A structural model of algebra achievement: Computational fluency and spatial visualisation as mediators of the effect of working memory on algebra achievement

Educational Psychology

Volumn 29, Issue 2, 2009, Pages 239-266

  Tolar, Tammy Daun ^a   Lederberg, Amy R ^b   Fletcher, Jack M ^a  

^a UNIVERSITY OF HOUSTON   (United States)

^b GEORGIA STATE UNIVERSITY   (United States)

Author keywords

Academic achievement; Cognitive ability; Mathematical cognition; Mathematics; Working memory

Indexed keywords

EID: 70449686430     PISSN: 01443410     EISSN: 14695820     Source Type: Journal    
DOI: 10.1080/01443410802708903     Document Type: Article

References (67)

1. Baddeley, A. (1999). Essentials of human memory. Hove, UK: Psychology Press.
2. Bell, A. (1996). Problem-solving approaches to algebra: Two aspects. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 167-185). Norwell, MA: Kluwer Academic.
3. Bennet, G.K., Seashore, H.G., & Wesman, A.G. (1989). Differential aptitude tests for personnel and career assessment: Space relations. San Antonio, TX: Psychological Corporation/Harcourt Brace.
4. Bennet, G.K., Seashore, H.G., & Wesman, A.G. (1991). Differential Aptitude Tests for personnel and career assessment: Technical manual. San Antonio, TX: Psychological Corporation/Harcourt Brace.
5. Bentler, P.M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238-246.
6. Blanton, M.L., & Kaput, J.J. (2002). Instructional contexts that support students' transition from arithmetic to algebraic reasoning: Elements of tasks and culture. Paper presented at the NCTM Annual Conference Research Pre-session, Las Vegas, NV.
7. Bull, R., & Johnston, R.S. (1997). Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology, 65, 1-24.
8. Bull, R., Johnston, R.S., & Roy, J.A. (1999). Exploring the roles of the visual-spatial sketch pad and central executive in children's arithmetical skills: Views from cognition and developmental neuropsychology. Developmental Neuropsychology, 15, 421-442.
9. Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children's mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19, 273-293.
10. Campbell, J.I.D., & Arbuthnott, K. (1996). Inhibitory processes in sequential retrieval: Evidence from variable-lag repetition priming. Brain and Cognition, 30, 59-80.
11. Carry, L.R., Lewis, C., & Bernard, J.E. (1980). Psychology of equation solving: An information processing study (Tech. Rep. SED 78-22293). Austin: University of Texas Department of Curriculum and Instruction.
12. Casey, M.B., Nuttall, R.L., & Pezaris, E. (1997). Mediators of gender differences in mathematics college entrance test scores: A comparison of spatial skills with internalized beliefs and anxieties. Developmental Psychology, 33, 669-680.
13. College Board. (1989). Guide to the use of the descriptive tests of mathematics skills. Princeton, NJ: Educational Testing Service.
14. College Board. (1995a). Descriptive tests of mathematics skills in elementary algebra skills. Princeton, NJ: Educational Testing Service.
15. College Board. (1995b). Descriptive tests of mathematics skills in intermediate algebra skills. Princeton, NJ: Educational Testing Service.
16. College Board. (2005). 2005 college-bound seniors: Total group profile report. Retrieved May 16, 2007, from http://www.collegeboard.com/prod_downloads/about/news_info/cbsenior/yr2005/2005-college-bound-seniors.pdf
17. Conway, A.R.A., Cowen, N., Bunting, M.F., Therriault, D.J., & Minkoff, S.R.B. (2002). A latent variable analysis of working memory capacity, short-term memory capacity, processing speed, and general fluid intelligence. Intelligence, 30, 163-183.
18. Conway, A.R.A., Kane, M.J., Bunting, M.F., Hambrick, D.Z., Wilhelm, O., & Engle, R.W. (2005). Working memory span tasks: A methodological review and user's guide. Psychonomic Bulletin and Review, 12, 769-786.
19. Cowan, N. (2000). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87-185.
20. 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.
21. Demetriou, A., Christou, C., Spanoudis, G., & Platsidou, M. (2002). The development of mental processing: Efficiency, working memory, and thinking. Monographs of the Society for Research in Child Development, 67, 1-169.
22. DeStefano, D., & LeFevre, J.-A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16, 353-386.
23. Ekstrom, R.B., French, J.W., Harman, H.H., & Derman, D. (1976). Manual for kit of factorreferenced cognitive tests. Princeton, NJ: Educational Testing Service.
24. Engle, R.W., Tuholski, S.W., Laughlin, J.E., & Conway, A. (1999). Working memory, shortterm memory, and general fluid intelligence: A latent-variable approach. Journal of Experimental Psychology: General, 128, 309-331.
25. English, L.D., & Sharry, P.V. (1996). Analogical reasoning and the development of algebraic abstraction. Educational Studies in Mathematics, 30, 135-157.
26. Espy, K.A., McDiarmid, M.M., Cwik, M.F., Stalets, M.M., Hamby, A., & Senn, T.E. (2004). The contribution of executive functions to emergent mathematical skills in preschool children. Developmental Neuropsychology, 26, 465-486.
27. Floyd, R.G., Evans, J.J., & McGrew, K.S. (2003). Relations between measures of CattellHorn-Carroll cognitive abilities and mathematics achievement across the school-age years. Psychology in the Schools, 40, 155-171.
28. Foegen, A., Olson, J., & Perkmen, S. (2005). Reliability and criterion validity of four revised algebra measures in districts B and C (Project AAIMS: Algebra Assessment and Instruction - Meeting Standards Technical Report #10). Retrieved March 1, 2006, from http://www.ci.hs.iastate.edu/aaims/technical.html
29. Foster, A.G., Winters, L.J., Gell, J.M., Rath, J.N., & Gordon, B.W. (1995). Merrill algebra 1: Applications and connections. New York: Glencoe/McGraw-Hill.
