Beyond natural numbers: negative number representation in parietal cortex

Development of common neural representations for distinct numerical problems

How the brain develops representations for abstract cognitive problems is a major unaddressed question in neuroscience. Here we tackle this fundamental question using arithmetic problem solving, a cognitive domain important for the development of mathematical reasoning. We first examined whether adults demonstrate common neural representations for addition and subtraction problems, two complementary arithmetic operations that manipulate the same quantities. We then examined how the common neural representations for the two problem types change with development. Whole-brain multivoxel representational similarity (MRS) analysis was conducted to examine common coding of addition and subtraction problems in children and adults. We found that adults exhibited significant levels of MRS between the two problem types, not only in the intraparietal sulcus (IPS) region of the posterior parietal cortex (PPC), but also in ventral temporal-occipital, anterior temporal and dorsolateral prefrontal cortices. Relative to adults, children showed significantly reduced levels of MRS in these same regions. In contrast, no brain areas showed significantly greater MRS between problem types in children. Our findings provide novel evidence that the emergence of arithmetic problem solving skills from childhood to adulthood is characterized by maturation of common neural representations between distinct numerical operations, and involve distributed brain regions important for representing and manipulating numerical quantity. More broadly, our findings demonstrate that representational analysis provides a powerful approach for uncovering fundamental mechanisms by which children develop proficiencies that are a hallmark of human cognition.

Exploring the Boundaries of the Number–Temporal Order Association

Past research has shown that numbers are associated with order in time such that performance in a numerical comparison task is enhanced when number pairs appear in ascending order, when the larger number follows the smaller one. This was found in the past for the integers 1–9 ( Ben-Meir, Ganor-Stern, & Tzelgov, 2013 ; Müller & Schwarz, 2008 ). In the present study we explored whether the advantage for processing numbers in ascending order exists also for fractions and negative numbers. The results demonstrate this advantage for fraction pairs and for integer-fraction pairs. However, the opposite advantage for descending order was found for negative numbers and for positive-negative number pairs. These findings are interpreted in the context of embodied cognition approaches and current theories on the mental representation of fractions and negative numbers.

Repetitive transcranial magnetic stimulation over left angular gyrus modulates the predictability gain in degraded speech comprehension

Increased neural activity in left angular gyrus (AG) accompanies successful comprehension of acoustically degraded but highly predictable sentences, as previous functional imaging studies have shown. However, it remains unclear whether the left AG is causally relevant for the comprehension of degraded speech. Here, we applied transient virtual lesions to either the left AG or superior parietal lobe (SPL, as a control area) with repetitive transcranial magnetic stimulation (rTMS) while healthy volunteers listened to and repeated sentences with high- versus low-predictable endings and different noise vocoding levels. We expected that rTMS of AG should selectively modulate the predictability gain (i.e., the comprehension benefit from sentences with high-predictable endings) at a medium degradation level. We found that rTMS of AG indeed reduced the predictability gain at a medium degradation level of 4-band noise vocoding (relative to control rTMS of SPL). In contrast, the behavioral perturbation induced by rTMS changed with increased signal quality. Hence, at 8-band noise vocoding, rTMS over AG versus SPL decreased the number of correctly repeated keywords for sentences with low-predictable endings. Together, these results show that the degree of the rTMS interference depended jointly on signal quality and predictability. Our results provide the first causal evidence that the left AG is a critical node for facilitating speech comprehension in challenging listening conditions.

Neurobiological underpinnings of math and reading learning disabilities

The primary goal of this review is to highlight current research and theories describing the neurobiological basis of math (MD), reading (RD), and comorbid math and reading disability (MD+RD). We first describe the unique brain and cognitive processes involved in acquisition of math and reading skills, emphasizing similarities and differences in each domain. Next we review functional imaging studies of MD and RD in children, integrating relevant theories from experimental psychology and cognitive neuroscience to characterize the functional neuroanatomy of cognitive dysfunction in MD and RD. We then review recent research on the anatomical correlates of MD and RD. Converging evidence from morphometry and tractography studies are presented to highlight distinct patterns of white matter pathways which are disrupted in MD and RD. Finally, we examine how the intersection of MD and RD provides a unique opportunity to clarify the unique and shared brain systems which adversely impact learning and skill acquisition in MD and RD, and point out important areas for future work on comorbid learning disabilities.

Understanding less than nothing: children's neural response to negative numbers shifts across age and accuracy

We examined the brain activity underlying the development of our understanding of negative numbers, which are amounts lacking direct physical counterparts. Children performed a paired comparison task with positive and negative numbers during an fMRI session. As previously shown in adults, both pre-instruction fifth-graders and post-instruction seventh-graders demonstrated typical behavioral and neural distance effects to negative numbers, where response times and parietal and frontal activity increased as comparison distance decreased. We then determined the factors impacting the distance effect in each age group. Behaviorally, the fifth-grader distance effect for negatives was significantly predicted only by positive comparison accuracy, indicating that children who were generally better at working with numbers were better at comparing negatives. In seventh-graders, negative number comparison accuracy significantly predicted their negative number distance effect, indicating that children who were better at working with negative numbers demonstrated a more typical distance effect. Across children, as age increased, the negative number distance effect increased in the bilateral IPS and decreased frontally, indicating a frontoparietal shift consistent with previous numerical development literature. In contrast, as negative comparison task accuracy increased, the parietal distance effect increased in the left IPS and decreased in the right, possibly indicating a change from an approximate understanding of negatives' values to a more exact, precise representation (particularly supported by the left IPS) with increasing expertise. These shifts separately indicate the effects of increasing maturity generally in numeric processing and specifically in negative number understanding.