Phonological storage and executive function deficits in children with mathematics difficulties

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Abstract

Children with mathematics difficulties suffer from working memory deficits. This study investigated the deficit profile of phonological storage and executive functions in working memory among children with mathematics difficulties. Based on multiple instruments and two assessment points, 68 children were screened out of 805 fifth graders. Of these 68 children, 18 were classified as children with only mathematics difficulties (MD), 20 were classified as children with mathematics and reading difficulties (MDRD), and 30 were typically developing (TD) peers matched on age and general ability. Measures for phonological storage, dual-task performance, inhibition, and updating of verbal and numerical materials were administered individually. Results showed that compared with the TD group, children with MD exhibited storage and inhibition deficits specific to numerical information and dual-task deficits of both verbal and numerical information, whereas children with MDRD showed extensive deficits on phonological storage and executive functions on both verbal and numerical tasks. Moreover, executive function deficits were not confined to phonological storage deficits. Implications of the findings for the working memory deficit profile and working memory training among children with mathematics difficulties were discussed.

Highlights

► We investigate executive functions with paired verbal and numerical tasks. ► Profiles of phonological storage and executive functions vary between mathematics difficulties subtypes. ► Children with MD show most numerical-related phonological storage and executive functions deficits. ► Children with MDRD showed extensive deficits in phonological storage and executive functions. ► Executive functions deficits were not confined to phonological storage deficits for children with mathematics difficulties.

Introduction

Mathematics is critical for individual development and, thus, receives a great emphasis in education. However, a large number of children experience mathematics difficulties (e.g., Shalev, Auerbach, Manor, & Gross-Tsur, 2000). Even in China, where students are reported to have the strongest mathematics competence in the world (Organization for Economic Cooperation, 2009), approximately 6% of elementary school children are identified with mathematics difficulties (Dong, Zhang, & Zhang, 2004). Compared with reading difficulties, mathematics difficulties have been studied much less. Most recently, the cognitive mechanisms underlying mathematics difficulties have received increasing attention. A general finding is that mathematics difficulties are closely related to working memory deficits (Geary, 2010, Geary et al., 2007, Geary et al., 2011, Toll et al., 2011), and training working memory has significantly positive effects on mathematics development among children with learning difficulties (Holmes, Gathercole, & Dunning, 2009). However, the working memory deficit profile in children with mathematics difficulties is still unclear. Studies that address this issue can answer critical questions about how to differentiate among subgroups of mathematics difficulties and develop more fine-grained working memory intervention programs for each subgroup. The purpose of this study was to investigate the working memory deficit profile in children with mathematics difficulties. Two major components of working memory, phonological storage and the executive function system, were systematically examined with paired verbal and numerical tasks. Working memory performance was compared among children with only mathematics difficulties (MD), children with mathematics and reading difficulties (MDRD), and typically developing (TD) peers.

Working memory refers to the ability of concurrently storing and manipulating information necessary to perform mental tasks (Baddeley, 2003). Phonological storage (i.e., phonological loop) and the executive function system are two major components. The former is specialized for storage and rehearsal of verbal and numerical information, whereas the latter is responsible for information integration and the coordination of cognitive processes such as dual-task performance, inhibition, updating, and switching (Baddeley, 1996, Baddeley and Logie, 1999, Miyake et al., 2000). Dual-task performance refers to the ability to coordinate performance on two tasks simultaneously. Inhibition is the ability to deliberately inhibit dominant, automatic, or prepotent responses when necessary. Updating is the process of encoding and evaluating incoming information for relevance to the task at hand and subsequent revision of the information held in memory. Switching is the ability to shift attention or to shift between strategies or response sets. Both phonological storage and the executive function system are critical for children’s mathematics development. Phonological storage is the base for counting and simple arithmetic (e.g., single-digit addition and subtraction) (Bull and Johnston, 1997, Hitch and McAuley, 1991, Noel et al., 2001, Passolunghi and Siegel, 2001), whereas the executive function system, especially dual-task performance, inhibition, and updating, is critical for multidigit computation, mental arithmetic performance, and problem solving (e.g., Iuculano et al., 2011, Noel, 2009, Passolunghi et al., 1999, Raghubar et al., 2010, Swanson et al., 2008).

Deficits in phonological storage and executive functions of working memory are closely associated with children’s poor mathematics performance (e.g., McLean and Hitch, 1999, Passolunghi and Siegel, 2001, Siegel and Ryan, 1989, van der Sluis et al., 2004, van der Sluis et al., 2005). However, the deficit profile of these two components in children with mathematics difficulties remains unclear. Results from previous studies were mixed with respect to whether these deficits were specific to numerical information or were general to both verbal and numerical information. Some studies found that children with mathematics difficulties experienced phonological storage and executive function deficits only in numerical tasks (Hitch and McAuley, 1991, McLean and Hitch, 1999, Siegel and Ryan, 1989, van der Sluis et al., 2005), whereas some showed that children with mathematics difficulties performed poorly on both verbal and numerical tasks of phonological storage and executive functions (Andersson and Lyxell, 2007, Passolunghi and Siegel, 2001, van der Sluis et al., 2004).

