, Lyons

B. G.

, & Hall

J. W.

(1985). Children's conformity to the cardinality rule as a function of set size and counting accuracy. Child Development, 56, 1429–1436.

13.

Fuson

K. C.

, Richards

, & Briars

D. J.

(1982). The acquisition and elaboration of the number word sequence. In Brainerd

(Ed.), Children's logical and mathematical cognition (pp. 33–91). New York: Springer-Verlag.

14.

Gelman

(1982). Basic numerical abilities. In Sternberg

R. J.

(Ed.), Advances in the psychology of intelligence: Vol. 1 (pp. 181–205). Hillsdale, NJ: Erlbaum.

15.

Gelman

(1977). How young children reason about small numbers. In Castellan

N. J.

Jr. , Pisoni

D. B.

, & Potts

G. R.

(Eds.), Cognitive Theory, Vol. 2 (pp. 219–238). New York: Wiley.

16.

Gelman

, & Gallistel

C. R.

(1978). The child's understanding of number. Cambridge, MA: Harvard.

17.

Gelman

, & Meck

(1986). The notion of principle: the case of counting. In Hiebert

(Ed.), The relationship between procedural and conceptual competence (pp. 29–57). Hillsdale, NJ: Erlbaum.

18.

Ginsburg

H. P.

, & Baroody

A. J.

(1983). The test of early mathematics ability (TEMA). Austin, TX: Pro-Ed.

19.

Klahr

, & Wallace

J. G.

(1973). The role of quantification operators in the development of conservation of quantity. Cognitive Psychology, 4, 301–327.

20.

Nie

N. H.

, Hall

C. H.

, Jenkins

J. G.

, Steinbrenner

, & Bent

D. H.

(1975). SPSS-statistical package for the social sciences (Second Edition). New York: McGraw-Hill Book Co.

21.

Resnick

L. B.

(1983). A developmental theory of number understanding. In Ginsburg

H. P.

(Ed.), The development of mathematical thinking (pp. 109–151). New York: Academic.

22.

Resnick

L. B.

, & Ford

W. W.

(1981). The psychology of mathematics for instruction. Hillsdale, NJ: Erlbaum.

23.

Schaeffer

, Eggleston

, & Scott

(1974). Number development in young children. Cognitive Psychology, 6, 357–379.

24.

Secada

W. G.

, Fuson

K. C.

, & Hall

(1983). The transition from counting-all to counting-on in addition. Journal for Research in Mathematics Education, 14, 47–57.

25.

Senders

V. L.

(1958). Measurement and statistics. New York: Oxford University.

26.

Siegler

R. S.

, & Robinson

(1982). The development of numerical understanding. In Reese

H. W.

(Ed.), Advances in child development and behavior (pp. 241–312). New York: Academic.

27.

Spradlin

J. E.

, Cotter

V. M.

, Stevens

, & Friedman

(1974). Performance of mentally retarded children on pre-arithmetic tasks. American Journal of Mental Deficiency, 78, 397–403.

28.

Strauss

A. A.

, & Lehtinen

L. E.

(1950). Psychopathology and education of the brain-injured child. New York: Grune & Stratton.

29.

von Glasersfeld

(1982). Subitizing: The role of figural patterns in the development of numerical concepts. Archives de Psychologie, 50, 191–218.

30.

Wagner

, & Walters

(1982). A longitudinal analysis of early number concepts: From numbers to number. In Forman

(Ed.), Action and thought (pp. 137–161). New York: Academic.

31.

Wang

M. C.

, Resnick

L. B.

, & Boozer

R. F.

(1971). The sequence of development of some early mathematical behaviors. Child Development, 42, 1767–1778.

32.

Williams

A. H.

(1965). Mathematical concepts, skills, and abilities of kindergarten entrants. Arithmetic Teacher, 12, 261–268.