Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia

[Symptoms diagnosis and treatment of dyscalulia]

Children with dyscalculia show deficits in basic numerical processing which cause difficulties in the acquisition of mathematical skills. This article provides an overview of current research findings regarding the symptoms, cause, and prognosis of dyscalculia, and it summarizes recent developments in the diagnosis, early intervention, and treatment thereof. Diagnosis has improved recently because newly developed tests focus not only on the math curriculum, but also on basic skills found to be impaired in dyscalculia. A controversial debate continues with regard to IQ achievement discrepancy. International studies have demonstrated the effectiveness of specialized interventions. This article summarizes the research findings from intervention studies, describes different treatment approaches, and discusses implications for clinical practice.

Are there rapid feedback effects on Approximate Number System acuity?

Humans are believed to be equipped with an Approximate Number System (ANS) that supports non-symbolic representations of numerical magnitude. Correlations between individual measures of the precision of the ANS and mathematical ability have raised the question of whether the precision can be improved by feedback training. A study (DeWind and Brannon, 2012) reported improvement in discrimination precision occurring within 600–700 trials of feedback, suggesting ANS malleability with rapidly improving acuity in response to feedback. We tried to replicate the rapid improvement in a control group design, while controlling for the use of perceptual cues. The results indicate no learning effects, but a minor constant advantage for the feedback group. The measures of motivation suggest that feedback has a positive effect on motivation and that the difference in discrimination is due to the greater motivation of participants with feedback. These results suggest that at least for adults the number sense may not respond to feedback in the short-term.

Early gamma oscillations during rapid auditory processing in children with a language-learning impairment: changes in neural mass activity after training

Children with language-learning impairment (LLI) have consistently shown difficulty with tasks requiring precise, rapid auditory processing. Remediation based on neural plasticity assumes that the temporal precision of neural coding can be improved by intensive training protocols. Here, we examined the extent to which early oscillatory responses in auditory cortex change after audio-visual training, using combined source modeling and time-frequency analysis of the human electroencephalogram (EEG). Twenty-one elementary school students diagnosed with LLI underwent the intervention for an average of 32 days. Pre- and post-training assessments included standardized language/literacy tests and EEG recordings in response to fast-rate tone doublets. Twelve children with typical language development were also tested twice, with no intervention given. Behaviorally, improvements on measures of language were observed in the LLI group following completion of training. During the first EEG assessment, we found reduced amplitude and phase-locking of early (45-75 ms) oscillations in the gamma-band range (29-52 Hz), specifically in the LLI group, for the second stimulus of the tone doublet. Amplitude reduction for the second tone was no longer evident for the LLI children post-intervention, although these children still exhibited attenuated phase-locking. Our findings suggest that specific aspects of inefficient sensory cortical processing in LLI are ameliorated after training.

Explicit and implicit issues in the developmental cognitive neuroscience of social inequality

The appearance of developmental cognitive neuroscience (DCN) in the socioeconomic status (SES) research arena is hugely transformative, but challenging. We review challenges rooted in the implicit and explicit assumptions informing this newborn field. We provide balanced theoretical alternatives on how hypothesized psychological processes map onto the brain (e.g., problem of localization) and how experimental phenomena at multiple levels of analysis (e.g., behavior, cognition and the brain) could be related. We therefore examine unclear issues regarding the existing perspectives on poverty and their relationships with low SES, the evidence of low-SES adaptive functioning, historical precedents of the "alternate pathways" (neuroplasticity) interpretation of learning disabilities related to low-SES and the notion of deficit, issues of "normativity" and validity in findings of neurocognitive differences between children from different SES, and finally alternative interpretations of the complex relationship between IQ and SES. Particularly, we examine the extent to which the available laboratory results may be interpreted as showing that cognitive performance in low-SES children reflects cognitive and behavioral deficits as a result of growing up in specific environmental or cultural contexts, and how the experimental findings should be interpreted for the design of different types of interventions-particularly those related to educational practices-or translated to the public-especially the media. Although a cautionary tone permeates many studies, still, a potential deficit attribution-i.e., low-SES is associated with cognitive and behavioral developmental deficits-seems almost an inevitable implicit issue with ethical implications. Finally, we sketch the agenda for an ecological DCN, suggesting recommendations to advance the field, specifically, to minimize equivocal divulgation and maximize ethically responsible translation.

