Catherine Thevenot

What's Behind a “+” Sign? Perceiving an Arithmetic Operator Recruits Brain Circuits for Spatial Orienting

Do mathematical symbols evoke spatial representations? Although behavioral studies have long demonstrated interactions between space and the processing of Arabic digits, how to interpret these results remains controversial. Here, we tested whether activity in regions supporting spatial processing contributes to the processing of symbols conveying fundamental arithmetic concepts-such as operation signs-even in the absence of associated digits. Using functional magnetic resonance imaging, we show that merely perceiving a + sign triggers activity in brain regions that support the orienting of spatial attention in adults. Activity in these regions was greater for + than for × signs, indicating that it is modulated by whether an operator reflects an operation that evokes numerical manipulation (rather than rote memorization). Finally, the degree to which subjects activated a spatial region in response to a + sign was correlated with the degree to which subjects benefited from being briefly presented with that sign before having to calculate a single-digit addition problem, an effect termed operator-priming. Therefore, not only are some arithmetic operators linked to spatial intuitions, but such intuitions might also have an important role during arithmetic calculation. More generally, our findings support the view that mathematical symbols inherently evoke spatial representations.

Spatial numerical associations in preschoolers

ABSTRACT Three-to-five-year-old French children were asked to add or remove objects to or from linear displays. The hypothesis of a universal tendency to represent increasing number magnitudes from left to right led to predict a majority of manipulations at the right end of the rows, whatever childrens hand laterality. Conversely, if numbers are not inherently associated with space, children were expected to favour laterality-consistent manipulations. The results showed a strong tendency to operate on the right end of the rows in right-handers, but no preference in left-handers. These findings suggest that the task elicited a left-to-right oriented representation of magnitudes that counteracted laterality-related responses in left-handed children. The young age of children and the lack of a developmental trend towards right preference weaken the hypothesis of a cultural origin of this oriented representation. The possibility that our results are due to weaker brain lateralisation in left-handers compared to right-handers is addressed in Discussion section.

Hippocampal spatial mechanisms relate to the development of arithmetic symbol processing in children

Understanding the meaning of abstract mathematical symbols is a cornerstone of arithmetic learning in children. Studies have long focused on the role of spatial intuitions in the processing of numerals. However, it has been argued that such intuitions may also underlie symbols that convey fundamental arithmetic concepts, such as arithmetic operators. In the present cross-sectional study, we used fMRI to investigate how and when associations between arithmetic operators and brain regions processing spatial information emerge in children from 3rd to 10th grade. We found that the mere perception of a ‘+’ sign elicited grade-related increases of spatial activity in the right hippocampus. That is, merely perceiving ‘+’ signs – without any operands – elicited enhanced hippocampal activity after around 7th grade (12–13 years old). In these children, hippocampal activity in response to a ‘+’ sign was further correlated with the degree to which calculation performance was facilitated by the preview of that sign before an addition problem, an effect termed operator-priming. Grade-related increases of hippocampal spatial activity were operation-specific because they were not observed with ‘×’ signs, which might evoke rote retrieval rather than numerical manipulation. Our study raises the possibility that hippocampal spatial mechanisms help build associations between some arithmetic operators and space throughout age and/or education.

Identifying Strategies in Arithmetic With the Operand Recognition Paradigm: A Matter of Switch Cost?

Determining adults and childrens strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we developed the operand recognition paradigm (ORP). It capitalizes on the fact that, contrary to retrieval, calculation procedures degrade the memory traces of the operands involved in a problem. As a consequence, the use of calculation procedures is inferred from relatively long recognition times of the operands. However, it has been suggested that recognition times within the ORP do not reflect strategies but the difficulty of switching from a difficult task (calculation) to a simpler one (recognition). In order to examine this possibility, in a series of 3 experiments we equalized switch-cost variations in all conditions through the introduction of intermediate tasks between problem solving and recognition. Despite this neutralization, we still obtained the classical effects of the ORP, namely longer recognition times after addition than after comparison. We conclude that the largest part of the ORP effects is related to different strategy use and not to difficulty-related switch costs. The possible applications and promising outcomes of the ORP in and outside the field of numerical cognition are discussed.

High working memory capacity favours the use of finger counting in six-year-old children

ABSTRACT In this study, we show that 6-year-old children with high working memory capacity are more likely to use their fingers in an addition task than children with lower capacity. Moreover and as attested by a strong correlation between finger counting and accuracy in the arithmetic task, finger counting appears to be a very efficient strategy. Therefore, discovering the finger counting strategy seems to require a large amount of working memory resources, which could lack in low-span children. Furthermore, when children with low working memory capacities use their fingers to solve addition problems, they more often use the laborious counting-all strategy than children with higher capacities who use more elaborated procedures such as the Min strategy. Consequently, we suggest that explicit teaching of finger counting during the first years of schooling should be promoted because it could help less gifted children to overcome their difficulties in arithmetic.

