Orly Rubinsten

Are numbers special? The comparison systems of the human brain investigated by fMRI.

Many studies have suggested that the intraparietal sulcus (IPS), particularly in the dominant hemisphere, is crucially involved in numerical comparisons. However, this parietal structure has been found to be involved in other tasks that require spatial processing or visuospatial attention as well. fMRI was used to investigate three different magnitude comparisons in an event-related-block design: (a) Which digit is larger in numerical value (e.g., 2 or 5)? (b) Which digit is brighter (e.g., 3 or 3)? (c) Which digit is physically larger (e.g., 3 or 3)? Results indicate a widespread cortical network including a bilateral activation of the intraparietal sulci for all different comparisons. However, by computing contrasts of brain activation between the respective comparison conditions and applying a cortical distance effect as an additional criterion, number-specific activation was revealed in left IPS and right temporal regions. These results indicate that there are both commonalities and differences in the spatial layout of the brain systems for numerical and physical comparisons and that especially the left IPS, while involved in magnitude comparison in general, plays a special role in number comparison.

Developmental dyscalculia: heterogeneity might not mean different mechanisms.

Research indicates that developmental dyscalculia (DD; a mathematical deficiency) involves a single brain area abnormality - in the intraparietal sulcus. This is surprising because, (i) the behavioural deficits are heterogeneous, (ii) multiple problems are most common in most cases (co-morbidity) and (iii) different aspects of intact number processing are represented in different brain areas. Hence, progress in the study of DD might be limited by conceptual issues. This work looks at biological and cognitive findings within DD and delineates frameworks for studying the neurocognitive basis of DD. We offer three alternative frameworks. These proposed frameworks have the potential of facilitating future discussions, work in the field and have implications for studies of similar disorders like dyslexia and attention-deficit/hyperactivity disorder.

Meta-analyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation.

The main aim of the present coordinate-based meta-analysis is to identify brain regions that are commonly activated in functional magnetic resonance imaging studies (fMRI) investigating number processing and calculation in children. Here, we include 19 developmental fMRI papers, five of which also examine children diagnosed with developmental dyscalculia and/or mathematical disability. Results reveal that children produce consistent fronto-parietal activation patterns in response to number processing and calculation. Importantly, activation patterns are clearly modulated by notation, task complexity, and competence level. Activation differences between children with and without dyscalculia are observable in number-relevant parietal regions as well as in (pre)frontal and occipital cortex.

Automatic activation of internal magnitudes: a study of developmental dyscalculia.

The association between Arabic numerals and the representations of magnitude in adult developmental dyscalculia was examined. University students compared physical size, vertical positioning (height), or grayness (different shades of gray) of 2 Arabic numerals. The numerical values could produce a Stroop-like numerical congruity effect (NCE; 3-5 vs. 3-5). The dyscalculia group did not show NCE in the grayness task, and their physical comparisons produced a significantly smaller NCE compared with that produced by the control group. Whereas previous research suggested that Arabic numerals activate representations of magnitude automatically, the results of this study indicate that this is not the case because (a) people with developmental dyscalculia require attention to associate internal representations of magnitude with Arabic numerals, and (b) activation of internal magnitudes depends on context (task).

Mathematics anxiety in children with developmental dyscalculia

BackgroundMath anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure.MethodsParticipants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively.ResultParticipants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group.ConclusionThese results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety.

Double Dissociation of Functions in Developmental Dyslexia and Dyscalculia

This work examines the association between symbols and their representation in adult developmental dyscalculia and dyslexia. Experiment 1 used comparative judgment of numerals, and it was found that in physical comparisons (e.g., 3-5 vs. 3-5) the dyscalculia group showed a significantly smaller congruity effect than did the dyslexia and the control groups. Experiment 2 used Navon figures (D. Navon, 1977) in Hebrew, and participants were asked to name the large or the small letters. Phoneme similarity modulated performance of the control and the dyscalculia groups and showed a very small effect in the dyslexia group. This suggests that the dyscalculia population has difficulties in automatically associating numerals with magnitudes but no problems in associating letters with phonemes, whereas the dyslexia population shows the opposite pattern.

