Difficulties with early numeracy can interfere with the acquisition of mathematics skills in later childhood. Early math intervention is therefore an important issue. Sixty-two 5- to 7-year-old pupils from kindergartens for children with special educational needs were given early mathematics intervention. The early numeracy program was specifically developed for young children with special educational needs and early numeracy difficulties by basing the instruction on perceptual gestalt theory. The results showed that the 62 children in the experimental group performed better at posttest than the 62 children in the comparison group. The children failed, however, to transfer their knowledge to novel math problems.
Get full access to this article
View all access options for this article.
References
1.
Ashcraft, M.H. (1992). Cognitive arithmetic: A review of data and theory . Cognition, 44, 75-106.
Campione, J.C., & Brown, A.L. (1990). Guided learning and transfer: Implications for approaches to assessment. In N. Frederiksen , R. Glaser, A. Lesgold, & M. G. Shafto (Eds.), Diagnostic monitoring of skill and knowledge acquisition (pp. 141-172). Hillsdale, NJ: Erlbaum.
6.
Campione, J.C., Brown, A.L., & Ferrara, R.A. (1982). Mental retardation and intelligence. In R. J. Sternberg (Ed.), Handbook of human intelligence (pp. 392-490). Cambridge, England: Cambridge University Press.
7.
Carpenter, T.P., Ansell, E., Franke, M.L., Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children's problem-solving processes. Journal for Research in Mathematics Education, 24, 428-441.
8.
Carpenter, T.P., & Moser, J.M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179-202.
9.
Clifford, M.M. (1984). Thoughts on a theory of constructive failure. Educational Psychologist, 19, 108-120.
10.
Cobb, P., Gravemeijer, K., Yackel, E., McClain, K., & Whitenack, J. (1997). Mathematizing and symbolizing: The emergence of chains of signification in one first-grade classroom. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition theory: Social, semiotic, and neurological perspectives (pp. 151-233). Hillsdale, NJ: Erlbaum.
11.
Day, J.D. (1986). Teaching summarization skills: Influences of student ability level and strategy difficulty. Cognition and Instruction , 3, 193-210.
12.
Day, J.D., & Hall, L.K. (1988). Intelligence-related differences in learning and transfer and enhancement of transfer among mentally retarded persons. American Journal on Mental Retardation, 93, 135-137.
13.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.
14.
Fennema, E.H. (1972). The relative effectiveness of a symbolic and a concrete model in learning a selected mathematical principle. Journal for Research in Mathematics Education, 3, 233-238.
15.
Flexer, R.J. (1986). The power of five: The step before the power of ten. Arithmetic Teacher, 34(3), 5-9.
16.
Frank, A.R. (1989). Counting skills: A foundation for early mathematics . Arithmetic Teacher, 37(1), 14-17.
17.
Fuson, K.C. (1988). Children's counting and concepts of number. New York: Springer-Verlag.
18.
Fuson, K.C., Perry, T., & Kwon, Y. (1994). Latino, Anglo, and Korean children's finger addition methods. In J. E. H. Van Luit (Ed.), Research on learning and instruction of mathematics in kindergarten and primary school (pp. 220-228). Doetinchem, The Netherlands: Graviant.
19.
Geary, D.C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363-383.
20.
Geary, D.C. (1995). Reflections of evolution and culture in children's cognition. American Psychologist, 50, 24-37.
21.
Geary, D.C., Bow-Thomas, C.C., & Yao, Y. (1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54, 372-391.
22.
Gelman, R., & Gallistel, C.R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
23.
Gick, M.L., & Holyoak, K.J. (1987). The cognitive basis of transfer. In S. M. Cornier & J. D. Hagman (Eds.), Transfer of learning: Contemporary research and applications (pp. 9-46). San Diego: Academic Press.
24.
Ginsburg, H. (1977). Children's arithmetic: The learning process. New York: Van Nostrand.
25.
Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht, The Netherlands: CD-β Press .
26.
Heddens, J.W. (1986). Bridging the gap between the concrete and the abstract. Arithmetic Teacher, 33(6), 14-17.
27.
Janssen, F.J.G., Bokhove, J., & Kraemer, J.-M. (1992). Leerlingvolgsysteem: Rekentoets medio groep 3 [Student monitoring system: Mathematics1 for grade 3]. Arnhem, The Netherlands: Cito.
Mercer, C.D., & Miller, S.P. (1992). Teaching students with learning problems in math to acquire, understand and apply basic math facts. Remedial and Special Education, 13(3), 19-35.
31.
Miller, S.P., & Mercer, C.D. (1993). Using data to learn about concretesemiconcrete-abstract instruction for students with math disabilities. Learning Disabilities Research & Practice, 8, 89-96.
32.
Miller, S.P., & Mercer, C.D. (1997). Educational aspects of mathematics disabilities . Journal of Learning Disabilities, 30, 47-56.
33.
Montague, M., & Applegate, B. (1993). Mathematical problem-solving characteristics of middle school students with learning disabilities. The Journal of Special Education, 27, 175-201.
34.
Norman, W.T. (1963). Towards an adequate taxonomy of personality attributes: Replicated factor structure in peer nomination personality ratings. Journal of Abnormal and Social Psychology, 66, 574-583.
