Fluency, accuracy, and gender predict developmental trajectories of arithmetic strategies

Journal of Educational Psychology

Volumn 103, Issue 3, 2011, Pages 617-631

  Carr, Martha ^a   Alexeev, Natalia ^a  

^a UNIVERSITY OF GEORGIA   (United States)

Author keywords

Arithmetic; Fluency; Gender; Mathematics achievement; Strategies

Indexed keywords

EID: 80051810421     PISSN: 00220663     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0023864     Document Type: Article

References (61)

1. Ashcraft M.H. Strategic processing in children's mental arithmetic: A review and proposal. Children's strategies: Contemporary views of cognitive development 1990, 185-211. Erlbaum, Hillsdale, NJ. D.F. Bjorklund (Ed.).
2. Ashcraft M.H., Donley R.D., Halas M.A., Vakali M. Working memory, automaticity and problem difficulty. The nature and origins of mathematical skill 1992, 301-329. Elsevier, Amsterdam, the Netherlands. 10.1016/S0166-4115(08)60890-0. J.I.D. Campbell (Ed.).
3. Aunola K., Leskinen E., Lerkkanen M.-K., Nurmi J.-E. Developmental dynamics of math performance from preschool to Grade 2. Journal of Educational Psychology 2004, 96:699-713. 10.1037/0022-0663.96.4.699.
4. Baroody A.J. Why children have difficulties mastering the basic number combinations and how to help them. Teaching Children Mathematics 2006, 13:22-31.
5. Baroody A.J., Brach C., Tai Y. The application and development of an addition goal sketch. Cognition and Instruction 2006, 24:123-170. 10.1207/s1532690xci2401_3.
6. Bauer D.J. 2004 Cattell Award Address: Observations on the use of growth mixture models in psychological research. Multivariate Behavioral Research 2007, 42:757-786. 10.1080/00273170701710338.
7. Benbow C.P. Academic achievement in mathematics and science of students between ages 13 and 23: Are there differences among students in the top one percent of mathematical ability?. Journal of Educational Psychology 1992, 84:51-61. 10.1037/0022-0663.84.1.51.
8. Biddlecomb B., Carr M. A longitudinal study of the development of mathematics strategies and underlying counting schemes. International Journal of Science and Mathematics Education 2011, 9:1-24. 10.1007/s10763-010-9202-y.
9. Bisanz J., LeFevre J.A. Strategic and nonstrategic processing in the development of mathematical cognition. Children's strategies: Contemporary views of cognitive development 1990, 213-244. Erlbaum, Hillsdale, NJ. D.F. Bjorklund (Ed.).
10. Boulton-Lewis G.M. Children's strategy use and interpretations of mathematical representations. The Journal of Mathematical Behavior 1998, 17:219-237. 10.1016/S0364-0213(99)80060-3.
11. Brownell W.A. Psychological considerations in the learning and the teaching of arithmetic. The teaching of arithmetic 1935, 1-31. Columbia University, Teachers College, New York, NY. W.D. Reeve (Ed.).
12. Bull R., Johnston R.S. Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology 1997, 65:1-24. 10.1006/jecp.1996.2358.
13. Carpenter T.P., Moser J.M. The acquisition of addition and subtraction concepts in Grades One through Three. Journal for Research in Mathematics Education 1984, 15:179-202. 10.2307/748348.
14. Carr M., Davis H. Gender differences in strategy use: A function of skills and preference. Contemporary Educational Psychology 2001, 26:330-347. 10.1006/ceps.2000.1059.
15. Carr M., Jessup D.L. Gender differences in first-grade mathematics strategy use: Social and metacognitive influences. Journal of Educational Psychology 1997, 89:318-328. 10.1037/0022-0663.89.2.318.
16. Carr M., Jessup D.L., Fuller D. Gender differences in first grade mathematics strategy use: Parent and teacher contributions. Journal for Research in Mathematics Education 1999, 30:20-46. 10.2307/749628.
