The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties

Steve Chinn

• Publisher: Routledge
• Year: 2014
• ISBN:
  9781317580997
• Edition: 1
• Topic: Education
• Subtopic: Education General

Mathematics plays an important part in every person's life, so why isn't everyone good at it? The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties brings together commissioned pieces by a range of hand-picked influential, international authors from a variety of disciplines, all of whom share a high public profile. More than fifty experts write about mathematics learning difficulties and disabilities from a range of perspectives and answer questions such as:

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• What are mathematics learning difficulties and disabilities?

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• What are the key skills and concepts for learning mathematics?

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• How will IT help, now and in the future?

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• What is the role of language and vocabulary?

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• How should we teach mathematics?

By posing notoriously difficult questions such as these and studying the answers The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties is the authoritative volume and is essential reading for academics in the field of mathematics. It is an incredibly important contribution to the study of dyscalculia and mathematical difficulties in children and young adults.

1

How can cognitive developmental neuroscience constrain our understanding of developmental dyscalculia?

Stephanie Bugden and Daniel Ansari

A developmental cognitive neuroscience approach

Developmental cognitive neuroscience is an evolving field that investigates the relationship between brain and cognitive development to understand the underlying mechanisms that subserve multiple cognitive processes such as attention, language, and math (for a review see: Munakata, Casey, & Diamond, 2004). Historically, neuroscience and behavioral research were conducted independently from one another. However, in recent years researchers have increasingly been trying to uncover how changes in the brain are related to the emergence of behavioral outcomes. Developmental cognitive neuroscience integrates multiple disciplines of research, such as psychology, neuroscience, cognitive science, genetics and social sciences to track the dynamic relationships between biology, cognition and behavior over the course of development. Non-invasive neuroimaging tools such as magnetic resonance imaging (MRI) and electroencephalography (EEG) afford researchers the ability to investigate these relationships between neurobiology and behavior in both typical and atypical populations. Using developmental cognitive neuroscience methods to investigate typical and atypical developmental trajectories can inform a variety of clinical applications such as diagnosis, intervention and treatment of developmental disorders (e.g. Developmental Dyscalculia (DD)) (Munakata et al., 2004).

The current chapter will explore how developmental cognitive neuroscience research is beginning to inform our understanding of DD. DD has received far less attention than reading disorders such as dyslexia (Gersten, Clarke, & Mazzocco, 2007), despite its similar incidence rates (5–7% of school-aged children) (Shalev, 2004). Although the number of published studies about DD has increased recently, researchers in the field of mathematical cognition are still struggling with the fundamental question of what constitutes the core deficit(s) of DD and how to define them.

Against this background, the chapter will begin with a brief review of the current behavioral evidence supporting multiple different causal theories of DD; followed by an overview of the neural correlates of numerical magnitude processing (numerical magnitude referring to the total number of items in a set) in both typically developing populations, as well as in DD. In subsequent sections, the neural correlates of arithmetic as well as visuospatial working memory will be explored. Additionally, how differences in anatomical brain structures can inform our understanding of the functional organization of numerical and arithmetic processing in children with dyscalculia compared to typically developing controls will be discussed. Finally, the advantages and educational implications of using developmental cognitive neuroscience to further our understanding of DD will be considered.

Developmental Dyscalculia: definition and behavioral evidence

DD is a specific learning disorder that is characterized by impairments in learning basic arithmetic facts, processing numerical magnitude, and performing accurate and fluent calculations (American Psychiatric Association, 2013). These difficulties must be quantifiably below what is expected for the individual’s chronological age, and must not be caused by poor educational or daily activities or by intellectual impairments (American Psychiatric Association, 2013). At the behavioral level, children with DD exhibit difficulties retrieving arithmetic facts from memory (Geary, Hoard, & Bailey, 2011) and they commonly rely on immature strategies such as finger counting when their age-matched peers are easily retrieving arithmetic facts from memory. It is generally agreed that children with DD rely on inefficient strategies and have severe difficulties retrieving arithmetic facts. However, despite recent advances in the field by describing the main symptoms of DD, such as arithmetic fact-retrieval difficulties, researchers are struggling with the fundamental question of what constitutes the core deficits of DD and what causes them.

