Measures and References: Operations

Return to Operations factor page.


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): Standardized test assessing procedural knowledge of Operations, including arithmetic with fractions and negative integers.


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(2), 181-203.

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.

Berg, D. H. (2008). Working memory and arithmetic calculation in children: The contributory roles of processing speed, short-term memory, and reading. Journal of Experimental Child Psychology, 99(4), 288-308.

Berry III, R. Q., Thunder, K., & McClain, O. L. (2011). Counter narratives: Examining the mathematics and racial identities of Black boys who are successful with school mathematics. Journal of African American Males in Education, 2(1).

Blanton, M., Stephens, A., Knuth, E., Gardiner, A., Isler, I., & Kim, J. (2015). The development of children's algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39-87.

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.

Chaddock-Heyman, L., Erickson, K. I., Kienzler, C., King, M., Pontifex, M. B., Raine, L. B., ... & Kramer, A. F. (2015). The role of aerobic fitness in cortical thickness and mathematics achievement in preadolescent children. PloS one, 10(8), e0134115.

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.

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.

Green, C. T., Bunge, S. A., Briones Chiongbian, V., Barrow, M., & Ferrer, E. (2017). Fluid reasoning predicts future mathematical performance among children and adolescents. Journal of Experimental Child Psychology, 157, 125-143.

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.

Imbo, I., & Vandierendonck, A. (2008). Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: Differences between children and adults? Psychological Research, 72(3), 331-346.

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.

Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H. (2011). Early place-value understanding as a precursor for later arithmetic performance -- A longitudinal study on numerical development. Research in Developmental Disabilities, 32(5), 1837-1851.

Namkung, J., Fuchs, L. S., & Koziol, N. (2018). Does initial learning about the meaning of fractions present similar challenges for students with and without adequate whole-number skill? Learning and Individual Differences, 61, 165-171.

Parham, Diane, L. (1998). The relationship of sensory integrative development to achievement in elementary students: Four-year longitudinal patterns. The Occupational Therapy Journal of Research, 18(3), 105-127.

Pieters, S., Desoete, A., Roeyers, H., Vanderswalmen, R., & Van Waelvelde, H. (2012). Behind mathematical learning disabilities: What about visual perception and motor skills? Learning and Individual Differences, 22(4), 498-504.

Pixner, S., Leyrer, M., & Moeller, K. (2014). Number processing and arithmetic skills in children with cochlear implants. Frontiers in Psychology, 5, 1479.

Ramdass, D., & Zimmerman, B. J. (2008). Effects of self correction strategy training on middle school student's self-efficacy, self-evaluation, and mathematics division learning. Journal of Advanced Academics, 20(1), 18-41.

Robinson, K. M., & Dube, A. K. (2009). Children's understanding of the inverse relation between multiplication and division. Cognitive Development, 24(3), 310-321.

Robinson, K. M., Arbuthnott, K. D., Rose, D., McCarron, M. C., Globa, C. A., & Phonexay, S. D. (2006). Stability and change in children's division strategies. Journal of Experimental Child Psychology, 93(3), 224-238.

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.

Seethaler, P. M., & Fuchs, L. S. (2006). The cognitive correlates of computational estimation skill among third-grade students. Learning Disabilities Research and Practice, 21(4), 233-243.

Skagerlund, K., & Traff, U. (2016). Processing of space, time, and number contributes to mathematical abilities above and beyond domain-general cognitive abilities. Journal of Experimental Child Psychology, 143, 85-101.

Star, J. R., & Rittle-Johnson, B. (2009). It pays to compare: An experimental study on computational estimation. Journal of Experimental Child Psychology, 102(4), 408-426.

Vanbinst, K., Ceulemans, E., Ghesquiere, P., & De Smedt, B. (2015). Profiles of children's arithmetic fact development: A model-based clustering approach. Journal of Experimental Child Psychology, 133, 29-46.

van der Ven, S. H. G., Straatemeier, M., Jansen, B. R. J., Klinkenberg, S., & van der Maas, H. L. J. (2015). Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems. Learning and Individual Differences, 43, 48-62.

Vasilyeva, M., Casey, B. M., Dearing, E., & Ganley, C. M. (2009). Measurement skills in low-income elementary school students: Exploring the nature of gender differences. Cognition and Instruction, 27(4), 401-428.

Vukovic, R. K., Kieffer, M. J., Bailey, S. P., & Harari, R. R. (2013). Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance. Contemporary Educational Psychology, 38, 1-10.

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

Witacre, I., Schoen, R., Champagne, Z., & Goddard, A. (2017). Relational thinking: What's the difference? Teaching Children Mathematics, 23(5), 302-308.