Executive function in learning mathematics by comparison: incorporating everyday classrooms into the science of learning

ABSTRACT

Individual differences in executive functions (EFs) are well established to be related to mathematics achievement, yet the mechanisms by which this occurs are not well understood. Comparing representations (problems, solutions, concepts) is central to mathematical thinking, and relational reasoning is known to rely upon EF resources. The current manuscript explored whether individual differences in EF predicted learning from a conceptually demanding mathematics lesson requiring relational reasoning. Analyses revealed that variations in EF predicted learning when measured at a delay. Thus, EF capacity may impact students’ overall mathematics achievement by constraining their resources available to learn from cognitively demanding reasoning opportunities in lessons. To assess the ecological validity of this interpretation, we report follow-up interviews with mathematics teachers who raised similar concerns that cognitively demanding activities such as comparing multiple representations in mathematics may differentially benefit their high versus struggling learners. Broader implications for ensuring that all students have access to, and benefit from, conceptually rich mathematics lessons are discussed. We also highlight the utility of integrating methods in science of learning (SL) research.

KEYWORDS:

• Analogy
• teaching
• mathematics education

Acknowledgments

The research reported here was supported by grants from the National Science Foundation, SMA-1548292, and the Institute of Education Sciences, US Department of Education, through R305A170488 to Lindsey Engle Richland at the University of Chicago. The opinions expressed are those of the authors and do not necessarily represent views of the Institute or the US Department of Education. Susanne M. Jaeggi has an indirect financial interest in the MIND Research Institute, whose interests are related to this work. Susanne M. Jaeggi is supported by the National Institute on Aging (Grant No. 1K02AG054665-01).

Disclosure statement

The opinions expressed are those of the authors and do not necessarily represent views of the Institute or the US Department of Education. Susanne M. Jaeggi has an indirect financial interest in the MIND Research Institute, whose interests are related to this work. No other authors declare any conflict of interest.

Additional information

Funding

National Science Foundation [grant number SMA-1548292]; Institute of Education Sciences, US Department of Education [grant number R305A170488]; National Institute on Aging [grant number 1K02AG054665-01].