Working Memory and Mathematical Cognitive Development: Limitations of Limited-Capacity Resource Models

Abstract

My charge in writing this commentary is to present a systematic review and appraisal of the articles comprising this special issue. To begin with, I want to underscore that this collection of articles unequivocally affirms that the study of individual differences in the development of mathematical abilities and its neuropsychological correlates has made significant progress since the publication of David Geary's (1993) seminal paper on this topic 15 years ago. Moreover, as the studies reported in these articles make several important empirical and methodological contributions to our understanding of mathematical cognitive development, they will no doubt serve as catalysts for the next generation of advances in this field. However, in addition to extolling such accomplishments, it is my responsibility to examine the shortcomings of these papers, if any, highlight whatever shared features can be identified, arrive at some general conclusions about this body of work, and formulate some judicious recommendations for future research.Given the relatively circumscribed scope of the subject matter treated here, one might anticipate that the type of analysis I just described should be reasonably straightforward. However, even a cursory reading of these articles reveals that they cover a comparatively broad range of age groups, populations, mathematical domains, research methods, and data-analytic strategies. More specifically, the age levels of the participants range from preschoolers to young adults, and the populations studied include typically developing children, youngsters with low achieve-

The involvement of working memory in children’s exact and approximate mental addition

“…Results offer a specification for mental addition of the general conclusions reached by recent studies (Andersson & Lyxell, 2007;Berch, 2008;D'Amico & Guarnera, 2005;Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007;Holmes et al, 2008;Passolunghi & Mammarella, 2010;Passolunghi, Mammarella, & Altoe, 2008), which showed that WM is related to and important for performance on mathematic tasks in children. Educational implications may be seen in our results, showing that children's difficulties in solving mental calculations are related to WM limitations and that particular attention should be devoted to support children when mental addition problems involve great WM resources.…”

Executive functions underlying multiplicative reasoning: Problem type matters

“…Most previous research on math and working memory has been conducted within the framework of Baddeley's theory and using dual tasks to assess working memory. Berch (2008) recommended that researchers examine the relationship between children's math ability and working memory constructs from alternative theoretical perspectives. Our research shows that mental capacity measures that are not based on dual tasks, or even a memory paradigm, predict children's math performance.…”

“…Recently, Berch (2008) pointed out limitations of Baddeley's multicomponent model and suggested that math researchers examine other approaches to working memory such as those of Cowan (2005) and Engle (2002). The latter models do not see working memory in terms of multiple stores; rather, they see it in terms of a highly activated state of long-term memory.…”

Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches

“…Digit span backward is most often described as a measure of verbal working memory, involving both the phonological loop and the central executive, and in some studies digit span backward does show effects of phonological similarity (Rosen & Engle, 1997). However, another possibility articulated most recently by Berch (2008) is that visual-spatial representations may play a role in digit span backward performance. This may be particularly true for younger children as developmental studies suggest there is less separation of the verbal and visual-spatial working memory systems before 8 years of age (Hale, Bronik, & Fry, 1997).…”