Silke M. Göbel

The left parietal and premotor cortices: motor attention and selection.

It is well established that the premotor cortex has a central role in the selection of movements. The role of parts of the parietal cortex in movement control has proved more difficult to describe but appears to be related to the preparation and the redirection of movements and movement intentions. We have referred to some of these processes as motor attention. It has been known since the time of William James that covert motor attention can be directed to an upcoming movement just as visuospatial attention can be directed to a location in space. While some parietal regions, particularly in the right hemisphere, are concerned with covert orienting and the redirecting of covert orienting it may be useful to consider other parietal regions, in the anterior inferior parietal lobule and in the posterior superior parietal lobule, particularly in the left hemisphere, as contributing to motor attention. Such parts of the parietal lobe are activated in neuroimaging experiments when subjects covertly prepare movements or switch intended movements. Lesions or transcranial magnetic stimulation (TMS) affect the redirecting of motor attention. The difficulties apraxic patients experience when sequencing movements may partly be due to an inability to redirect motor attention from one movement to another. The role of the premotor cortex in selecting movements is also lateralized to the left hemisphere. Damage to left hemisphere movement selection mechanisms may also contribute to apraxia. If, however, it remains intact after a stroke then the premotor cortex may contribute to the recovery of arm movements. A group of patients with unilateral left hemisphere lesions and impaired movements in the contralateral right hand was studied. Functional magnetic resonance imaging showed that in some cases the premotor cortex in the intact hemisphere was more active when the stroke-affected hand was used. TMS in the same area in the same patients had the most disruptive effect on movements. In summary, patterns of motor impairment and recovery seen after strokes can partly be explained with reference to the roles of the parietal and premotor cortices in motor attention and selection.

Functionally Specific Reorganization in Human Premotor Cortex

After unilateral stroke, the dorsal premotor cortex (PMd) in the intact hemisphere is often more active during movement of an affected limb. Whether this contributes to motor recovery is unclear. Functional magnetic resonance imaging (fMRI) was used to investigate short-term reorganization in right PMd after transcranial magnetic stimulation (TMS) disrupted the dominant left PMd, which is specialized for action selection. Even when 1 Hz left PMd TMS had no effect on behavior, there was a compensatory increase in activity in right PMd and connected medial premotor areas. This activity was specific to task periods of action selection as opposed to action execution. Compensatory activation changes were both functionally specific and anatomically specific: the same pattern was not seen after TMS of left sensorimotor cortex. Subsequent TMS of the reorganized right PMd did disrupt performance. Thus, this pattern of functional reorganization has a causal role in preserving behavior after neuronal challenge.

Response-Selection-Related Parietal Activation during Number Comparison

Neuroimaging studies of number comparison have consistently found activation in the intraparietal sulcus (IPS). Recently, it has been suggested that activations in the IPS vary with the distance between the numbers being compared. In number comparison, the smaller the distance between a number and the reference the longer the reaction time (RT). Activations in the right or left IPS, however, have also been related to attentional and intentional selection. It is possible, therefore, that activity in this region is a reflection of the more basic stimulus and response-selection processes associated with changes in RT. This fMRI experiment investigated the effect of numerical distance independently from RT. In addition, activations during number comparison of single-digit and double-digit stimuli were compared. During number comparison blocks, subjects had to indicate whether digits were greater or smaller than a reference (5 or 65). In control blocks, they were asked to perform a perceptual task (vertical line present/absent) on either numerical or nonnumerical stimuli. Number comparison versus rest yielded a large bilateral parietal-posterior frontal network. However, no areas showed more activation during number comparison than during the control tasks. Furthermore, no areas were more active during comparison of numbers separated by a small distance than comparisons of those separated by a large distance or vice versa. A left-lateralized parietal-posterior frontal network varied significantly with RT. Our findings suggest that magnitude and numerical-distance-related IPS activations might be difficult to separate from fundamental stimulus and response-selection processes associated with RT changes. As is the case with other parameters, such as space, magnitude may be represented in the context of response selection in the parietal cortex. In this respect, the representation of magnitude in the human IPS may be similar to the representation of magnitude in other nonhuman primates.

