Measures and References: Number Sense

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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.

Symbolic Magnitude Processing Test (SYMP) (Brankaer et al., 2017): Measures Symbolic Number knowledge, a key component of Number Sense, with a pencil and paper task, where students quickly compare magnitudes of one and two-digit numbers and cross out the larger of the two numbers.


Anobile, G., Pisa, U., & Stievano, P. (2013). Visual sustained attention and numerosity sensitivity correlate with math achievement in children. Journal of Experimental Child Psychology, 116, 380-391.

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.

Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333-339.

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.

Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41(6), 189-201.

Brankaer, C., Ghesquiere, P., & Smedt, B. De. (2017). Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test). Behavior Research, 49, 1361-1373.

Bull, R., Marschark, M., Davidson, W., Murphy, D., Nordmann, E., Remelt, S., & Sapere, P. (2010). Numerical approximation and math achievement in deaf children. In poster presentation at the International Congress on the Education of the Deaf, Vancouver, Canada.

Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance : A meta-analysis. Acta Psychologica, 148, 163-172.

Fuson, K. C. (1990). Conceptual structures for multiunit numbers: Implications for learning and teaching multidigit addition, subtraction, and place value. Cognition and Instruction, 7(4), 343-403.

Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., … Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLoS ONE, 8(6), 1-9.

Loehr, A. M., & Rittle-Johnson, B. (2017). Putting the "th" in tenths: providing place-value labels helps reveal the structure of our base-10 numeral system. Journal of Cognition and Development, 18(2), 226-245.

Malone, A. S., Loehr, A. M., & Fuchs, L. S. (2017). The role of domain-general cognitive abilities and decimal labels in at-risk fourth-grade students' decimal magnitude understanding. Learning and Individual Differences, 58, 90-96.

Mix, K. S., Levine, S. C., Young, C., & Hambrick, D. Z. (2016). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psychology: General, 145(9), 1206-1227.

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.

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

Reys, R., Reys, B., Emanuelsson, G., Johansson, B., McIntosh, A., & Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan, and the United States. School Science and Mathematics, 99(2), 61-70.

Schindler, M., Hußmann, S., Nilsson, P., & Bakker, A. (2017). Sixth-grade students' reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Mathematics Education Research Journal, 29(4), 471-492.

Schneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359-372.

Stacey, K., & MacGregor, M. (1997). Building foundations for algebra. Mathematics Teaching in the Middle School, 2(4), 252-60.

Thomas, N. (2004). The development of structure in the number system. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education 4, 305-.312.

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., 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.