Neurodevelopment of relational reasoning: Implications for mathematical pedagogy

Abstract

a b s t r a c tReasoning ability supports the development of mathematics proficiency, as demonstrated by correlational and longitudinal evidence, and yet this skill is not emphasized in traditional elementary mathematics curricula. We propose that targeting reasoning skills from elementary school onward could help more students succeed in advanced mathematics courses. Here, we review the links between reasoning and mathematics, discuss the neural basis and development of reasoning ability, and identify promising school curricula.

Fluid reasoning predicts future mathematical performance among children and adolescents

“…One account for the strong relation between FR and math assessments is that both engage a common underlying cognitive ability called relational reasoning, or the ability to jointly consider multiple relations between different components of a problem (Halford, Wilson & Phillips, 1998; Carpenter, Fennema, Franke, 2013; Miller Singley & Bunge, 2014; Richland, Holyoak, Stigler, 2004; White, Alexander, Daugherty, 1998). The emerging ability to reason relationally may form the foundation for mathematical conceptual development, from the time children learn to compare the value of one number to another, to the time they learn to extract the value of a fraction by comparing the value of the numerator to the value of the denominator, to when they learn algebra and have to solve for an unknown variable by keeping in mind the relationship between numbers on both sides of the equal sign, and so on (Miller Singley & Bunge, 2014). …”

“…We argue that math curriculum should incorporate opportunities for students to practice a core aspect of FR known as relational thinking, or the ability to jointly consider several relations among mental representations (Miller-Singley & Bunge, 2014). One example of a curriculum that incorporates relational thinking practice into math exercises is called Early Algebra (Carpenter, Franke & Levi, 2003).…”

“…Many other approaches can be used to incorporate FR skill building opportunities into math curriculum (e.g. Miller-Singley & Bunge, 2014). …”

“…One mechanism by which FR could support math skill acquisition is related to the fact that both FR and math problems engage a common underlying cognitive process called relational reasoning, or the ability to jointly consider multiple relationships between different components of a problem (Halford, Wilson & Phillips, 1998; Miller Singley & Bunge, 2014). According to this framework, understanding mathematics requires the ability to form abstract representations of quantitative and qualitative relations between variables (Halford, Wilson & Phillips, 1998).…”

Adolescent Brain Development

“…Other links between cognitive control abilities and school performance have been made. For example, working memory performance and its neural correlates are associated with arithmetic skills [34], while improved reasoning about increasingly complex relations may support maths learning [35]. Improved cognitive control also allows adolescents to improve their ability to organise and monitor memory representations and memory retrieval [36].…”