Approximate Number Sense, Symbolic Number Processing, or Number-Space Mappings: What Underlies Mathematics Achievement?.

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, childrens performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.

The Cultural Number Line: A Review of Cultural and Linguistic Influences on the Development of Number Processing

Approximate processing of numerosities is a universal and preverbal skill, while exact number processing above 4 involves the use of culturally acquired number words and symbols. The authors first review core concepts of numerical cognition, including number representation in the brain and the influential view that numbers are associated with space along a “mental number line.” Then, they discuss how cultural influences, such as reading direction, finger counting, and the transparency of the number word system, can influence the representation and processing of numbers. Spatial mapping of numbers emerges as a universal cognitive strategy. The authors trace the impact of cultural factors on the development of number skills and conclude that a cross-cultural perspective can reveal important constraints on numerical cognition.

Impact of High Mathematics Education on the Number Sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.

Direction counts: a comparative study of spatially directional counting biases in cultures with different reading directions.

Western adults associate small numbers with left space and large numbers with right space. Where does this pervasive spatial-numerical association come from? In this study, we first recorded directional counting preferences in adults with different reading experiences (left to right, right to left, mixed, and illiterate) and observed a clear relationship between reading and counting directions. We then recorded directional counting preferences in preschoolers and elementary school children from three of these reading cultures (left to right, right to left, and mixed). Culture-specific counting biases existed before reading acquisition in children as young as 3 years and were subsequently modified by early reading experience. Together, our results suggest that both directional counting and scanning activities contribute to number-space associations.

Children’s Arithmetic Development It Is Number Knowledge, Not the Approximate Number Sense, That Counts

In this article, we present the results of an 11-month longitudinal study (beginning when children were 6 years old) focusing on measures of the approximate number sense (ANS) and knowledge of the Arabic numeral system as possible influences on the development of arithmetic skills. Multiple measures of symbolic and nonsymbolic magnitude judgment were shown to define a unitary factor that appears to index the efficiency of an ANS system, which is a strong longitudinal correlate of arithmetic skills. However, path models revealed that knowledge of Arabic numerals at 6 years was a powerful longitudinal predictor of the growth in arithmetic skills, whereas variations in magnitude-comparison ability played no additional role in predicting variations in arithmetic skills. These results suggest that verbal processes concerned with learning the labels for Arabic numerals, and the ability to translate between Arabic numerals and verbal codes, place critical constraints on arithmetic development.

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.

Touch perception reveals the dominance of spatial over digital representation of numbers

We learn counting on our fingers, and the digital representation of numbers we develop is still present in adulthood [Andres M, et al. (2007) J Cognit Neurosci 19:563–576]. Such an anatomy–magnitude association establishes tight functional correspondences between fingers and numbers [Di Luca S, et al. (2006) Q J Exp Psychol 59:1648–1663]. However, it has long been known that small-to-large magnitude information is arranged left-to-right along a mental number line [Dehaene S, et al. (1993) J Exp Psychol Genet 122:371–396]. Here, we investigated touch perception to disambiguate whether number representation is embodied on the hand (“1” = thumb; “5” = little finger) or disembodied in the extrapersonal space (“1” = left; “5” = right). We directly contrasted these number representations in two experiments using a single centrally located effector (the foot) and a simple postural manipulation of the hand (palm-up vs. palm-down). We show that visual presentation of a number (“1” or “5”) shifts attention cross-modally, modulating the detection of tactile stimuli delivered on the little finger or thumb. With the hand resting palm-down, subjects perform better when reporting tactile stimuli delivered to the little finger after presentation of number “5” than number “1.” Crucially, this pattern reverses (better performance after number “1” than “5”) when the hand is in a palm-up posture, in which the position of the fingers in external space, but not their relative anatomical position, is reversed. The human brain can thus use either space- or body-based representation of numbers, but in case of competition, the former dominates the latter, showing the stronger role played by the mental number line organization.