Measures and References: Operations

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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.

Numerical Operations Subtest of the Wechsler Individual Achievement Test (WIAT-III; Wechsler, 2009): Assesses students' ability to write numbers, count, and solve simple arithmetic problems


Best, J. R., Miller, P. H., & Naglieri, J. A. (2011). Relations between executive function and academic achievement from ages 5 to 17 in a large, representative national sample. Learning and Individual Differences, 21(4), 327-336.

Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 37-50.

De Smedt, B., Holloway, I. D., & Ansari, D. (2011). Effects of problem size and arithmetic operation on brain activation during calculation in children with varying levels of arithmetical fluency. NeuroImage, 57(3), 771-781.

Geary, D. C., & Burlingham-Dubree, M. (1989). External validation of the strategy choice model for addition. Journal of Experimental Child Psychology, 47(2), 175-192.

Hassinger-Das, Jordan, N. C., Glutting, J., Irwin, C., & Dyson, N. (2014). Domain general mediators of the relation between kindergarten number sense and first-grade mathematics achievement. Journal of Experimental Child Psychology, 118, 1-24.

Hecht, S. A., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills : A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology, 79, 192-227.

Hyde, D. C., Khanum, S., & Spelke, E. (2014). Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 131(1), 92-107.

Kleemans, T., Segers, E., & Verhoeven, L. (2012). Naming speed as a clinical marker in predicting basic calculation skills in children with specific language impairment. Research in Developmental Disabilities, 33, 882-889.

Linsen, S., Verschaffel, L., Reynvoet, B., & De Smedt, B. (2014). The association between children's numerical magnitude processing and mental multi-digit subtraction. Acta Psychologica, 145, 75-83.

Östergren, R., & Traff, U. (2013). Early number knowledge and cognitive ability affect early arithmetic ability. Journal of Experimental Child Psychology, 115, 405-421.

Rosenberg-Lee, M., Ashkenazi, S., Chen, T., Young, B., Geary, D. C., & Menon, V. (2015). Brain hyper-connectivity and operation-specific deficits during arithmetic problem solving in children with developmental dyscalculia. Developmental Science, 18(3), 351-372.

Rubinsten, O., & Tonnock, R. (2010). Mathematics anxiety in children with developmental dyscalculia. Behavioral and Brain Functions, 6(46), 1-13.

Viterbori, P., Usai, M. C., Traverso, L., & De Franchis, V. (2015). How preschool executive functioning predicts several aspects of math achievement in Grades 1 and 3: A longitudinal study. Journal of Experimental Child Psychology, 140, 38-55.

Wechsler, D. (2009). Wechsler Individual Achievement Test 2nd Edition (WIAT III). San Antonio, TX: The Psychological Corp.