Successful aging: The role of cognitive gerontology

ABSTRACT This commentary explores the relationships between the construct of successful aging and the experimental psychology of human aging—cognitive gerontology. What can or should cognitive gerontology contribute to understanding, defining, and assessing successful aging? Standards for successful aging reflect value judgments that are culturally and historically situated. Fundamentally, they address social policy; they are prescriptive. If individuals or groups are deemed to be aging successfully, then their characteristics or situations can be emulated. If an individual or a group is deemed to be aging unsuccessfully, then intervention should be considered. Although science is never culture-free or ahistorical, cognitive gerontology is primarily descriptive of age-related change. It is not prescriptive. It is argue that cognitive gerontology has little to contribute to setting standards for successful aging. If, however, better cognitive function is taken as a marker of more successful aging—something not universally accepted—then cognitive gerontology can play an important assessment role. It has a great deal to contribute in determining whether an individual or a group evidences better cognitive function than another. More importantly, cognitive gerontology can provide tools to evaluate the effects of interventions. It can provide targeted measures of perception, attention, memory, executive function, and other facets of cognition that are more sensitive to change than most clinical measures. From a deep understanding of factors affecting cognitive function, cognitive gerontology can also suggest possible interventions. A brief narrative review of interventions that have and have not led to improved cognitive function in older adults. Finally, the enormous range is addressed in the estimates of the proportion of the population that meets a standard for aging successfully, from less than 10% to more than 90%. For research purposes, it would be better to replace absolute cutoffs with correlational approaches (e.g., Freund & Baltes, 1998, Psychology and Aging, 13, 531–543). For policy purposes, cutoffs are necessary, but we propose that assessments of successful aging be based not on absolute cutoffs but on population proportions. An example of one possible standard is this: Those more than 1 standard deviation above the mean are aging successfully; those more than 1 standard deviation below the mean are aging unsuccessfully; those in between are aging usually. Adoption of such a standard may reduce the wide discrepancies in the incidence of successful aging reported in the literature.

Dexterity and Finger Sense: A Possible Dissociation in Children With Cerebral Palsy

Both hand and finger sensory perception and motor abilities are essential for the development of skilled gestures and efficient bimanual coordination. While finger dexterity and finger sensory perception can be impaired in children with cerebral palsy (CP), the relationship between these two functions in this population is not clearly established. The common assumption that CP children with better sensory function also demonstrate better motor outcomes has been recently challenged. To study these questions further, we assessed both finger dexterity and finger gnosia, the ability to perceive one’s own fingers by touch, in groups of 11 children with unilateral (i.e., hemiplegic CP) and 11 children with bilateral spastic CP (i.e., diplegic CP) and compared them with typical children. In our sample, children with hemiplegia exhibited finger dexterity deficit in both hands and finger gnosia deficit only in their paretic hand. In contrast, children with diplegia exhibited finger gnosia deficits in both hands and finger dexterity deficit only in their dominant hand. Thus, our results indicated that children with spastic hemiplegia and diplegia present different sensory and motor profiles and suggest that these two subgroups of CP should be considered separately in future experimental and clinical research. We discuss the implications of our results for rehabilitation.

Frequency of finger looking during finger counting is related to children's working memory capacities

ABSTRACT Finger counting can be useful in solving arithmetic problems, noticeably because it reduces the working memory demand of mental calculations. However, proprioceptive information might not be sufficient to keep track of the number of fingers raised during problem solving, and visual input may play an important role in this process. The present study was designed to address this question and shows that 8-year-old children look at their fingers in 60% of the trials during finger counting when solving additive problems. Moreover, our results reveal that the frequency of finger looking is negatively correlated with working memory capacities and is higher for more difficult problems. These findings suggest that finger looking is recruited in managing the cognitive demand of the arithmetic task, probably by providing additional external cues to monitor the number of steps that have to be incremented during finger counting.

SPATIAL-NUMERICAL ASSOCIATIONS ENHANCE THE SHORT-TERM MEMORIZATION OF DIGIT LOCATIONS

Little is known about how spatial-numerical associations (SNAs) affect the way individuals process their environment, especially in terms of learning and memory. In this study, we investigated the potential effects of SNAs in a digit memory task in order to determine whether spatially organized mental representations of numbers can influence the short-term encoding of digits positioned on an external display. To this aim, we designed a memory game in which participants had to match pairs of identical digits in a 9 × 2 matrix of cards. The nine cards of the first row had to be turned face up and then face down, one by one, to reveal a digit from 1 to 9. When a card was turned face up in the second row, the position of the matching digit in the first row had to be recalled. Our results showed that performance was better when small numbers were placed on the left side of the row and large numbers on the right side (i.e., congruent) as compared to the inverse (i.e., incongruent) or a random configuration. Our findings suggests that SNAs can enhance the memorization of digit positions and therefore that spatial mental representations of numbers can play an important role on the way humans process and encode the information around them. To our knowledge, this study is the first that reaches this conclusion in a context where digits did not have to be processed as numerical values.

Arithmetic word problems describing discrete quantities: E.E.G evidence for the construction of a situation model

In this research, university students were asked to solve arithmetic word problems constructed either with discrete quantities, such as apples or marbles, or continuous quantities such as meters of rope or grams of sand. An analysis of their brain activity showed different alpha levels between the two types of problems with, in particular, a lower alpha power in the parieto-occipital area for problems describing discrete quantities. This suggests that processing discrete quantities during problem solving prompts more mental imagery than processing continuous quantities. These results are difficult to reconcile with the schema theory, according to which arithmetic problem solving depends on the activation of ready-made mental frames stored in long-term memory and triggered by the mathematical expression used in the texts. Within the schema framework, the nature of the objects described in the text should be quickly abstracted during problem solving because it cannot impact the semantic structure of the problem. On the contrary, our results support the situation model theory, which places greater emphasis on the problem context in order to account for individuals behaviour. On a more methodological point of view, this study constitutes the first attempt to infer the characteristics of individuals mental representations of arithmetic text problems from EEG recordings. This opens the door for the application of brain activity measures in the field of arithmetic word problem.