Mental number line training in children with developmental dyscalculia
Research Highlights
► Evaluation of a training program for children with developmental dyscalculia. ► Training of spatial representation of numbers. ► Improved number processing after training. ► Modulation of brain activation after training.
Introduction
Developmental dyscalculia (DD) is a specific learning disorder of mathematical abilities presumed to be due to impairments in brain function (Cohen Kadosh et al., 2007, Kucian et al., 2006, Mussolin et al., 2009, Price et al., 2007, Shalev, 2004). Children with DD show a variety of fundamental deficits in number processing, including basic competences such as the representation of quantity and numbers (Bachot et al., 2005, Koontz and Berch, 1996, Landerl et al., 2004, Landerl et al., 2009, Rousselle and Noel, 2007). This representation is thought to be similar to a number line on which we organize, arrange and classify numbers (Dehaene, 2003). The formation of such a mental number line constitutes a vital step in the development of mathematical skills (von Aster and Shalev, 2007). It is thought that children start to develop their internal representations of numbers long before formal schooling. With the entrance into school and the acquisition of the symbolic number system and arithmetical skills these representations become more precise and are expanded to an increasing numerical range (Barth et al., 2005, Berch et al., 1999, Schweiter et al., 2005). In agreement, a recent study showed that formal education and numerical enculturation sharpens magnitude representation specifically (Soltesz et al., 2010). Moreover, the authors claim that the development of symbolic number knowledge, acquired during the first years of school, develop independently of non-symbolic number comparison skills. The gain in precision of the mental number line is characterized by a shift from a logarithmic to a linear ruler representation (Berteletti et al., 2010, Siegler and Booth, 2004, Siegler and Opfer, 2003). Relative to a linear representation of numbers, a logarithmic representation exaggerates the distance between the magnitudes of numbers at the low end of the range and minimizes the distance between magnitudes of numbers in the middle and upper ends of the range (Siegler and Booth, 2004). The developmental trajectory of this number representation follows a continuing refinement throughout childhood, with adult-like levels of acuity attained surprisingly late (Halberda and Feigenson, 2008). Furthermore, the representational change to a linear fit was found to correlate positively with mathematical skills and the precision of the internal number representation correlates with math achievement scores (Halberda et al., 2008, Siegler and Booth, 2004), indicating that the nature and quality of number representation decisively influences the development of calculation capabilities.
A recent study examining the link between number representation and dyscalculia (Piazza et al., 2010) showed that number representation is severely impaired in dyscalculics, with 10-year-old dyscalculics scoring at the level of 5-year-old normally achieving children. This study also reported that the severity of the representational impairment predicts the defective performance on tasks involving the manipulation of symbolic numbers. Observed deficits of mental representation of numbers in children with DD are in line with neuro-imaging findings pointing to functional impairments and structural and microstructural alterations in parietal brain regions thought to represent the locus of the mental number line (Kaufmann et al., 2009, Kucian et al., 2006, Mussolin et al., 2009, Price et al., 2007, Rotzer et al., 2008, Rykhlevskaia et al., 2009, Soltesz et al., 2007). Therefore, it is hypothesized that targeted training to improve the representation of numbers in dyscalculic children will have a beneficial effect on mathematical competence in these children, which is reflected by changes in neuronal activation in math relevant brain regions.
Two previous studies have evaluated different approaches for training number representation in children (Siegler and Ramani, 2009, Wilson et al., 2006a). The first called “Number Race” by Wilson et al. (2006a) is an adaptive software game principally designed to enhance quantity representation. Evaluation of this training in children age 7–9 years with mathematical learning difficulties suggests that the remediation is successful in producing an improvement in basic numerical cognition (Wilson et al., 2006b). However, this study had some limitations, such as only a small sample size of children with mathematical difficulties (n = 9) was examined and a control group was lacking.
The second approach is a linear number board game tested by Siegler and Ramani (2009) against a circular board in a group of low-income preschoolers. As predicted, playing the linear number board game increased numerical knowledge in these children significantly, and these children learned more from subsequent practice and feedback on addition tasks (Ramani and Siegler, 2008, Siegler and Ramani, 2009, Whyte and Bull, 2008). In contrast, playing with the circular number board did not result in any improvement in numerical understanding. The authors argue that the linear board game lead to greater learning than the circular game because the linear board more closely resembles the desired mental representation of numbers.
These two promising approaches lend support to the importance and efficacy of intervention programs with math tasks which aim to improve basic competences such as the representation of quantity and numbers. Both demonstrated promising improvements in fundamental numerical understanding, suggesting that children with developmental dyscalculia may benefit tremendously from such an intervention program.