Historically, researchers sought to understand the causes of DD by investigating differences between children with DD and typical controls in domain-general abilities, such as working memory. Some studies have observed deficits in semantic long-term memory and working memory abilities that impair children’s ability to convert arithmetic facts into long-term memory (Geary, 1993). Within the behavioral literature, results have been controversial, with some studies finding working memory deficits in children with DD (Geary, Brown, & Samaranayake, 1991; Geary, 2004; McLean & Hitch, 1999), while other studies found no working memory deficits compared to typically developing controls (Landerl et al., 2004). In an attempt to further understand the conflicting findings, Passolunghi and Mammarella (2012) recently investigated the specific role of visuospatial working memory and visual memory processing tasks in children with DD. During the visual memory tasks, children were presented with a set of houses and had to remember and recognize the same houses on a following trial. During the complex visuospatial working memory tasks, participants were given sequences of dot positions in a matrix and were asked to recall the last position or last dot from the sequence, in addition to having to press the space bar every time a specific dot appeared on the screen. They found that only children with persistent and severe difficulties in solving mathematical word problems had impairment in complex visuospatial working memory tasks, where high attentional control was necessary to complete the tasks. But they showed no impairments on visual memory recognition tasks. Additionally, Szücs et al. (2013) found that children with DD showed greater impairments in visuospatial working memory and short-term memory as well as inhibition compared to typical controls. Taken together, children with DD have demonstrated specific impairments in visuospatial working memory (Ashkenazi, Rosenberg-Lee, Metcalfe, Swigart, &Menon, 2013; McLean & Hitch, 1999). From these data, it was suggested that visuospatial working memory provides a work space to hold and manipulate numerical magnitude representations. An impaired visuospatial working memory system in children with DD would negatively impact the development of numerical magnitude representations and basic arithmetic (Ashkenazi et al., 2013).

From these studies, the causal link between a domain-general deficit in visuospatial working memory and domain-specific processes such as numerical magnitude and arithmetic skills in DD remains unclear. Indeed, a recent meta-analysis has provided evidence that children with DD demonstrate numerically specific working memory impairment in comparison to typically developing controls. These deficits are pronounced in working memory tasks that require numerical manipulations, such as backward digit recall; rather than domain-general working memory impairment. Therefore, these findings reflect the domain-specific nature of working memory deficits (Peng & Fuchs, 2014). However, it does not necessarily imply that these domain-general mechanisms cause DD. If that were the case, then it is likely we would see widespread impairments in multiple cognitive domains (Alloway, Gathercole, Kirkwood, & Elliot, 2009; Price & Ansari, 2013).

In contrast to the search for domain-general deficits as proximal causes of DD, recent approaches have focused on low-level, domain-specific numerical abilities as the potential root cause of DD. For example, Butterworth and colleagues (1999, 2005) have proposed that DD is caused by a domain-specific impairment in the core capacity to represent and manipulate numerical information known as the ‘defective number module hypothesis’ (Butterworth, 1999, 2005; Iuculano et al., 2008). The first evidence supporting this hypothesis came from a study conducted by Landerl and colleagues (2004) who found that children with DD demonstrated difficulties in processing numerical information, such as counting dots, accessing semantic (the numerical magnitude represented by Arabic numerals) and verbal numerical representations and reciting number sequences. However, in contrast to the domain-general account, they found that children with DD were normal or above average on tasks involving phonological working memory and accessing non-numerical verbal information. The defective number module hypothesis assumes a deficit at the level of numerical magnitude representations regardless of the format of presentation. In other words, this hypothesis predicts that children with DD will be equally poor at judging which of two dot arrays is numerically larger (e.g. nonsymbolic discrimination) as they will be at deciding whether the numeral 9 represents a numerical magnitude that is larger or smaller than the numerical magnitude referenced by numeral 7. However, data on the numerical magnitude processing abilities of children with DD have not always been consistent with this hypothesis.

Instead, Rouselle and Noël (2007) argue that the deficit is not with the format-independent representation, but in the connections between number symbols (Arabic digits, i.e. 3, or number words, i.e. three) and their respective meanings. They found that children with DD were slower and less accurate at discriminating between Arabic digits compared to children without DD; however, they failed to exhibit deficits when comparing nonsymbolic quantities (i.e. arrays of dots). Taken together, these findings demonstrate that magnitude representation remains intact in children with DD; however, they have deficits in semantically encoding numerical symbols, also known as the ‘access deficit hypothesis’ – children with DD have more difficulties than children without DD in accessing the connection between numerical symbols and the quantities they represent (Rousselle & Noël, 2007).

It is evident that current findings in the DD literature are contradictory, and there is no clear conclusion as to what causes DD. Furthermore, there are no universally agreed upon criteria for diagnosing children with DD and, as a result, it is difficult for researchers to make conclusions about what underlying cognitive mechanisms impair DD children’s ability to learn basic arithmetic.

As a consequence of the lack of universal classification criteria for DD, studies investigating behavioral and neural correlates of this disorder include samples with varying profiles. Some studies have included samples with milder forms of math deficits (Geary, Hoard, Byrd-Craven, & DeSoto, 2004; Jordan, Hanich, & Kaplan, 2003), while others use more strict criteria, for example Mazzocco and colleagues limited their sample to children below the 10th percentile on math achievement (Mazzocco & Myers, 2003; Mazzocco, Devlin, & McKenney, 2008). Therefore, constraining current theoretical models of DD remains problematic.

