Using cognitive training studies to unravel the mechanisms by which the approximate number system supports symbolic math ability

Abstract

A picture is emerging that preverbal nonsymbolic numerical representations derived from the approximate number system (ANS) play an important role in mathematical development and sustained mathematical thinking. Functional imaging studies are revealing developmental trends in how the brain represents number. We propose that combining behavioral and neuroimaging techniques with cognitive training approaches will help identify the fundamental relationship between the ANS and symbolic mathematics. Understanding this relationship should ultimately benefit educators by providing ways to harness the ANS and hopefully improve math readiness in young children.

Does the Approximate Number System Serve as a Foundation for Symbolic Mathematics?

“…If ANS and symbolic number tasks recruit overlapping brain regions, then training on one may result in neural changes that benefit both. Future studies should test this hypothesis by combining cognitive training paradigms with functional brain imaging methods to uncover how the brain changes in response to ANS training (Bugden, DeWind, & Brannon, 2016). …”

Improving Preschoolers’ Arithmetic through Number Magnitude Training: The Impact of Non-Symbolic and Symbolic Training

“…The unique-representation view considers the Approximate Number System (ANS) to be the root of numerical and arithmetical skills (see [2–3] for a review). This number sense, which is already present in infants (e.g.…”

“…It has been shown that six-month-old infants are able to discriminate between two sets of items differing by a ratio of 1:2 [14] and this threshold ratio increases with age to reach approximately 10:11 at adulthood [15, 16]. According to this view, both symbolic and non-symbolic magnitude comparisons show ratio effects [11, 17, 18] and similar brain areas would be activated for both types of stimuli ([19–21], see [2, 17] for a review). These studies suggest that symbolic and non-symbolic magnitude processing activate one approximate magnitude representation system, the ANS [22].…”

Shared and distinct neural circuitry for nonsymbolic and symbolic double‐digit addition

“…Recent cognitive-training studies have found that practice with nonsymbolic addition and subtraction problems (e.g., adding and subtracting sets of dots) leads to enhanced symbolic arithmetic abilities, suggesting a causal link between nonsymbolic and symbolic calculations (Hyde, Khanum, & Spelke, 2014;Park, Bermudez, Roberts, & Brannon, 2016;Park & Brannon, 2013Szkudlarek & Brannon, 2018). Such findings suggest the possibility that there may be a common set of neural mechanisms supporting both nonsymbolic and symbolic arithmetic (Bugden, DeWind, & Brannon, 2016). Thus, an intriguing possibility is that the relationship between nonsymbolic and symbolic representations is stronger when performing mental arithmetic than when comparing quantities.…”