The goal of the present study was to develop and evaluate a computer-based training program for dyscalculic children based on cognitive neuroscience and brain imaging findings. The intervention aims to improve number representation in a similar manner to the aforementioned intervention studies. In addition, the training should also strengthen the link between representations of numbers and space, which are known to be closely associated (Dehaene et al., 1993). The development of a precise spatial representation of numbers is crucial for the understanding of the principle of ordinality of numbers, which relates to the ability to rank numbers in order of magnitude. Moreover, the training aimed to improve both the ability to estimate a given quantity of dots, as a very basic aspect of number processing, as well as more demanding arithmetical skills.
Despite the high prevalence of dyscalculia of 3–6% (Gross-Tsur et al., 1996, von Aster et al., 2007), which is similar to that of dyslexia, dyscalculia research is generally under-represented and the scientific evaluation of appropriate intervention programs in dyscalculic children is missing, except of the initial study of Wilson et al. (2006b). Therefore, the present study attempts to evaluate a custom-designed training program in a group of dyscalculic children by means of behavioral outcome. Moreover, it represents the first evaluation of neuro-plastic changes in brain function in children with developmental dyscalculia, which will provide additional insides in neuronal correlates of dyscalculia and learning. Functional magnetic resonance imaging (fMRI) studies in dyslexia have demonstrated changes in brain activity after training (Eden et al., 2004, Simos et al., 2002, Temple et al., 2003). Therefore, we expect that children with developmental dyscalculia will improve their internal representation of numbers and consequently show better performance on mathematical tasks after completion of the training, since the more sophisticated spatial representation is assumed to rely on a linear number representation. Based on previous training studies, we hypothesize that our training will lead to a modification of brain activation patterns including frontal and parietal regions. On the one hand, the parietal lobe underpins domain-general mechanisms, like attention and working memory, and on the other hand, it hosts the most specific brain center for numerical understanding. The training is expected to influence both processes antithetically, inducing a general reduction of brain activation, but also fostering an increase in activation when an initially impaired activation can be assumed, such as in dyscalculic children.
In line with reported findings, main effects of training are expected to result in a relative decrease in blood oxygenation level dependent (BOLD) signal in the fronto-parietal activation pattern including mainly areas supporting domain-general cognitive processes in both groups (Delazer et al., 2003, Ischebeck et al., 2006, Ischebeck et al., 2007, Pauli et al., 1994). In particular, deceased activation in the parietal lobule after training has been reported in the intraparietal sulcus (IPS), superior parietal lobules extending into the precuneus, and the inferior parietal lobe; in terms of the frontal lobe, reduced activation has been allocated to the superior and inferior frontal gyrus, the precentral gyrus, and supplemental motor area (Delazer et al., 2003, Ischebeck et al., 2006, Ischebeck et al., 2007). Regarding neuronal correlates of the mental number line in children with developmental dyscalculia, reduced activation in areas playing a pivotal role, such as the intraparietal sulcus is anticipated. After completion of the training, a restoration of deficient brain activation in children with developmental dyscalculia is expected, facilitating an increase of activity in affected parietal regions in these children.
Section snippets
Study design
Children with dyscalculia and control children were evaluated by behavioral tests and fMRI before and after completion of the 5-week training program. Control children were evaluated three times during the study, firstly for neuropsychological testing, secondly for fMRI scanning and testing before the training and finally for fMRI scanning and testing after the 5-week training session. In contrast, dyscalculic children were evaluated after a 5-week rest period in addition to before and after
Behavioral performance
Table 1 includes testmetric features and demographic data for all participants. The estimated general intelligence of all subjects was in the normal range, and no significant difference in estimated General IQ based on all subtests but Arithmetic was found between groups when correcting for Arithmetic. However, comparison of estimated General IQ including all five subtests and of single subtests revealed significantly lower parameters in DD children except for Picture Arrangement. This is not
Discussion
Despite the relatively high prevalence of developmental dyscalculia, few studies to date have attempted to develop or evaluate targeted interventions based on neuro-cognitive knowledge of this impairment. In the present study, we developed a custom computer-based training program and performed the first assessment of the efficacy and neuro-cognitive effects of this targeted training for remediation of dyscalculia by means of neuropsychological tests and fMRI examinations. The results obtained
Acknowledgment
We would like to thank all children and their parents, who participated in this study. This research was supported by a grant from the Swiss National Science Foundation (Project No. 3200B0-116834) and the NOMIS Foundation.
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