Numerical Cognition Selections

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Symbolic (Number) and Non-symbolic (Line and Circle) Fractions

Starling-Alves, I., Wronski, M.R. & Hubbard, E.M. (2022). Math anxiety differentially impairs symbolic, but not nonsymbolic, fraction skills across development. Annals of the New York Academy of Sciences 1509(1):113-129. doi: 10.1111/nyas.14715. Epub 2021 Nov 15.

Hubbard, E.M. & Matthews, P.G. (2021) Ratio-based perceptual foundations for rational numbers, and perhaps whole numbers, too? Behavioral and Brain Sciences 44:e192. doi: 10.1017/S0140525X2100114X.

Kalra, P.B., Hubbard, E.M. & Matthews, P.G. (2020). Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children. Contemporary Educational Psychology 62:101896. doi: 10.1016/j.cedpsych.2020.101896.

Kalra, P.B., Binzak, J.V., Matthews, P.G. & Hubbard, E.M. (2020). Symbolic fractions elicit an analog magnitude representation in school-age children. Journal of Experimental Child Psychology

Binzak, J.V. & Hubbard, E.M. (2020). No calculation necessary: Accessing rational magnitudes through fraction notation. Cognition, 199: 104219 org/10.1016/j.cognition.2020.104219

Toomarian, E.Y., Meng, R. & Hubbard, E.M. (2019). Individual differences in implicit and explicit spatial processing of fractions. Frontiers in Psychology, 10:596. doi: 10.3389/fpsyg.2019.00596

• This paper investigates how spatial representations of fractions relate to general fraction knowledge. The study has adult participants compare magnitudes of various fractions to 1/2 in order to observe SNARC effects and compares these results to other mathematical tests, such as number line-estimation tasks. The results show that number-line estimation served as a better predictor of mathematical achievement than SNARC effects, suggesting that explicit spatial processing of fractions may be more efficient than implicit processing.

Matthews PG & Hubbard EM. (2016). Making space for spatial proportions. Journal of Learning Disabilities, DOI: 10.1177/0022219416679133

Matthews, P.M., Lewis, M.R. & Hubbard, E.M. (2016). Individual differences in nonsymbolic ratio processing predict symbolic math performance. Psychological Science, 27(2):191-202. doi:10.1177/0956797615617799

Lewis, M.R., Matthews, P.M. & Hubbard, E.M. (2015). Neurocognitive Architectures and the Nonsymbolic Foundations of Fractions Understanding. In D.B. Berch, D.C. Geary, and K.M. Koepke (Eds.) Development of Mathematical Cognition-Neural Substrates and Genetic Influences. (p. 141-160) Elsevier. ISBN: 978-0128018712.

 

Spatial-Numerical Associations

To hear more about the SNARC effect, and some of what previous research has demonstrated, you can listen to this podcast by our own Liz Toomarian.

Toomarian, E.Y. & Hubbard, E.M. (2018). On the genesis of spatial-numerical associations: Evolutionary and cultural factors co-construct the mental number line. Neuroscience and Biobehavioral Reviews, 90:184–199 doi: 10.1016/j.neubiorev.2018.04.010 [14]

Viarouge, A., Hubbard, E.M,, & Dehaene, S. (2014). The organization of spatial reference frames involved in the SNARC effect. Quarterly Journal of Experimental Psychology. 67(8):1484-1499 (DOI:10.1080/17470218.2014.897358)

Viarouge, A., Hubbard, E.M. & McCandliss, B.D. (2014). The cognitive mechanisms of the SNARC effect: An individual differences approach. PLOS One. 9(4): e95756 (doi: 10.1371/journal.pone.0095756).

 

The Symbol-Grounding Problem

Hubbard, E.M., Diester, I., Cantlon, J.F., Ansari, D., van Opstal, F. & Troiani, V. (2008). The evolution of numerical cognition: from number neurons to linguistic quantifiers. Journal of Neuroscience, 28(46):11819–11824 (doi:10.1523/jneurosci.3808-08.2008).