Additionally, the heterogeneity of DD contributes to the difficulties of capturing one core deficit (Fias, Menon, & Szücs, 2013) and, therefore, it is probable that various cognitive and neural mechanisms may contribute to different behavioral profiles of DD (Henik, Rubinsten, & Ashkenazi, 2011; Karagiannakis, Baccaglini-Frank, & Papadatos, 2014; Skagerlund & Träff, 2014). Taking a multidisciplinary approach by including both behavioral and cognitive neuroscience methodology is optimal for furthering our conceptual understanding of DD. Exploring the functional and structural composition of the dyscalculic brain will advance our knowledge of the source(s) of cognitive deficits in children who have DD at the neurobiological level.

The following section aims to discuss the cognitive neuroscience evidence that supports or disputes current theoretical explanations for the mechanisms related to poor arithmetic performance in adults as well as children with DD. We first begin with an outline of the current neuroscience evidence of numerical magnitude processing in the typical adult and developing brain. Evidence from typically developing populations provides a framework to inform our understanding of the neurological impairments observed in DD children. Subsequently, the to-date limited neuroscience evidence both from functional and structural studies aiming to better understand the neurobiological correlates of DD will be discussed. Additionally, the neural correlates of arithmetic development in both typically developing children, as well as children with DD will be reviewed. In conclusion, future directions for developmental cognitive neuroscience are considered.

The neural correlates of numerical magnitude processing

Numerical magnitude processing in the typical adult brain

Historically, neuropsychological studies have found associations between brain damage to areas in the parietal lobe (see Figure 1.1(a)) and numerical and calculation impairments (Dehaene & Cohen, 1997; Delazer & Benke, 1997; Lemer, Dehaene, Spelke, & Cohen, 2003; Warrington, 1982). Neuropsychological studies were the first to pinpoint brain regions involved in mathematical and numerical processes and have formed the basis for theoretical frameworks to conceptualize numerical and calculation abilities in the typical adult brain. The most prominent model associating different subcomponents of mathematical cognition with specific brain circuitry (built on the results of neuropsychological studies) is the ‘Triple Code Model’ (Dehaene & Cohen, 1995). The Triple Code Model of number processing predicts that there are three underlying neurological representational systems that are recruited for different numerical tasks. First, the quantity code, which is associated with the bilateral intraparietal sulcus (IPS), embodies the nonverbal semantic representation of numerical magnitude, and is hypothesized to be analogous to a spatially oriented number line. Second, the visual number code is involved in visually encoding strings of numbers. This system has been proposed to recruit regions belonging to the ‘ventral visual pathway’ including the bilateral occipito-temporal regions. And last, the ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• List of figures
• List of tables
• Contributors
• Acknowledgements
• The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties
• 1 How can cognitive developmental neuroscience constrain our understanding of developmental dyscalculia?
• 2 Number difficulties in young children: deficits in core number?
• 3 Dots and digits: how do children process the numerical magnitude? Evidence from brain and behaviour
• 4 When and why numerosity processing is associated with developmental dyscalculia
• 5 Predictive indicators for mathematical learning disabilities/dyscalculia in kindergarten children
• 6 The link between mathematics and logical reasoning: implications for research and education
• 7 How specific is the specific disorder of arithmetic skills?
• 8 Arithmetic difficulties of children with hearing impairment
• 9 Arithmetic difficulties among socially disadvantaged children and children with dyscalculia
• 10 Meeting the needs of the ‘bottom eighty per cent’: towards an inclusive mathematics curriculum in Uganda
• 11 Dyscalculia in Arabic speaking children: assessment and intervention practices
• 12 Mathematics learning and its difficulties among Chinese children in Hong Kong
• 13 The acquisition of mathematics skills of Filipino children with learning difficulties: issues and challenges
• 14 The enigma of dyscalculia
• 15 Deep diagnosis, focused instruction, and expanded math horizons
• 16 Preschool children’s quantitative knowledge and long-term risk for functional innumeracy
• 17 Learning disabilities: mathematics characteristics and instructional exemplars
• 18 Targeted interventions for children with difficulties in learning mathematics
• 19 Focused MLD intervention based on the classification of MLD subtypes
• 20 Numbersense: a window into dyscalculia and other mathematics difficulties
• 21 The Center for Improving Learning of Fractions: a progress report
• 22 Lights and shadows of mental arithmetic: analysis of cognitive processes in typical and atypical development
• 23 Teacher training: solving the problem
• 24 Mathematics anxiety, working memory, and mathematical performance: the triple-task effect and the affective drop in performance
• 25 Mathematical resilience: what is it and why is it important?
• 26 Linguistic factors in the development of basic calculation
• 27 Promoting word problem solving performance among students with mathematics difficulties: the role of strategy instruction that primes the problem structure
• 28 Mathematical storyteller kings and queens: an alternative pedagogical choice to facilitate mathematical thinking and understand children’s mathematical capabilities
• 29 The effects of computer technology on primary school students’ mathematics achievement: a meta-analysis
• 30 Representing, acting, and engaging: UDL and mathematics
• 31 Dyscalculia in Higher Education: systems, support and student strategies
• Index