# Cognitive and Motivational Underpinnings of Mathematical Learning Difficulties: A Discussion

## Abstract

Part III of this volume is about the cognitive and motivational underpinnings of mathematical learning difficulties. In this chapter, I present a brief summary of the nine chapters in this section, followed by a short discussion of two common and important themes that occur throughout the chapters. One of them involves the heterogeneity of the category we call mathematical learning difficulties, that is, the criteria by which children are assessed and diagnosed with this term (or with the term developmental dyscalulia), and the resultant difficulties that this heterogeneity produces. The second common theme involves the pervasive and important role of working memory and our need to understand its influence as well as our need to separate working memory difficulties from more central difficulties with number.

## Keywords

Heterogeneity Working memory Genetics fMRI Numerical magnitude ADHD Spatial reasoning Math language Math anxiety## References

- Agrillo, C. (2015). Numerical and arithmetic abilities in non-primate species. In R. C. Kadosh & A. Dowker (Eds.),
*The Oxford handbook of numerical cognition*(pp. 214–236). Oxford, UK: Oxford University Press.Google Scholar - Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory.
*Cognition, 44*, 75–106.CrossRefGoogle Scholar - Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance.
*Journal of Experimental Psychology: General, 130*, 224–237.CrossRefGoogle Scholar - Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety.
*Psychonomic Bulletin & Review, 14*, 243–248.CrossRefGoogle Scholar - Brannon, E. M., & Park, J. (2015). Phylogeny and ontogeny of mathematical and numerical understanding. In R. C. Kadosh & A. Dowker (Eds.),
*The Oxford handbook of numerical cognition*(pp. 203–213). Oxford, UK: Oxford University Press.Google Scholar - Byrnes, J. P., & Miller, C. D. (2006). The relative importance of predictors of math and science achievement: An opportunity-propensity analysis.
*Contemporary Educational Psychology, 32*, 599–629.CrossRefGoogle Scholar - Cummins, J. (2000).
*Language, power and pedagogy*. Clevedon, UK: Multi lingual Matters.CrossRefGoogle Scholar - Dehaene, S. (1992). Varieties of numerical abilities.
*Cognition, 44*(1–2), 1–42.Google Scholar - Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study.
*Developmental Psychology, 47*(6), 1539–1552.CrossRefGoogle Scholar - McCabe, J. A., Redick, T. S., & Engle, R. W. (2016). Brain-training pessimism, but applied-memory optimism.
*Psychological Science in the Public Interest, 17*, 187–191.CrossRefGoogle Scholar - Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2003). Elementary subtraction.
*Journal of Experimental Psychology: Learning, Memory, and Cognition, 29*, 1339–1352.Google Scholar - Simons, D. J., Boot, W. R., Charness, N., Gathercole, S. E., Chabris, C. F., Hambrick, D. Z., & Stine-Morrow, E. A. L. (2016). Do “brain training” programs work?
*Psychological Science in the Public Interest, 17*, 103–186.CrossRefGoogle Scholar - VanLehn, K. (1990).
*Mind bugs: The origins of procedural misconceptions*. Cambridge, MA: MIT Press.Google Scholar - Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson, & K. W. Fischer (Eds.),
*Human behavior, learning, and the developing brain*(pp. 212–238). Atypical development). New York: Guilford.Google Scholar