Dyscalculia from a developmental and differential perspective.

Developmental dyscalculia (DD) and its treatment are receiving increasing research attention. A PsychInfo search for peer-reviewed articles with dyscalculia as a title word reveals 31 papers published from 1991–2001, versus 74 papers published from 2002–2012. Still, these small counts reflect the paucity of research on DD compared to dyslexia, despite the prevalence of mathematical difficulties. In the UK, 22% of adults have mathematical difficulties sufficient to impose severe practical and occupational restrictions (Bynner and Parsons, 1997; National Center for Education Statistics, 2011). It is unlikely that all of these individuals with mathematical difficulties have DD, but criteria for defining and diagnosing dyscalculia remain ambiguous (Mazzocco and Myers, 2003). What is treated as DD in one study may be conceptualized as another form of mathematical impairment in another study. Furthermore, DD is frequently—but, we believe, mistakenly- considered a largely homogeneous disorder. Here we advocate a differential and developmental perspective on DD focused on identifying behavioral, cognitive, and neural sources of individual differences that contribute to our understanding of what DD is and what it is not.

Are Arabic and verbal numbers processed in different ways

Four experiments were conducted in order to examine effects of notation--Arabic and verbal numbers--on relevant and irrelevant numerical processing. In Experiment 1, notation interacted with the numerical distance effect, and irrelevant physical size affected numerical processing (i.e., size congruity effect) for both notations but to a lesser degree for verbal numbers. In contrast, size congruity had no effect when verbal numbers were the irrelevant dimension. In Experiments 2 and 3, different parameters that could possibly affect the results, such as discriminability and variability (Experiment 2) and the block design (Experiment 3), were controlled. The results replicated the effects obtained in Experiment 1. In Experiment 4, in which physical size was made more difficult to process, size congruity for irrelevant verbal numbers was observed. The present results imply that notation affects numerical processing and that Arabic and verbal numbers are represented separately, and thus it is suggested that current models of numerical processing should have separate comparison mechanisms for verbal and Arabic numbers.

Is an ant larger than a lion

In order to examine the influence exerted by an irrelevant semantic variable in a comparative judgment task, we employed a Stroop-like paradigm. The stimuli were pairs of animal names that were different in their physical and semantic sizes (e.g., ant lion). Participants were asked to judge which of the two words was larger either in physical or in semantic size. Size congruity effect (i.e., faster reaction times with congruent than with incongruent stimuli) appeared in both semantic and physical judgments. The semantic distance effect (i.e., large semantic distances are processed faster than smaller ones), appeared only when the semantic dimension was relevant to the task. The findings indicate that when a word (animal name) is presented, its meaning is accessed automatically. Part of this meaning (at least with our stimuli) relates to the size of the animal in real life. Processing of meaning of the size of the words is carried out in parallel with the extraction of the physical features of the presented stimuli.

Quantities, amounts, and the numerical core system

Numerical cognition is essential to many aspects of life and arithmetic abilities predict academic achievements better than reading (Estrada et al., 2004). Accordingly, it is important to understand the building blocks of numerical cognition, the neural tissue involved, and the developmental trajectories. In the last two decades research has made impressive strides forward in studying numerical cognition and brain mechanisms involved in arithmetic. This advance was marked by suggestions of a numerical core system that can be characterized as a set of intuitions for quantities innately available to humans (Brannon et al., 2006) and animals (Cantlon and Brannon, 2007). We suggest that another system, evolved to perceive and evaluate non-countable dimensions like size or amount of substance may be important for the evolution of the numerical system and numerical abilities. The current opinion article examines this idea and the possible interplay between, on the one hand perception and evaluation of continuous dimensions and, on the other, the numerical system.