Young children with advanced mathematical skill (N = 276) were followed for two years, during kindergarten through 1st grade or 1st through 2nd grade. Children were randomly assigned to an intervention condition reflecting a constructivist approach or a control condition. Mean scores for the control group on standardized math verbal, and visual-spatial measures increased or remained the same. Boys gained more than girls on the quantitative and visual-spatial measures. The treatment group made greater gains than the control group on quantitative measures only. Gender did not interact with treatment condition. Correlations among the quantitative, verbal, and visual-spatial factors remained stable for control children, but the correlation between quantitative and verbal factors increased for the intervention group.
References
1.
Abbott, R. , & Berninger, V. (1993). Structural equation modeling of relationships among developmental skills and writing skills in primary and intermediate grade writers . Journal of Educational Psychology, 85, 478-508 .
2.
Antell, S.E. , & Keating, D.P. (1983). Perception of numerical invariance in neonates . Child Development, 54, 695-701 .
3.
Assouline, S. , & Lupkowski, A. (1992). Extending the talent search model: The potential of the SSAT-Q for identification of mathematically talented elementary students . In N. Colangelo, S. G. Assouline, & D. L. Ambroson (Eds.). Talent development: Proceedings from the 1991 Henry B. and Jocelyn Wallace National Research Symposium on Talent Development (pp. 223-232). Unionville, NY: Trillium.
4.
Benbow, C.P. (1988). Sex differences in mathematical reasoning ability in intellectually talented preadolescents: their nature, effects, and possible causes . Behavioral and Brain Sciences, 11, 169-183 .
5.
Bentler, P.M. , & Wu, E.J.C. (1995). EQS for Macintosh user's guide. Encino, CA: Multivariate Software .
6.
Case, R. (1985). Intellectual development: Birth to adulthood. New York: Academic Press .
7.
Case, R. (1992). The mind's staircase. Hillsdale, NJ: Erlbaum .
8.
Case, R., & Okamoto, Y. (Eds.). (1996). The role of central conceptual structures in the development of children's thought . Monographs of the Society for Research in Child Development, 61, Serial No. 246 (Nos. 1-2).
9.
Casey, M.B. , Nuttall, R. , Pezaris, E. , & Benbow, C.P. (1991). The influence of spatial ability on gender differences in mathematics college entrance scores across diverse samples . Developmental Psychology, 31, 697-705 .
10.
Connolly, A. (1988). Key Math-Revised. Circle Pines, MN: American Guidance .
11.
Crammond, J. (1992). Analyzing the basic cognitive-developmental processes of children with specific types of learning disability. In R. Case (Ed.), The mind's staircase (pp. 285-302). Hillsdale, NJ: Erlbaum .
12.
Dale, P.S. , Robinson, N.M. , & Crain-Thoreson, C. (1995). Linguistic precocity and the development of reading: The role of extra-linguistic factors . Applied Psycholinguistics, 16, 173-187 . Dark, V.J. , & Benbow, C.P. (1990). Enhanced problem translation and short-term memory components of mathematical talent . Journal of Educational Psychology, 82, 420-429 .
13.
Dark, V.J. , & Benbow, C.P. (1991). Differential enhancement of working memory with mathematical versus verbal precocity . Journal of Educational Psychology, 83, 48-60 .
14.
Duckworth, E. (1987). "The having of wonderful ideas" and other essays on teaching and learning. New York: Teachers College Press .
15.
Friedman, L. (1995). The space factor in mathematics: Gender differences . Review of Educational Research, 65, 22-50 .
16.
Geary, D.C. (1994). Children's mathematical development. Washington, DC: American Psychological Association .
17.
Geary, D.C. , & Brown, S.C. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children . Developmental Psychology, 27, 398-406 .
18.
Hedges, L.V. , & Nowell, A. (1995). Sex differences in mental test scores, variability, and numbers of high-scoring individuals . Science, 269, 41-45 .
19.
Hiebert, J. , Carpenter, T.P. , Fennema, E. , Fuson, K. , Human, P. , Murray, H. , Olivier, A. , & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics . Educational Researcher , 25, 12-21 .
20.
Hyde, J.S. , Fennema, E. , & Lamon, S.J. (1990). Gender differences in mathematics performance: A meta-analysis . Psychological Bulletin,107, 139-155 .
21.
Huhn, H. , & Feldt, L.S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs . Journal of Educational Statistics, 1, 69-82 .
22.
Kamii, C. (1985). Young children re-invent arithmetic. New York: Teachers College Press .
23.
Kamii, C. (1994). Young children continue to reinvent arithmetic, third grade. Implications of Piaget's theory. New York : Teachers College Press .
24.
