American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: Editor-in-chief: Ratko Pavlović
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American Journal of Educational Research. 2016, 4(18), 1249-1256
DOI: 10.12691/education-4-18-2
Open AccessArticle

The Effects of Training on Computational Fluency and Working Memory on Students’ Achievement and Retention in Algebra

Jennifer O. Parcutilo1, and Charita A. Luna1

1University of Science and Technology of Southern Philippines, Philippines

Pub. Date: November 28, 2016

Cite this paper:
Jennifer O. Parcutilo and Charita A. Luna. The Effects of Training on Computational Fluency and Working Memory on Students’ Achievement and Retention in Algebra. American Journal of Educational Research. 2016; 4(18):1249-1256. doi: 10.12691/education-4-18-2


Many students, despite a good understanding of mathematical concepts, are hindered by simple calculations. Recent cognitive researches claimed that working memory which is the limited capacity system of the brain that allows simultaneous storage and processing of temporary information may be improved through trainings and, consequently, improved mathematics performance. The purpose of this study is to investigate the effect of the dual task training on computational fluency with a load of working memory task compared to the traditional basic mathematics drill on the students’ achievement and retention in high school algebra. This research made use of two randomly chosen intact groups of fourth year high school students who were given both pretest and posttest using three validated instruments. A 3-week follow-up test was administered to assess algebra retention. This study found that the students who received the dual task training have significantly higher gains in their computational fluency and working memory ability. However, both groups were comparable in terms of their algebra achievement and retention after the 6-week training. The computational fluency was also found to be a predictor of the students’ achievement and retention in algebra. Thus, the working memory training has no direct effect on the students’ algebra achievement but mediated the effect of computational fluency. A longer and uninterrupted experimental period is recommended for further studies with a focus on binary number tasks as this was found to predict computational fluency.

working memory computational fluency training

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[1]  Alloway, T.P., Bibile, V., & Lau, G. (2013). Computerized working memory training: Can it lead to gains in cognitive skills in students? Computers in Human Behavior, 29, 632-638.
[2]  Baddeley, A.D. (1986). Working memory. Oxford University Press, UK: Clarendon.
[3]  Bull, R., & Johnston, R. S. (1997). Children's arithmetic difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology, 65, 1-24.
[4]  Carpenter, P. A., Just, M. A. & Shell, P. (1990). What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test. Psychological Review , 97: 404-31.
[5]  Calhoon, M.B., Emerson, R. W., Flores, M., Houchins, D. (2007). Computational Fluency Performance Profile of High School Students with Mathematics Disabilities. Remedial and Special Education, 28(5), 292-303.
[6]  Delany, S., Ball D.L., Hill, H. Schilling, S. & Zopf, D. (2008). “Mathematical knowledge for teaching”: adapting US measures for use in Ireland. Journal of Mathematics Teacher Education V.2(3), 171-197.
[7]  Duncan, J. (2001). An adaptive coding model of neural function in the prefrontal cortex. Nature Reviews: Neuroscience, 2:820-29.
[8]  Engle, R. W., Tuholski, S. W., Laughlin, J. E. & Conway, A. R. (1999b). Working memory, short-term memory, and general fluid intelligence: A latentvariable approach. Journal of Experimental Psychology: General, 128(3), 309-31.
[9]  Geary, D.C. (1993). Mathematical disabilities: cognitive, neuropsychological, and genetic components. Psychological bulletin, 114(2), 345.
[10]  Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J.R., et al. (2009). Assisting students struggling with mathematics: Response to intervention for elementary and middle schools. Washington, DC: U.S. Department of Education Institute of Educational Sciences.
[11]  Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner & C. Kieran (Eds.),. Research issues in the learning and teaching of algebra, 60-86. Reston, VA: National Council of Teachers of Mathematics.
[12]  Hitch, G. J., & McAuley, E. (1991). Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology, 82, 375-386.
[13]  Holmes, J., Gathercole, S.E., & Dunning, D.L. (2009). Adaptive training leads to sustained enhancement of poor working memory in children. Developmental Science, 12(4), F9-F15.
[14]  Henry, L.A., Messer, D.J. & Nash, G. (2014). Testing for near and far transfer effects with a short, face-to-face adaptive working memory training intervention in typical children. Infant and child development, 23: 84-103.
[15]  Jaeggi, S.M., Buschkuehl, M., Jonides, J. & Perrig, W.J. (2008). Improving Fluid Intelligence with Training on Working Memory.
[16]  Karbach, J., Strobach, T. & Schubert, T. (2015). Adaptive working -memory training benefits reading, but not mathematics in middle childhood. Child Neuropsychology,21(3), 285-301.
[17]  Keeler, M.L. & Swanson, H.L. (2001). Does Strategy Knowledge Influence Working Memory in Children with Mathematical Disabilities?. Journal of Learning Disabilities, 34(5), 418, 17 pages.
[18]  Kyllonen, P. C. & Christal, R. E. (1990). Reasoning ability is (little more than) working memory capacity?! Intelligence, 14:389-433.
[19]  Melby-Lervag, M. & Hulme, C. (2012). Is working memory training effective? A meta-analytic review. Developmental Psychology, 49(2), 270-291.
[20]  Miller, E. K. & Cohen, J. D. (2001). An integrative theory of prefrontal cortex function. Annual Review of Neuroscience 24:167-202.
[21]  National Council of Teachers of mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
[22]  National Mathematics Advisory Panel. (2008). Final Report: Foundations for Success. Western initiative for strengthening education in math. WISE Math.
[23]  National Research Council. (2001). Looking at Mathematics and Learning. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Adding it up: Helping children learn mathematics (pp. 1-16). Washington, DC: National Academy Press.
[24]  Prabhakaran, V., Narayanan, K., Zhao, Z. & Gabrieli, J. D. E. (2000). Integration of diverse information in working memory within the frontal lobe. Nature Neuroscience, 3:85-90.
[25]  Raghubar, K.P., Barnes, M.A. & Hecht, S.A. (2009). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20(2010), 110-122.
[26]  Sfard, A. (2000). On reform movement and the limits of mathematical discourse. Mathematical Thinking and Learning, 2(3), 157-189.
[27]  Siegel, L. S., & Ryan, E. B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60, 973-980.
[28]  Swanson, H. L. (1993). Working memory in learning disability subgroups. Journal of Experimental Child Psychology, 56, 87-114.
[29]  Tolar, T.D., Lederberg, A.R. & Fletcher, J.M. (2009). A Structural Model of Algebra Achievement: Computational Fluency and Spatial Visualisation as Mediators of the Effect of Working Memory on Algebra Achievement. Educational Psychology, 29(2), 239.
[30]  Van der Molen, M.J., Van Luit, J.E.H., Van der Molen, M.W., Klugkist, I.,& Jongmans, M.J. (2010). Effectiveness of a computerized working memory training in adolescents with mild to borderline intellectual disabilities. Journal of Intellectual Disability Research, 54(5), 433-447.
[31]  Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning Disabilities Quarterly.