Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?

Abstract

The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (n=280; 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations (PCs), and word problems (WPs) in fall and then reassessed on PCs and WPs in spring. Development was indexed via latent change scores, and the interplay between numerical and domain-general abilities was analyzed via multiple regression. Results suggest that the development of different types of formal school mathematics depends on different constellations of numerical versus general cognitive abilities. When controlling for 8 domain-general abilities, both aspects of basic numerical cognition were uniquely predictive of PC and WP development. Yet, for PC development, the additional amount of variance explained by the set of domain-general abilities was not significant, and only counting span was uniquely predictive. By contrast, for WP development, the set of domain-general abilities did provide additional explanatory value, accounting for about the same amount of variance as the basic numerical cognition variables.Inquiries should be sent to Lynn S. Fuchs, 228 Peabody, Vanderbilt University, Nashville, TN 37203. Publisher's Disclaimer: The following manuscript is the final accepted manuscript. It has not been subjected to the final copyediting, fact-checking, and proofreading required for formal publication. It is not the definitive, publisher-authenticated version. The American Psychological Association and its Council of Editors disclaim any responsibility or liabilities for errors or omissions of this manuscript version, any version derived from this manuscript by NIH, or other third parties. The published version is available at www.apa.org/pubs/journals/dev NIH Public Access Author ManuscriptDev Psychol. Author manuscript; available in PMC 2011 November 1. Published in final edited form as:Dev Psychol. 2010 November ; 46(6): 1731-1746. doi:10.1037/a0020662. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptLanguage, attentive behavior, nonverbal problem solving, and listening span were uniquely predictive.Keywords mathematics development; procedural calculations; word problems; basic numerical cognition; domain-general abilitiesAchieving mathematics competence in its many forms during the elementary school years provides the foundation for learning algebra and other higher forms of mathematics and eventually for success in the labor market and a society that increasingly depends on quantitative skills (National Mathematics Advisory Panel, 2008). Yet, the cognitive mechanisms that support learning of formal mathematics during elementary school are not well understood: specifically, the relative contributions of children's basic numerical cognition that emerges without formal schooling (e.g., competence in number, counting, and simple arithmetic) as contra...

Separating math from anxiety: The role of inhibitory mechanisms

“…The importance of WM also relies on this construct's good predictive value. Indeed, several studies revealed that WM can be considered a strong predictor of mathematics performance in simple arithmetic (Caviola, Mammarella, Lucangeli, & Cornoldi, 2014;Fuchs et al, 2010), and in arithmetical and geometrical problem solving (Giofrè, Mammarella, Ronconi, & Cornoldi, 2013;Passolunghi, Mammarella, & Altoè, 2008). In addition, WM impairments have been demonstrated in participants with DD (Krajewksi, & Schneider, 2009;Mammarella, Caviola, Lucangeli, & Cornoldi, 2013;Passolunghi & Siegel, 2001;Schuchardt, Maehler, & Hasselhorn, 2008).…”

Mathematical development: the role of broad cognitive processes

“…Children transition from these automatic, basic quantitative competencies (biological evolution-based; Geary, 2007) to formal, complex mathematical competencies (culturally-based), such as counting words (vocabulary), Arabic numerals, the decimal system, and the rest of mathematical theory through broad, domain-general cognitive processes, including reasoning, language, memory, visual and auditory processes, among others (Geary, Hoard, Nugent, & Byrd-Craven, 2008). However, the specific contribution of broad cognitive processes on mathematics achievement is not clearly understood, particularly from a developmental perspective (Fuchs et al, 2010).…”

“…Visual-spatial processing (as a component of working memory, or as an independent cognitive process) remains a factor theorized to support basic calculation skills, as well as advanced mathematics and geometry; however, empirical evidence is lacking or contradictory (Geary, 1993;Fuchs et al, 2010;McGrew & Wendling, 2010). From an evolutionary perspective, visual-spatial cognitive processes probably precede auditory cognitive processes, and they are most likely highly elaborated and robust given the importance of visual information for primates.…”

“…Commonly used indicators of processing speed include perceptual processing speed (e.g., asking subjects to look at a series of digits and circle the two digits that are identical as quickly as they can), and semantic processing speed (e.g., asking subjects to look at a series of object drawings and circle the two drawings that "go together," which requires the identification of common semantic categories such as "food," "clothes," "things in the sky," etc.). Processing speed has been empirically linked to domain specific quantitative skills related to counting (Geary, 1993), the amount of time required to solve calculations, and problem solving (Fuchs et al, 2010;McGrew & Hessler, 1995;McGrew & Wendling, 2010). (Cattell, 1963;Horn, 1968;Horn & Cattell, 1966) and the Carroll threestratum model of cognitive abilities (Carroll, 1993).…”

“…Mathematical development is related to domain specific cognitive processes (cognitive processes that are specific to mathematics), as well as broad cognitive processes such as working memory, language, and reasoning (Fuchs et al, 2010). Domain specific cognitive processes include: Subitizing or numerosity (i.e., the ability to automatically and accurately determine the quantity of sets of up to three or four items; Wynn, Bloom, & Chiang, 2002); magnitude estimation (i.e., the inexact, but quick estimation of quantities larger than 3 or 4; Pica et al, 2004); ordinality (i.e., understanding of the concepts "more than" and "less than"; Feigenson, Carey, & Hauser, 2002); counting (i.e., understanding of counting principles such as one to one correspondence; Gelman & Gallistel, 1978); arithmetic sensitivity (i.e., sensitivity to increases and decreases in the quantity of small sets of items; Kobayashi, Hiraki, Mugitani, & Hasegawa, 2004); and geometry (i.e., basic understanding of spatial relations; Dehaene, Izard, Pica, & Spelke, 2006).…”