Why are some people better at math than others?
Poor numeracy is a serious concern, as numeracy skills are at least as important as literacy skills for job outcomes (Bynner & Parsons, 1997). University students’ levels of calculation fluency and conceptual understanding of mathematics have declined significantly. As part of our research program, we are investigating individual differences in university students’ numeracy skills, particularly differences in the mental representations and processes students use to solve arithmetic problems. Our research shows differences in how more- and less-skilled students represent arithmetic operations, and in the solution strategies they use to solve problems. More-skilled students tend to represent basic arithmetic facts in a verbal code (e.g., “six plus two is eight”) and have memorized the basic facts. Less-skilled students tend to represent basic facts spatially, as movement along a mental number line and use a variety of strategies to solve problems, such as counting (e.g., (e.g., 6+2= six, seven, eight). Moreover, in contrast to existing models of adult arithmetic performance, we found evidence that addition and multiplication operations are represented differently (Penner-Wilger & LeFevre, submitted). This research has implications for the development of math pedagogy, especially for how operations are conceptually introduced.
This line of research was funded by a Natural Sciences and Engineering Research Council (NSERC) Julie Payette Award and a Canada Graduate Scholarship (both to myself).
• The calculation fluency of Canadian undergraduates has declined by 20% in the past decade (LeFevre, Penner-Wilger et al., 2014). Thus, high-school and university instructors cannot expect students to be comfortable solving even simple arithmetic problems ‘in their heads’.
There is evidence to suggest that this decline may be the result of the introduction of calculators in elementary schools (LeFevre, Penner-Wilger et al., 2014). Our findings suggest that calculators are necessary for basic computations, potentially impeding students’ understanding by diverting their attention from the conceptual focus of lessons.
Skill differences in arithmetic are related to differences in how students represent operations. The same operations (i.e., addition and subtraction) are represented differently across individuals (Penner-Wilger et al., submitted) and different operations (i.e., addition and multiplication) are not represented the same way within individuals (Penner-Wilger & LeFevre, submitted). These findings have implications for models of arithmetic performance.
Find out more:
Penner-Wilger, M., Landy, D. H., Zhang, X., & Weitzer, A. (2011). Going through the motions: Skill differences in the representation of arithmetic operations. Proceedings of the 33rd Annual Cognitive Science Society. Austin, TX: Cognitive Science Society.
Penner-Wilger, M., & LeFevre, J. (2011). Cross-operational differences in mental arithmetic: Is 2 + 2 the same as 2 x 2? Manuscript submitted for publication.
LeFevre, J., Penner-Wilger, M., Pyke, A., Shanahan, T., Deslauriers, W. A., Trbovich, P., & Roberts, M. A. (2014). Putting two and two together: Declines in arithmetic fluency among young Canadian adults. Carleton University Cognitive Science Technical Report 2014-01. URL http://www.carleton.ca/ics/TechReports.