35.
O'Sullivan, J.T., & Pressley, M. (1984). Completeness of instruction and strategy transfer . Journal of Experimental Child Psychology, 38, 275-288.
36.
Parajes, F., & Kranzler, J. (1995). Self-efficacy beliefs and general mental ability in mathematical problem-solving. Contemporary Educational Psychology, 20, 426-443.
37.
Paris, S.G., Newman, R.S., & McVey, K.A. (1982). Learning the functional significance of mnemonic actions: A microgenetic study of strategy acquisition . Journal of Experimental Child Psychology, 34, 490-509.
38.
Peterson, P.L., Fennema, E., & Carpenter, T. (1989). Using knowledge of how students think about mathematics . Educational Leadership, 46(4), 42-46.
39.
Rose, S.A., Feldman, J.F., & Wallace, I.F. (1992). Infant information processing in relation to six-year cognitive outcomes. Child Development, 63, 1126-1141.
40.
Ross, R., & Kurtz, R. (1993). Making manipulatives work: A strategy for success . Arithmetic Teacher, 40(5), 254-257.
41.
Rousseau, L., Bates, T., & Beattie, I. (1985). The structure of school mathematics. Vector, 26, 35-46.
42.
Salomon, G., & Perkins, D.N. (1989). Rocky roads to transfer: Rethinking mechanisms of a neglected phenomenon. Educational Psychologist, 24, 113-142.
43.
Sawada, D. (1985). Mathematical symbols: Insight through invention . Arithmetic Teacher, 32(6), 20-22.
44.
Schopman, E.A.M. (1998). Stimulating early numeracy: The effects of remedial intervention on the early numeracy achievement in young children with special educational needs. Doetinchem, The Netherlands: Graviant.
45.
Schopman, E.A.M., & Van Luit, J.E.H. (1996). Learning and transfer of preparatory arithmetic strategies among young children with a developmental lag. Journal of Cognitive Education, 5, 117-131.
46.
Siegler, R.S., & Jenkins, E. (1989). How children discover new strategies. Hillsdale, NJ: Erlbaum.
47.
Sophian, C. (1987). Early developments in children's use of counting to solve quantitative problems. Cognition and Instruction , 4, 61-90.
48.
Starkey, P., & Cooper, R.G., Jr. (1995). The development of subitizing in young children. British Journal of Developmental Psychology , 13, 399-420.
49.
Starkey, P., & Gelman, R. (1982). The development of addition and subtraction abilities prior to formal schooling in arithmetic. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 99-116). Hillsdale, NJ : Erlbaum.
50.
Stokes, T.F., & Baer, D.M. (1977). An implicit technology of generalization. Journal of Applied Behavior Analysis, 10, 349-367.
51.
Temple, C.M. (1991). Procedural dyscalculia and number fact dyscalculia: Double dissociation in developmental dyscalculia. Cognitive Neuropsychology, 8, 155-176.
52.
Tissink, J., Hamers, J.H.M., & Van Luit, J.E.H. (1993). Learning potential tests with domain-general and domain-specific tasks. In J. H. M. Hamers, K. Sijtsma, & A. J. J. M. Ruijssenaars (Eds.), Learning potential assessment: Theoretical, methodological and practical issues (pp. 243-266). Amsterdam: Swets & Zeitlinger.
53.
Van de Rijt, B.A.M., & Van Luit, J.E.H. (1998). Effectiveness of the AEM program for teaching children early mathematics. Instructional Science, 26, 337-358.
54.
Van Luit, J.E.H., & Naglieri, J.A. (1999). Effectiveness of the MASTER program for teaching special children multiplication and division. Journal of Learning Disabilities, 32, 98-107.
55.
Van Luit, J.E.H., & Schopman, E.A.M. (1998). Als speciale kleuter tel je ook mee! Voorbereidende rekenactiviteiten voor kleuters met een ontwikkelingsachterstand [Young children with special educational needs count, too! Early mathematics activities for young children with special educational needs]. Doetinchem, The Netherlands: Graviant.
56.
Van Luit, J.E.H., & Van de Rijt, B.A.M. (1995). Rekenhulp voor kleuters [Remedial math for children at kindergarten age]. Doetinchem , The Netherlands: Graviant.
57.
Van Luit, J.E.H., Van de Rijt, B.A.M., & Pennings, A.H. (1994). Utrechtse Getalbegrip Toets [Utrecht Test of Number Sense]. Doetinchem, The Netherlands: Graviant.
58.
Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner , & E. Souberman, Eds. & Trans.). Cambridge, MA: Harvard University Press.
59.
Wechsler, D. (1974). Wechsler intelligence scale for children—Revised . San Antonio, TX: Psychological Corp.
60.
Wertheimer, M. (1959). Productive thinking. New York : Harper & Row.
61.
Wilson, C.L., & Sindelar, P.T. (1991). Direct instruction in math word problems: Students with learning disabilities. Exceptional Children, 57, 512-519.
62.
Wynn, K. (1992). Children's acquisition of the number words and the counting system. Cognitive Psychology, 24, 220-251.
63.
Yackel, E., & Cobb, P. (1996). Sociomath norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education , 27, 458-477.
