Generative processing underlies the mutual enhancement of arithmetic fluency and math-grounding number sense

Number skills are popularly bound to arithmetic knowledge in its symbolic form, such as "five + nine = fourteen," but mounting evidence suggests that these symbolic relations are actually grounded, i.e., computed (see Harnad, 1990) on noisy internal magnitude representations that bear our general understanding of numbers and further improve with math experience (Figure 1). Multiple lines of evidence support the idea of semantics-based arithmetic, including behavioral research on humans (Gallistel and Gelman, 1992), animals (Gallistel and Gelman, 2000; Rugani et al., 2009), development (Halberda et al., 2008), mathematical disability, i.e., dyscalculia (Butterworth, 1999; review, Butterworth et al., 2011), and computational modeling (Stoianov et al., 2004; review, Zorzi et al., 2005). Even more intimate relation between the number skills and the internal noisy magnitudes was recently demonstrated in several studies showing finer magnitude representations in subjects with greater arithmetic fluency (e.g., Nys et al., 2013; Piazza et al., 2013), also caused by extensive math studying during higher education (Lindskog et al., 2014). Here we discuss how these findings could be explained within a generative framework of cognition, according to which top-down predictive connections play a key role in the computing of low- to high-level representations (e.g., Friston, 2010; Clark, 2013).