30. Friedman, L. (1995). The space factor in mathematics: Gender differences. Review of Educational Research, 65, 22-50.
31. Gallagher, A.M. (1992). Sex differences in problem solving strategies used by high-scoring examinees on the SAT-M (Publication no. ED 352420). Retrieved June 14, 2007 from http://eric.ed.gov.
32. Gathercole, S.E., Pickering, S.J., Knight, C., & Stegmann, Z. (2004). Working memory skills and educational attainment: Evidence from national curriculum assessments at 7 and 14 years of age. Applied Cognitive Psychology, 18, 1-16.
33. Geary, D.C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345-362.
34. Geary, D.C., Saults, S.J., Liu, F., & Hoard, M.K. (2000). Sex differences in spatial cognition, computational fluency, and arithmetical reasoning. Journal of Experimental Child Psychology, 77, 337-353.
35. Heid, M.K. (1996). A technology-intensive functional approach to the emergence of algebraic thinking. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 239-255). Norwell, MA: Kluwer Academic.
36. Hu, L.T., & Bentler, P.M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.
37. Janvier, C. (1996). Modeling and the initiation into algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 225-236). Norwell, MA: Kluwer Academic.
38. Jarvis, H.L., & Gathercole, S.E. (2003). Verbal and non-verbal working memory and achievement on National Curriculum tests at 11 and 14 years of age. Educational and Child Psychology, 20, 123-140.
39. Joreskog, K., & Sorbom, D. (2006). LISREL 8.80 student edition. Lincolnwood, IL: Scientific Software International.
40. Kane, M.J., Hambrick, D.Z., Tuholski, S.W., Wilhelm, O., Payne, T.W., & Engle, R.W. (2004). The generality of working memory capacity: A latent-variable approach to verbal and visuospatial memory span and reasoning. Journal of Experimental Psychology: General, 133, 189-217.
41. Kaput, J.J. (1999). Teaching and learning a new algebra with understanding. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Mahwah, NJ: Erlbaum.
42. Kieran, C. (1990). Cognitive processes involved in learning school algebra. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 96-112). New York: Cambridge University Press.
43. Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-414). New York: MacMillan.
44. Kline, R.B. (2005). Principles and practice of structural equation modeling. New York: Guilford Press.
45. Lee, K., Ng, S.-F., Ng, E.-L., & Lim, Z.-Y. (2004). Working memory and literacy as predictors of performance on algebraic word problems. Journal of Experimental Child Psychology, 89, 140-158.
46. Lehto, J. (1995). Working memory and school achievement in the ninth form. Educational Psychology, 15, 271-283.
47. Mardia, K.V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530.
48. Mardia, K.V., & Foster, K. (1983). Omnibus tests of multinormality based on skewness and kurtosis. Communications in Statistics, 12, 207-221.
49. Mason, J. (1989). Mathematical abstraction as the result of a delicate shift of attention. For the Learning of Mathematics, 9(2), 2-8.
50. Mason, J. (1996). Expressing generality and roots in algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Norwell, MA: Kluwer Academic.
51. McNeil, N.M., & Alibali, M.W. (2005). Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76, 883-899.
52. Miyake, A., Friedman, N.P., Rettinger, D.A., Shah, P., & Hegarty, M. (2001). How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis. Journal of Experimental Psychology: General, 130, 621-640.
53. Oberauer, K., Heinz-Martin, S., Wilhelm, O., & Werner, W.W. (2003). The multiple faces of working memory: Storage, processing, supervision, and coordination. Intelligence, 31, 167-193.
54. Peters, M. (1995). Revised Vandenberg & Kuse Mental Rotations Tests: Forms MRT-A to MRT-D. Guelph, ON, Canada: University of Guelph Department of Psychology.
55. Reuhkala, M. (2001). Mathematical skills in ninth-graders: Relationships with visuo-spatial abilities and working memory. Educational Psychology, 21, 387-399.
56. Rohde, T.E., & Thompson, L.A. (2007). Predicting academic achievement with cognitive ability. Intelligence, 35, 83-92.
57. Rojano, T. (1996). The role of problems and problem solving in the development of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 55-62). Norwell, MA: Kluwer Academic.
58. Royer, J.M., Tronsky, L.N., & Chan, Y. (1999). Math-fact retrieval as the cognitive mechanism underlying gender differences in math test performance. Contemporary Educational Psychology, 24, 181-266.
59. Sattler, J.M. (2008). Assessment of children: Cognitive foundations (5th ed.). San Diego, CA: Jerome M. Sattler.
60. Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191-228.
61. Shepard, S., & Metzler, D. (1978). Mental rotation: Effects of dimensionality of objects and types of tasks. Journal of Experimental Psychology: Human Perception and Performance, 14, 3-11.
62. Sleeman, D. (1986). Introductory algebra: A case study of student misconceptions. Journal of Mathematical Behavior, 5, 25-52.
63. Steiger, J.H. (1990). Structural model evaluation and modifications: An interval estimation approach. Multivariate Behavioral Research, 25, 173-180.
64. Swanson, H.L., & Jerman, O. (2006). Math disabilities: A selective meta-analysis of the literature. Review of Educational Research, 76, 249-274.
65. Unsworth, N., Heitz, R.P., Schrock, J., & Engle, R.W. (2005). An automated version of the operation span task. Behavior Research Methods, 37, 498-505.
66. Vandenberg, S.G., & Kuse, A.R. (1978). Mental rotations: A group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47, 599-604.
67. Wechsler, D. (1997). Wechsler Adult Intelligence Scale (3rd ed.). San Antonio, TX: Psychological Corporation.