Impact of High Mathematics Education on the Number Sense

Abstract

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

“…If we assume that w correctly indexes ANS acuity, and if we only had recourse to this measure in our correlation analyses, we would be led to conclude that the data do not support the existence of a relationship between ANS acuity and arithmetic proficiency (as Castronovo & Göbel, 2012;Gilmore et al, 2011;Inglis et al, 2011;Price et al, 2012). On ASSESSING THE APPROXIMATE NUMBER SYSTEM the other hand, if we consider that CV is an adequate index of ANS acuity, we would have to conclude the opposite, as we found a significant correlation between CV and our arithmetic measure (as Mejias & Schiltz, 2013).…”

“…from 6 to 40 dots in Price et al, 2012; from 30 to 100 dots in Guillaume et al, 2013) and in the presentation duration of the dot arrays (e.g. 150ms duration in Castronovo & Göbel, 2012; no time constraint in Sasanguie et al, 2013). Such a variability in both number and presentation duration may induce differences in the involvement of nonnumerical perceptual processes.…”

“…Recently, several studies investigating the relationship between math ability and basic numerical ability combined both numerical comparison and numerical estimation tasks (e.g., Castronovo & Göbel, 2012;Lyons, Price, Vassen, Blomaert, & Ansari, 2014;Sasanguie et al, 2013). Surprisingly, however, none of these systematically examined the relationship between w and CV.…”

Indexing the approximate number system

“…Bonny & Lourenco, 2013;Castronovo & Göbel, 2012;Halberda, Ly, Willmer, Naiman, & Germine, 2012;Inglis et al, 2011;Libertus et al, 2011Libertus et al, , 2012Lyons & Beilock, 2011;Mazzocco et al, 2011a;Piazza et al, 2010;Price et al, 2012;Sasanguie, Göbel, Moll, Smets, & Reynvoet, 2013). It makes the INDEXING THE APPROXIMATE NUMBER SYSTEM 5 theoretical assumption that the ANS operates according to the Weber-Fechner law (e.g.…”

Konstruktywizm Jeana Piageta i koncepcja zmysłu liczby a edukacja matematyczna

“…Potwierdzeniem tej tezy są badania zespołu Pierre'a Pica (Pica, Lemer, Izard i Dehaene, 2004), które wskazują, że dorośli z kultur zachodnich mają bardziej precyzyjny ANS niż dorośli z kultur, w których nie ma symbolicznego zapisu liczb (do podobnych wniosków doszli m.in. : Castronovo i Göbel, 2012;Lindskog, Winman i Juslin, 2014;Piazza, Pica, Izard, Spelke i Dehaene, 2013). Z drugiej strony może być tak, że bardziej dokładny system ANS u dzieci może sprzyjać lepszemu opanowaniu znaczenia liczebników.…”