Neurokognitive Grundlagen der typischen und atypischen Zahlenverarbeitung

Zusammenfassung: Numerische Kenntnisse bilden ein wichtiges Fundament für die schulische und berufliche Entwicklung. Viele Kinder leiden jedoch unter großen Schwierigkeiten beim Erlernen numerischer Kompetenzen und werden oft mit einer «entwicklungsbedingten Dyskalkulie» diagnostiziert. Eine wachsende Anzahl von Studien mit Hilfe bildgebender Verfahren zeigt nun, dass spezifische Regionen im Gehirn von Kindern mit Dyskalkulie einen atypischen Entwicklungsverlauf beim Erlernen basisnumerischer Kompetenzen – wie dem Vergleichen numerischer Mengen – aufweisen. Diese Studien deuten somit auf eine domänenspezifische Ursache der Rechenschwäche hin. In der vorliegenden Übersichtsarbeit möchten wir die Befunde zur typischen und atypischen Gehirnentwicklung der Zahlenverarbeitung von einer neurowissenschaftlichen Perspektive diskutieren. Weiters werden wichtige Implikationen für Diagnostik und Intervention besprochen.

Malleability of the approximate number system: effects of feedback and training

Prior research demonstrates that animals and humans share an approximate number system (ANS), characterized by ratio dependence and that the precision of this system increases substantially over human development. The goal of the present research was to investigate the malleability of the ANS (as measured by Weber fraction) in adult subjects in response to feedback and to explore the relationship between ANS acuity and acuity on another magnitude comparison task. We tested each of 20 subjects over six 1-h sessions. The main findings were that (a) Weber fractions rapidly decreased when trial-by-trial feedback was introduced in the second session and remained stable over continued training, (b) Weber fractions remained steady when trial-by-trial feedback was removed in session 6, (c)Weber fractions from the number comparison task were positively correlated with Weber fractions from a line length comparison task, (d) improvement in Weber fractions in response to feedback for the number task did not transfer to the line length task, (e) finally, the precision of the ANS was positively correlated with math, but not verbal, standardized aptitude scores. Potential neural correlates of the perceptual information and decision processes are considered, and predictions regarding the neural correlates of ANS malleability are discussed.

Preschoolers' precision of the approximate number system predicts later school mathematics performance

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.

Specialization in the human brain: the case of numbers

How numerical representation is encoded in the adult human brain is important for a basic understanding of human brain organization, its typical and atypical development, its evolutionary precursors, cognitive architectures, education, and rehabilitation. Previous studies have shown that numerical processing activates the same intraparietal regions irrespective of the presentation format (e.g., symbolic digits or non-symbolic dot arrays). This has led to claims that there is a single format-independent, numerical representation. In the current study we used a functional magnetic resonance adaptation paradigm, and effective connectivity analysis to re-examine whether numerical processing in the intraparietal sulci is dependent or independent on the format of the stimuli. We obtained two novel results. First, the whole brain analysis revealed that format change (e.g., from dots to digits), in the absence of a change in magnitude, activated the same intraparietal regions as magnitude change, but to a greater degree. Second, using dynamic causal modeling as a tool to disentangle neuronal specialization across regions that are commonly activated, we found that the connectivity between the left and right intraparietal sulci is format-dependent. Together, this line of results supports the idea that numerical representation is subserved by multiple mechanisms within the same parietal regions.

Changes in frontal-parietal activation and math skills performance following adaptive number sense training: preliminary results from a pilot study

Number sense is believed to be critical for math development. It is putatively an implicitly learned skill and may therefore have limitations in terms of being explicitly trained, particularly in individuals with altered neurodevelopment. A case series study was conducted using an adaptive, computerised programme that focused on number sense and general problem-solving skills. The study was designed to investigate training effects on performance as well as brain function in a group of children with Turner syndrome who are at risk for math difficulties and altered development of math-related brain networks. Standardised measurements of math and math-related cognitive skills as well as functional magnetic resonance imaging (fMRI) were used to assess behavioural and neurobiological outcomes following training. Participants demonstrated significantly increased basic math skills, including number sense, and calculation as well as processing speed, cognitive flexibility and visual-spatial processing skills. With the exception of calculation, increased scores also were clinically significant (i.e., recovered) based on reliable change analysis. Participants additionally demonstrated significantly increased bilateral parietal lobe activation and decreased frontal-striatal and mesial temporal activation following the training programme. These findings show proof of concept for an accessible training approach that may be potentially associated with improved number sense, math and related skills, as well as functional changes in math-related neural systems, even among individuals at risk for altered brain development.

