• Jonathan Brendefur Boise State University
  • S. Strother Boise State University
  • K. Thiede Boise State University
  • S. Appleton Meridian School District



Multiplication, Fact Fluency, Student Achievement, Cognition


Using specific components of three broad learning theories—cognitive, social-interactional, and behavioral—students in 3rd, 4th and 5th grade classrooms were given multiplication fact fluency instruction over a period of five weeks for 10-15 minutes each day. Two different approaches were utilized with two distinct groups of students for the purpose of comparing different approaches to fluency development. Results indicate that students using a strategy-based approach for fluency development by means of instructional tasks emphasizing social-interactional and cognitive theories (particularly Bruner’s theory of Modes of Representation) increased multiplication fact fluency, with a greater degree of consistency, than students using a drill-based approach emphasizing behavioristic techniques such as repetition and memorization.

Author Biography

Jonathan Brendefur, Boise State University

Curriculum, Instruction and Policy Studies



Baek, J. M. (2006). Children's mathematical understanding and invented strategies for multidigit multiplication. Teaching Children Mathematics, 12(5), 242.

Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2009). The array representation and primary children's understanding and reasoning in multiplication. Educational Studies in Mathematics, 70, 217-241.

Baroody, A. J., & Dowker, A. (Eds.). (2003). The development of arithmetic concepts and skills: Constructing adaptive expertise. Mahwah, NJ: Lawrence Earlbaum Associates.

Beishuizen, M., & Anghileri, J. (1998). Which mental strategies in the early number curriculum? A comparision of British ideas and Dutch views. British Educational Research Journal, 24(5), 519-538.

Boonlerts, S., & Inprasitha, M. (2013). The Textbook Analysis on Multiplication: The Case of Japan, Singapore and Thailand. Creative Education, 4(4).

Brownell, W. A. (1935). Psychological considerations in the learning and teaching of arithmetic. In W. D. Reeve (Ed.), The teaching of arithmetic, Tenth yearbook of the National Council of Teachers of Mathematics (pp. 1-31). New York, NY: Teachers College Press.

Bruner, J. S. (1964). The course of cognitive growth. American Psychologist, 19(1), 1-15.

Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, Mass: Belkapp Press.

Campbell, J. I., Chen, Y., & Maslany, A. J. (2013). Retrieval-induced forgetting of arithmetic facts across cultures. Journal of Cognitive Psychology, 25(6), 759-773.

Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. Romberg (Eds.), Mathematics Classrooms that Promote Teaching for Understanding (pp. 19 - 32). Mahwah, NJ: Lawerance Erlbaum Associates.

Chung, I. (2004). A Comparative Assessment of Constructivist and Traditionalist Approaches to Establishing Mathematical Connections in Learning Multiplication. Education, 125(2), 271.

Cobb, P., Yackel, E., & Wood, T. (1993). Discourse, mathematical thinking, and classroom practice. In E. A. Forman, N. Minick & C. A. Stone (Eds.), Contexts for learning: Sociocultural dynamics in children’s development (pp. 91-119). New York: Oxford University Press.

Codding, R. S., Burns, M. K., & Lukito, G. (2011). Meta‐Analysis of Mathematic Basic‐Fact Fluency Interventions: A Component Analysis. Learning Disabilities Research & Practice, 26(1), 36-47.

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., . . . Duckworth, K. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428-1446.

Freudenthal, H. (1973). Mathematics as an educational task: Springer.

Freudenthal, H. (1991). Revisiting Mathematics Education: China Lectures.

Fuson, K. C. (2003). Toward computational fluency in multidigit multiplication and division. Teaching Children Mathematics, 9(6), 300-305.

Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15.

Geary, D. C., Bow-Thomas, C., Liu, F., & Siegler, R. S. (1996).

Development of arithmetical competencies in Chinese and American children: Influence of age, language, and schooling. Child Development, 67(5), 2022-2044.

Geary, D. C., Hoard, M. K., Byrd‐Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78(4), 1343-1359.

Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155-177.

Gray, E., Pitta, D., & Tall, D. (2000). Objects, actions, and images: A perspective on early number development. The Journal of Mathematical Behavior, 18(4), 401-413.

Henry, V. J., & Brown, R. S. (2008). First-grade basic facts: An investigation into teaching and learning of an accelerated, high-demand memorization standard. Journal for Research in Mathematics Education, 39(2), 153-183.

Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 65-97). New York: Macmillan.

Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74(3), 834-850.

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: helping children learn mathematics

Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33-49.

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National mathematics advisory panel. Washington, D.C.: US Department of Education.

Nelson, P. M., Burns, M. K., Kanive, R., & Ysseldyke, J. E. (2013). Comparison of a math fact rehearsal and a mnemonic strategy approach for improving math fact fluency. Journal of school psychology, 51(6), 659-667.

NMAP. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington D.C.: U.S. Department of Education, Office of Planning, Evaluation and Policy Development.

Reese, C. M., Miller, K. E., Mazzeo, J., & Dossey, J. A. (1997). NAEP 1996 Mathematics Report Card for the Nation and the States. Washington, DC: National Center for Education Statistics.

Russell, S. J. (2000). Developing computational fluency with whole numbers in the elementary grades. The New England Math Journal, 32(2), 40-54.

Speiser, R., Schneps, M. H., Heffner-Wong, A., Miller, J. L., & Sonnert, G. (2012). Why is paper-and-pencil multiplication difficult for many people? The Journal of Mathematical Behavior, 31(4), 463-475.

Star, J. R., & Madnani, J. K. (2004). Which way is the "best"? Students' conceptions of optimal strategies for solving equations. Paper presented at the Annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Toronto, Canada.

Steffe, L. P. (1979). A reply to "Formal thinking Strategies: A prerequisite for learning basic facts"? Journal for Research in Mathematics Education, 10(5), 370-374.

Thornton, C. A. (1978). Emphasizing thinking strategies in basic fact instruction. Journal for Research in Mathematics Education, 9(3), 214-227.

Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics instruction – The Wiskobas Project. . Reidel: Dordrecht, The Netherlands.

Van Amerom, B. A. (2003). Focusing on informal strategies when linking arithmetic to early algebra. Educational Studies in Mathematics, 54(1), 63-75.

Van Putten, C. M., van den Brom-Sniiders, P. A., & Beishuizen, M. (2005). Progressive mathematization of long division strategies in Dutch primary schools. Journal for Research in Mathematics Education, 36(1), 44-73.

Wong, M., & Evans, D. (2007). Improving basic multiplication fact recall for primary school students. Mathematics Education Research Journal, 19(1), 89-106.

Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning Disability Quarterly, 29(4), 269-289.

Young-Loveridge, J., & Mills, J. (2009). Teaching multi-digit multiplication using array-based materials. Crossing divides, 635-642.




How to Cite

Brendefur, J., Strother, S., Thiede, K., & Appleton, S. (2015). DEVELOPING MULTIPLICATION FACT FLUENCY. Advances in Social Sciences Research Journal, 2(8).