17. Carr M., Steiner H.H., Kyser B., Biddlecomb B. A comparison of predictors of early emerging gender differences in mathematics competency. Learning and Individual Differences 2008, 18:61-75. 10.1016/j.lindif.2007.04.005.
18. Clements D.H., Sarama J. Learning trajectories in mathematics education. Mathematical Thinking and Learning 2004, 6:81-89. 10.1207/s15327833mtl0602_1.
19. Cooney J.B., Ladd S.F. The influence of verbal protocol methods on children's mental computation. Learning and Individual Differences 1992, 4:237-257. 10.1016/1041-6080(92)90004-X.
20. Enders C.K., Tofighi D. The impact of misspecifying class-specific residual variances in growth mixture models. Structural Equation Modeling: A Multidisciplinary Journal 2008, 15:75-95. 10.1080/10705510701758281.
21. Fennema E., Carpenter T.P., Jacobs V.R., Franke M.L., Levi L. A longitudinal study of gender differences in young children's mathematical thinking. Educational Researcher 1998, 27:6-11.
22. Frensch P.A., Geary D.C. Effects of practice on component processes in complex mental addition. Journal of Experimental Psychology: Learning, Memory, and Cognition 1993, 19:433-456. 10.1037/0278-7393.19.2.433.
23. Fuchs L.S., Compton D.L., Fuchs D., Paulsen K., Bryant J.D., Hamlett C.L. The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology 2005, 97:493-513. 10.1037/0022-0663.97.3.493.
24. Fuson K.C., Stigler J.W., Bartsch K. Grade placement of addition and subtraction topics in Japan, Mainland China, the Soviet Union, Taiwan, and the United States. Journal for Research in Mathematics Education 1988, 19:449-456. 10.2307/749177.
25. Geary D.C. Cognitive addition: On the convergence of statistical and conceptual models. Bulletin of the Psychonomic Society 1987, 25:427-430.
26. Geary D.C. Children's mathematical development 1994, American Psychological Association, Washington, DC.
27. Geary D.C., Brown S.C. Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology 1991, 27:398-406. 10.1037/0012-1649.27.3.398.
28. Geary D.C., Brown S.C., Samaranayaka V.A. Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. Developmental Psychology 1991, 27:787-797. 10.1037/0012-1649.27.5.787.
29. Geary D.C., Hamson C.O., Hoard M.K. Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology 2000, 77:236-263. 10.1006/jecp.2000.2561.
30. Geary D.C., Hoard M.K., Byrd-Craven J., DeSoto M.C. Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology 2004, 88:121-151. 10.1016/j.jecp.2004.03.002.
31. Geary D.C., Salthouse T.A., Chen G.-P., Fan L. Are East Asian versus American differences in arithmetical ability a recent phenomenon?. Developmental Psychology 1996, 32:254-262. 10.1037/0012-1649.32.2.254.
32. Georgia Department of Education The Georgia Department of Education Criterion-Referenced Competency Tests (CRCT): Content descriptions-Mathematics http://www.doe.k12.ga.us.
33. Gersten R., Chard D. Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education 1999, 33:18-28. 10.1177/002246699903300102.
34. Gersten R., Jordan N.C., Flojo J.R. Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities 2005, 38:293-304. 10.1177/00222194050380040301.
35. Goldman S.R., Pellegrino J.W., Mertz D.L. Extended practice of basic addition facts: Strategy changes in learning-disabled students. Cognition and Instruction 1988, 5:223-265. 10.1207/s1532690xci0503_2.
36. Groen G.J., Parkman J.M. A chronometric analysis of simple addition. Psychological Review 1972, 79:329-343. 10.1037/h0032950.
37. Ilg F., Ames L.B. Developmental trends in arithmetic. Journal of Genetic Psychology 1951, 79:3-28.
38. Jordan N.C. Do words count? Connections between mathematics and reading difficulties. Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities 2007, 107-120. Brookes, Baltimore, MD. D.B. Berch, M.M. Mazzocco (Eds.).
39. Jordan N.C., Hanich L.B., Kaplan D. A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with co-morbid mathematics and reading difficulties. Child Development 2003, 74:834-850. 10.1111/1467-8624.00571.