Mental number line training in children with developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability that affects the acquisition of mathematical skills in children with normal intelligence and age-appropriate school education (prevalence 3-6%). One essential step in the development of mathematical understanding is the formation and automated access to a spatial representation of numbers. Many children with DD show a deficient development of such a mental number line. The present study aimed to develop a computer-based training program to improve the construction and access to the mental number line. Sixteen children with DD aged 8-10 years and 16 matched control children completed the 5-week computer training. All children played the game 15 min a day for 5 days a week. The efficiency of the training was evaluated by means of neuropsychological tests and functional magnetic resonance imaging (fMRI) during a number line task. In general, children with and without DD showed a benefit from the training indicated by (a) improved spatial representation of numbers and (b) the number of correctly solved arithmetical problems. Regarding group differences in brain activation, children with DD showed less activation in bilateral parietal regions, which reflects neuronal dysfunction in pivotal regions for number processing. Both groups showed reduced recruitment of relevant brain regions for number processing after the training which can be attributed to automatization of cognitive processes necessary for mathematical reasoning. Moreover, results point to a partial remediation of deficient brain activation in dyscalculics after consolidation of acquired and refined number representation. To conclude, the present study represents the first attempt to evaluate a custom-designed training program in a group of dyscalculic children and results indicate that the training leads to an improved spatial representation of the mental number line and a modulation of neural activation, which both facilitate processing of numerical tasks.

Symbolic and nonsymbolic number comparison in children with and without dyscalculia

Developmental dyscalculia (DD) is a pervasive difficulty affecting number processing and arithmetic. It is encountered in around 6% of school-aged children. While previous studies have mainly focused on general cognitive functions, the present paper aims to further investigate the hypothesis of a specific numerical deficit in dyscalculia. The performance of 10- and 11-year-old children with DD characterised by a weakness in arithmetic facts retrieval and age-matched control children was compared on various number comparison tasks. Participants were asked to compare a quantity presented in either a symbolic (Arabic numerals, number words, canonical dots patterns) or a nonsymbolic format (noncanonical dots patterns, and random sticks patterns) to the reference quantity 5. DD children showed a greater numerical distance effect than control children, irrespective of the number format. This favours a deficit in the specialised cognitive system underlying the processing of number magnitude in children with DD. Results are discussed in terms of access and representation deficit hypotheses.

Numerical representation in the parietal lobes: abstract or not abstract?

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex.

Intuitive numbers guide decisions

Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills) consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations) also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a) perceived differences between numbers, b) the extent to which proportional differences are weighed in decisions, and, ultimately, c) the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.

An open trial assessment of "The Number Race", an adaptive computer game for remediation of dyscalculia

Background

In a companion article [1], we described the development and evaluation of software designed to remediate dyscalculia. This software is based on the hypothesis that dyscalculia is due to a "core deficit" in number sense or in its access via symbolic information. Here we review the evidence for this hypothesis, and present results from an initial open-trial test of the software in a sample of nine 7–9 year old children with mathematical difficulties.

Methods

Children completed adaptive training on numerical comparison for half an hour a day, four days a week over a period of five-weeks. They were tested before and after intervention on their performance in core numerical tasks: counting, transcoding, base-10 comprehension, enumeration, addition, subtraction, and symbolic and non-symbolic numerical comparison.

Results

Children showed specific increases in performance on core number sense tasks. Speed of subitizing and numerical comparison increased by several hundred msec. Subtraction accuracy increased by an average of 23%. Performance on addition and base-10 comprehension tasks did not improve over the period of the study.

Conclusion

Initial open-trial testing showed promising results, and suggested that the software was successful in increasing number sense over the short period of the study. However these results need to be followed up with larger, controlled studies. The issues of transfer to higher-level tasks, and of the best developmental time window for intervention also need to be addressed.