Several issues are related to these conflicting findings. First, the group of children with mathematics difficulties is heterogeneous. There are two major groups of children with mathematics difficulties: children with only MD and children with MDRD. Children with MDRD have been postulated to be cognitively different from children with MD. That is, children with MDRD suffer from more comprehensive and serious cognitive impairments than those with MD (e.g., Jordan and Montani, 1997, van der Sluis et al., 2004). However, some previous studies did not differentiate these two groups of mathematics difficulties (Hitch and McAuley, 1991, Passolunghi and Siegel, 2001). Some included both types of children without separating them into subgroups, as children labeled as MD in such studies also showed significantly weaker reading abilities than their TD peers (Andersson and Lyxell, 2007, Siegel and Ryan, 1989).

Second, tasks tapping the executive function system were not comprehensive in previous studies. As mentioned, the executive function system includes several functions: dual-task performance, inhibition, updating, and switching (Baddeley, 1996, Miyake et al., 2000). Of these functions, dual-task performance, inhibition, and updating are considered to be especially important for mathematics development (Andersson and Lyxell, 2007, Geary, 2004, Iuculano et al., 2011, McKenzie et al., 2003, Passolunghi and Cornoldi, 2000, St Clair-Thompson and Gathercole, 2006). Specifically, dual-task performance is important for mathematics tasks that require children to process several pieces of information simultaneously; for example, when solving a word problem, children need to retrieve math facts, maintain intermediate numbers, and choose strategy simultaneously (McKenzie et al., 2003). Inhibition plays an important role in problem solving and computation where children need to inhibit irrelevant information that is liable to overload memory (Geary, 2004, Passolunghi and Cornoldi, 2000, Swanson, 2006). Updating is closely related to reading comprehension (Palladino, Cornoldi, De Beni, & Pazzaglia, 2002); thus, it is assumed to be important for mathematics tasks that involve reading comprehension (e.g., problem solving) (Passolunghi & Pazzaglia, 2004). However, most previous studies measured executive functions using only complex span tasks that mainly reflect dual-task performance (e.g., Hitch and McAuley, 1991, McLean and Hitch, 1999, Passolunghi and Siegel, 2001, van der Sluis et al., 2005). To understand the executive function deficit profile in children with mathematics difficulties, it is necessary to systematically investigate all executive functions that are closely related to mathematics.

Third, the impairments in executive functions among children with mathematics difficulties may be attributed to their phonological storage deficits, and few studies have addressed this issue. The phonological storage and executive functions are closely related in working memory (Baddeley and Logie, 1999, Daneman and Carpenter, 1980, Engle et al., 1999). With respect to mathematics, phonological storage is assumed to support the processes in executive functions (e.g., carrying operations, forming effective problem-solving strategies) by retaining relevant intermediate information (e.g., interim numbers in a calculation, verbal or numerical information in a word problem) (Alloway, 2006, Fürst and Hitch, 2000, Noel et al., 2001, Swanson and Sachse-Lee, 2001). Thus, it is possible that inefficient phonological storage may create a “bottleneck” that constricts information flow to higher levels of executive function processing. Most previous research examined working memory deficits of children with mathematics difficulties by merely comparing them with typically developing children on phonological storage and executive functions. Without controlling for phonological storage ability, it is not clear whether impairments in executive function reflect the deficits in executive functions or just impairments in phonological storage.

To sum up, the purpose of this study was to investigate the deficit profile of phonological storage and executive functions in working memory among children with mathematics difficulties. By comparing children with MD, children with MDRD, and TD peers, we examined three questions: (a) whether children with MD and children with MDRD had phonological storage deficits and whether these deficits were the same for verbal and numerical information, (b) whether children with MD and children with MDRD showed deficits in different measures of executive functions (dual-task performance, inhibition, and updating) and whether these executive function deficits varied across verbal and numerical information, and (c) whether executive function deficits in children with MD and children with MDRD can be attributed to their phonological storage deficits.

Section snippets

Participants

We used a multiple-instrument and two-time assessment approach to identify participants in this study. In the first assessment, we administered three tests (see “Screening measures” section below) to 805 fifth graders from five typical public elementary schools in one county of Beijing, China. (According to the records of the county education bureau, all five schools ranked in the middle regarding the fifth graders’ reading and mathematics performance in that county.) The screening measures

Results

Descriptive statistics for all of the working memory tasks of each group are displayed in Table 2. Based on the entire sample of 68 children, we transformed raw scores for each of phonological storage and executive function tasks to z scores (M = 0.00, SD = 1.00). The group performances on different tasks are illustrated in Fig. 1.

To further analyze the group differences on all tasks, MANOVAs, ANOVAs, post hoc testing (Bonferroni), and effect sizes (η2) were computed for all tasks. According to

Discussion

The purpose of this study was to investigate whether children with mathematics difficulties had phonological storage and executive function deficits, whether these deficits were specific to information type (verbal vs. numerical), and whether deficits in executive functions were attributed to phonological storage deficits. Results showed that children with mathematics difficulties, both MD and MDRD subtypes, suffered from deficits in phonological storage and deficits in executive functions. The

Acknowledgments

Part of this work was supported by a National Science Foundation of China (NSFC) grant (30970908). We thank all students, teachers, principals, and parents for their participation. We also thank Sun Yanping, Yin Yi, Hu Tianting, Guo Nan, and Liu Yunkun for their help with data collection. We also thank Eunsoo Cho and Amanda Miller for their comments on previous version of the manuscript. The data were collected by Peng Peng in partial fulfillment of the requirement for a master in psychology at

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