Lupkowski-Shoplik, A.E. , Sayler, M.F. , & Assouline, S.G. (1993, May). Mathematics achievement of talented elementary students: Basic concepts vs. computation . Paper presented at the Henry B. and Jocelyn Wallace National Research Symposium on Talent Development, The Connie Belin Center for Gifted Education , University of Iowa.
25.
Maccoby, E. , & Jacklin, C.N. (1974). The psychology of sex differences. Stanford, CA: Stanford University Press .
26.
Mills, C.J. , Ablard, K.E. , & Stumpf, H. (1993). Gender differences in academically talented young students' mathematical reasoning: Patterns across age and subskills . Journal of Educational Psychology, 85, 340-346 .
27.
Mulles, I.V.S. , Dossey, J.A. , Owen, E.H. , & Phillips, G.W. (1993). NAEP 1992: Mathematics report card for the nations and the states (Report 23-ST02, prepared by the Educational Testing Services under contract of the National Center for Education Statistics). Princeton, NJ: ETS .
28.
National Council of Teachers of Mathematics ( 1989). Curriculum and evaluation standards for school mathematics . Reston, VA: National Council of Teachers of Mathematics .
29.
Okamoto, Y. (1992a). A developmental analysis of children's knowledge and processes for solving arithmetic word problems. Unpublished doctoral dissertation , Stanford University .
30.
Okamoto, Y. ( 1992b, April). Implications of the notion of central conceptual structures for assessment . Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
31.
Okamoto, Y. , & Case, R. (1996). Exploring the microstructure of children's central conceptual structures in the domain of number . In R. Case & Y. Okamoto (Eds.). The role of central conceptual structures in the development of children's thought . Monographs of the Society for Research in Child Development , 61, Serial No. 246 (Nos. 1-2), pp. 27-58 .
32.
Pletan, M. , Robinson, N.M. , Beminger, V.W. , & Abbott, R.D. (1995). Parents' observations of kindergartners who are advanced in mathematical reasoning . Journal for the Education of the Gifted, 19, 30-44 .
33.
Plomin, R. , & Daniels, J. (1987). Why are children within the family so different from each other? The Brain andBehavioral Sciences, 10, 1-16 .
34.
Robinson, N.M. , Abbott, R.D. , Berninger, V.W. , & Busse, J. (1996). The structure of abilities in math-precocious young children: Gender similarities and differences . Journal of Educational Psychology, 88, 341-352 .
35.
Robinson, N.M. , & Robinson, H.B. (1992). The use of standardized tests with young children. In P. S. Klein & A. J. Tannenbaum (Eds.). To be young and gifted (pp. 141-170). Norwood, NJ: Ablex .
36.
Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development in social context. New York: Oxford University Press .
37.
Romberg, T.A. , & Collis, K.F. (1987). Different ways children learn to add and subtract . Journal for Mathematics Education Monographs, 2.
38.
Siegler, R.S. (1988). Individual differences in strategy choice: Good students, not-so-good students, and perfectionists . Child Development, 59, 833-851 .
Simon, T.J. , Hespos, S.J. , & Rochat, P. (1995). Do infants understand simple arithmetic? A replication of Wynn (1992) . Cognitive Development, 10, 253-269 .
41.
Stanley, J.C. (1990). Finding and helping young people with exceptional mathematical reasoning ability. In M. J. A. Howe (Ed.), Encouraging the development of exceptional skills and talents (pp. 211-221). Leicester , UK: British Psychological Society .
42.
Stanley, J.C. (1994). Gender differences for able elementary school students on above-grade level ability and achievement tests . In N. Colangelo, S. G. Assouline , & D. L. Ambroson (Eds.), Talent development Vol. 2: Proceedings from the 1993 Henry B. and Jocelyn Wallace National Research Symposium on Talent Development (pp. 141-148). Vandalia, OH: Ohio Psychology Press.
43.
Starkey, P. , Spelke, E. , & Gelman, R. (1990). Numerical abstraction by human infants . Cognition, 36, 97-127 .
44.
Thorndike, R. , Hagen, E. , & Sattler, J. (1986). The Stanford-Binet Intelligence Scale (4th ed.). Chicago: Riverside .
45.
Vogel, G. (1997). The calculus of school reform . Science, 277, 1192-1194 .
46.
Walberg, H. , & Tsai, B. (1983). Matthew effects in education . American Educational Research Journal, 20, 359-373 .
47.
Waxman, B. , Robinson, N.M. , & Mukhopadhyay, S. (1997). Teachers nurturing young, math-talented children, RM 96228. Storrs, CT: National Research Center on the Gifted and Talented . Woodcock, R.W. , & Johnson, M.B. (1989, 1990). Woodcock-Johnson Psycho-Educational Battery-Revised. Allen, TX: DLM Teaching Resources .
48.
Wynn, K. (1992). Addition and subtraction by human infants . Nature, 358, 749-750 .
