The role of domain-general and domain-specific skills in the identification of arithmetic strategies

Abstract

Individuals solve arithmetic problems in different ways and the strategies they choose are indicators of advanced competencies such as adaptivity and flexibility, and predict mathematical achievement. Understanding the factors that encourage or hinder the selection of different strategies is therefore important for helping individuals to succeed in mathematics. Our research contributed to this goal by investigating the skills required for selecting the associativity shortcut-strategy, where problems such as ‘16 + 38 – 35’ are solved by performing the subtraction (38 – 35 = 3) before the addition (3 + 16 = 19). In a well-powered, pre-registered study, adults completed two tasks that involved ‘a + b – c’ problems, and we recorded a) whether and b) when, they identified the shortcut. They also completed tasks that measured domain-specific skills (calculation skill and understanding of the order of operations) and domain-general skills (working memory, inhibition and switching). Of all the measures, inhibition was the most reliable predictor of whether individuals identified the shortcut, and we discuss the roles it may play in selecting efficient arithmetic strategies.

Understanding the complexities of mathematical cognition: A multi-level framework

“…Beyond working memory, relationships have also been found between inhibitory control and proficiency with specific components of mathematics. For example, children’s inhibitory control is associated with adaptive strategy selection ( Lemaire & Lecacheur, 2011 ), counting proficiency ( Lan et al, 2011 ), number fact retrieval ( Cragg, Keeble, et al, 2017 ), rational number processing ( Abreu-Mendoza et al, 2018 ), and use of conceptually based arithmetic strategies ( Eaves et al, 2022 ; Robinson & Dubé, 2013 ). Experimental approaches have also provided supporting evidence for a role of inhibitory control in number fact retrieval ( De Visscher & Noël, 2014 ; Eaves et al, 2022 ; Megías et al, 2015 ).…”