The study assessed a range of basic arithmetic abilities of 15 trainable mentally retarded students. Tasks were administered to the students individually over three sessions. Subjects were generally capable of rule-governed counting and other counting skills such as the cardinality rule. A number of subjects were capable of mentally comparing numbers and choosing the larger. At least one subject appeared to have invented a more economical mental addition strategy. Some subjects demonstrated a basic form of problem solving: They used the addition identity and commutativity principles to short-cut computational effort. Implications for the classroom teacher and future research are described.
Get full access to this article
View all access options for this article.
References
1.
FusonK. C., & MierkiewiczD. (1980, April). A detailed analysis of the act of counting. Paper presented at the annual meeting of the American Educational Research Association, Boston.
2.
AllardiceB. S. & GinsburgH. P. (1983). Children's learning problems in mathematics. In GinsburgH. P. (Ed.), The development of mathematical thinking. New York: Academic Press.
3.
BaroodyA. J. (in press). The case of Felicia: A young child's strategies for reducing memory demands during mental addition. Cognition and Instruction. (a)
4.
BaroodyA. J. (in press). The value of informal approaches to mathematics instruction and remediation. Arithmetic Teacher. (b)
5.
BaroodyA. J. & GinsburgH. P. (1982). Preschoolers’ informal mathematical skills: Research and diagnosis. American Journal of Diseases of Children, 136, 195–197.
6.
BaroodyA. J., GinsburgH., & WaxmanB. (1983). Children's use of mathematical structure. Journal for Research in Mathematics Education, 14(5), 361–368.
7.
BrownA. L., & DeLoacheJ. S. (1978). Skills, plans, and self-regulation. In SieglerR. S. (Ed.), Children's thinking: What develops?Hillsdale, NJ: Lawrence Erlbaum Associates.
8.
BrownL., & BellamyT. (1972). A sequential procedure for teaching addition to trainable mentally retarded students. The Training School Bulletin, 69, 31–44.
9.
BrownL., BellamyT., & GadberryE. (1971). A procedure for the development of rudimentary concepts in low functioning trainable students. The Training School Bulletin, 68, 178–185.
10.
BurtonT. A. (1974). Education for trainables: An impossible dream?Mental Retardation, 12, 46.
11.
ColemanR. (1970). A pilot demonstration of the utility of reinforcement techniques in trainable programs. Education and Training of the Mentally Retarded, 5, 68–70.
12.
DollE. A. (1931). A survey and program for special types of education in Trenton, N.J. White House Conference on Child Health and Protection, Section III. Washington, DC.
13.
DunnL. M. (1963). Exceptional children in the schools. New York: Holt, Rinehart & Winston.
14.
EstesB. W., & CombsA. (1966). Perception of quantity. Journal of Genetic Psychology, 108, 333–336.
15.
FusonK. C., RichardsJ., & BriarsD. J. (1982). The acquisition and elaboration of the number word sequence. In BrainardC. (Ed.), Children's logical and mathematical cognition. Secaucus, NJ: Springer-Verlag.
16.
GelmanR., & GallistelC. (1978). Young children's understanding of number. Cambridge: Harvard University Press.
17.
GelmanR., & TuckerM. F. (1975). Further investigations of the young child's conception of number. Child Development, 46, 167–175.
18.
GinsburgH. P. (1977). Children's arithmetic: The learning process. New York: D. Van Nostrand.
19.
GinsburgH. P. (1980). Children's surprising knowledge of arithmetic. Arithmetic Teacher, 28(1), 42–44.
20.
GinsburgH. P., & RussellR. L. (1981). Mathematical thinking in inner city black preschool children. Monographs of the Society for Research in Child Development.
21.
GoldbergI. I., & RookeM. L. (1967). Research and educational practices with mentally deficient children. In HaringN. G. & SchiefelbuschR. L. (Eds.), Methods in special education. New York: McGraw-Hill.
22.
GroenG. J., & ResnickL. B. (1977). Can preschool children invent addition algorithm?Journal of Educational Psychology, 69(6), 645–652.
23.
HirshorenA., & BurtonT. A. (1979). Teaching academic skills to trainable mentally retarded children: A study in tautology. Mental Retardation, 17(4), 177–179.
24.
IlgF., & AmesL. B. (1951). Developmental trends in arithmetic. The Journal of Genetic Psychology, 79, 3–28.
25.
KailR. (1979). The development of memory. San Francisco: W. H. Freeman.
26.
KirkS. A. (1957). Public school provisions for severely retarded children: A survey of practices in the United States. Albany, New York: State Interdepartmental Health Resources Board.
27.
McCarthyJ. J., & ScheerenbergerR. C. (1966). A decade of research on the education of the mentally retarded. Mental Retardation Abstracts, 3, 481–501.
28.
ResnickL. B. (1983). A developmental theory of number understanding. In GinsburgH. P. (Ed.), The development of mathematical thinking. New York.
29.
ResnickL. B., & FordW. (1981). The psychology of mathematics for instruction. Hillsdale, NJ: Lawrence Erlbaum Associates.
30.
SchaefferB., EgglestonV., & ScottJ. (1974). Number development in young children. Cognitive Psychology, 6, 357–379.
31.
SpradlinJ. E., CotterV. M., StevensC., & FriedmanM. (1974). Performance of mentally retarded children on pre-arithmetic tasks. American Journal of Mental Deficiency, 78, 397–403.
32.
StarkeyP., & GelmanR. (1982). The development of addition and subtraction abilities prior to formal schooling in arithmetic. In CarpenterT. P., MoserJ. M., & RombergT. A. (Eds.), Addition and subtraction. Hillsdale, NJ: Lawrence Erlbaum Associates.
33.
WarrenS. A. (1963). Academic achievement of trainable pupils with five or more years of schooling. The Training School Bulletin, 60, 75–86.
