Measures and References: Arithmetic Fact Retrieval

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Numerous measures exist to gain a full picture of a student's learning strengths and challenges. Following are examples of measures used to assess this Learner Factor. These measures should be administered and interpreted by experienced professionals.

Open-ended formats (Kling & Bay-William, 2014): Using a range of measures including student interviews, observations, writing prompts, and short, untimed quizzes around solving simple arithmetic problems can help capture students' accuracy, flexibility, and efficiency which are core components of Arithmetic Fact Retrieval.


Andersson, U. (2008). Working memory as a predictor of written arithmetical skills in children: the importance of central executive functions. The British Journal of Educational Psychology, 78(Pt 2), 181-203.

Barrouillet, P., & Lepine, R. (2005). Working memory and children's use of retrieval to solve addition problems. Journal of Experimental Child Psychology, 91, 183-204.

Bellon, E., Fias, W., & De Smedt, B. (2016). Are individual differences in arithmetic fact retrieval in children related to inhibition? Frontiers in Psychology, 7, 1-11.

Burns, M. K., Ysseldyke, J., Nelson, P. M., & Kanive, R. (2015). Number of repetitions required to retain single-digit multiplication math facts for elementary students. School Psychology Quarterly, 30(3), 398-405.

Carr, M., & Taasoobshirazi, G. (2017). Is strategy variability advantageous? It depends on grade and type of strategy. Learning and Individual Differences, 54, 102-108.

De Smedt, B., Taylor, J., Archibald, L., & Ansari, D. (2010). How is phonological processing related to individual differences in children's arithmetic skills? Developmental Science, 13(3), 508-520.

De Visscher, A., & Noel, M. P. (2014). The detrimental effect of interference in multiplication facts storing: Typical development and individual differences. Journal of Experimental Psychology: General, 143(6), 2380-2400.

Fanget, M., Thevenot, C., Castel, C., & Fayol, M. (2011). Retrieval from memory or procedural strategies for addition problems: The use of the operand-recognition paradigm in 10-year-old children. Swiss Journal of Psychology, 70(1), 35-39.

Geary, D. C., Hoard, M. K., & Nugent, L. (2012). Independent contributions of the central executive, intelligence, and in-class attentive behavior to developmental change in the strategies used to solve addition problems. Journal of Experimental Child Psychology, 113(1), 49-65.

Hecht, S. A., & Vagi, K. J. (2010). Sources of group and Individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843-859.

Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85(2), 103-119.

Kling, G. & Bay-Williams, J. (2012). Assessing basic fact fluency. Teaching Children Mathematics, 20(8), 488 - 497.

Mabbott, D. J., & Bisanz, J. (2008). Computational skills, working memory, and conceptual knowledge in older children with mathematics learning disabilities. Journal of Learning Disabilities, 41(1), 15-28.

McMullen, J., Brezovsjy, B., Rodriquez-Aflecht, G., Pongsakdi, N., Hannula-Sormunen, M. M., & Lehtinen, E. (2016). Adaptive Number Knowledge : Exploring the foundations of adaptivity with whole-number arithmetic. _Learning and Individual Differences, 47, _172-181.

Mussolin, C., & Noel, M.P. (2008). Specific retrieval deficit from long-term memory in children with poor arithmetic facts abilities. The Open Psychology Journal, 1, 26-34.

Powell, S. R., Fuchs, L. S., Fuchs, D., & Fletcher, J. M. (2009). Effects of fact retrieval tutoring on third-grade students with math difficulties with and without reading difficulties. Learning Disabilities Research and Practice, 24(1), 1-11.

Roussel, J. L., Fayol, M., & Barrouillet, P. (2002). Procedural vs. direct retrieval strategies in arithmetic: A comparison between additive and multiplicative problem solving. European Journal of Cognitive Psychology, 14(1), 61-104.

Schleepen, T. M. J., Van Mier, H. I., & De Smedt, B. (2016). The contribution of numerical magnitude comparison and phonological processing to individual differences in fourth graders' multiplication fact ability. PLoS ONE, 11(6), 1-20.

Simmons, F. R., & Singleton, C. (2007). Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. Dyslexia, 14, 77-94.

Vanbinst, K., Ansari, D., Ghesqui, P., & Smedt, B. De. (2016). Symbolic numerical magnitude is as important to arithmetic as phonological awareness Is to reading. PLoS ONE, 11(3), 1-11.

Vanbinst, K., Ghesquiere, P., & De Smedt, B. (2014). Arithmetic strategy development and its domain-specific and domain-general cognitive correlates: A longitudinal study in children with persistent mathematical learning difficulties. Research in Developmental Disabilities, 35(11), 3001-3013.