40. Jordan N.C., Kaplan D., Oláh L.N., Locuniak M.N. Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development 2006, 77:153-175.
41. Kerkman D.D., Siegler R.S. Measuring individual differences in children's addition strategy choices. Learning and Individual Differences 1997, 9:1-18. 10.1016/S1041-6080(97)90017-0.
42. Kilpatrick J., Swafford J., Findell B. Adding it up: Helping children learn mathematics 2001, National Academy Press, Washington, DC.
43. Leahey E., Guo G. Gender differences in mathematical trajectories. Social Forces 2001, 80:713-732. 10.1353/sof.2001.0102.
44. Lemaire P., Arnaud L. Young and older adults' strategies in complex arithmetic. The American Journal of Psychology 2008, 121:1-16. 10.2307/20445440.
45. Lo Y., Mendell N.R., Rubin D.B. Testing the number of components in a normal mixture. Biometrika 2001, 88:767-778. 10.1093/biomet/88.3.767.
46. Lubke G., Muthén B. Performance of factor mixture models as a function of model size, covariate effects, and class-specific parameters. Structural Equation Modeling 2007, 14:26-47. 10.1207/s15328007sem1401_2.
47. Muthén B. Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class-latent growth modeling. New methods for the analysis of change 2001, 291-322. American Psychological Association, Washington, DC. 10.1037/10409-010. L.M. Collins, A.G. Sayer (Eds.).
48. Muthén B. The potential of growth mixture modeling. Infant and Child Development 2006, 15:623-625. 10.1002/icd.482.
49. Muthén B., Muthén L.K. Mplus user's guide 1998-2006, Muthén & Muthén, Los Angeles, CA. 4th ed.
50. Principles and standards for school mathematics 2000, National Council of Teachers of Mathematics, Author, Reston, VA.
51. Curriculum focal points for prekindergarten through Grade 8 mathematics: A quest for coherence 2006, National Council of Teachers of Mathematics, Author, Reston, VA.
52. Foundations for success: The final report of the National Mathematics Advisory Panel 2008, National Mathematics Advisory Panel, U.S. Department of Education, Washington, DC.
53. Nylund K.L., Asparouhov T., Muthén B. Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling 2007, 14:535-569.
54. Royer J.M., Tronsky L.N., Chan Y., Jackson S.J., Marchant H. Math-fact retrieval as the cognitive mechanism underlying gender differences in math test performance. Contemporary Educational Psychology 1999, 24:181-266. 10.1006/ceps.1999.1004.
55. Seegers G., Boekaerts M. Gender-related differences in self-referenced cognitions in relation to mathematics. Journal for Research in Mathematics Education 1996, 27:215-240. 10.2307/749601.
56. Siegler R.S. Individual differences in strategy choices: Good students, not-so-good students, and perfectionists. Child Development 1988, 59:833-851. 10.2307/1130252.
57. Siegler R.S. Emerging minds: The process of change in children's thinking 1996, Oxford University Press, New York, NY.
58. Steffe L.P., Cobb P., von Glaserfeld E. Construction of arithmetical meanings and strategies 1988, Springer-Verlag, New York, NY.
59. Svenson O., Sjöberg K. Evolution of cognitive processes for solving simple additions during the first three school years. Scandinavian Journal of Psychology 1983, 24:117-124. 10.1111/j.1467-9450.1983.tb00483.x.
60. Widaman K.F., Little T.D., Geary D.C., Cormier P. Individual differences in the development of skill in mental addition: Internal and external validation of chronometric models. Learning and Individual Differences 1992, 4:167-213. 10.1016/1041-6080(92)90002-V.
61. Zimmerman B.J., Martinez-Pons M. Student differences in self-regulated learning: Relating grade, sex, and giftedness to self-efficacy and strategy use. Journal of Educational Psychology 1990, 82:51-59. 10.1037/0022-0663.82.1.51.