How Memory Counts in Mathematical Development.

Memory has been well-established as a predictor of mathematics achievement in child development. Nevertheless, empirical evidence remains elusive on the unique role of the different forms of memory and their specific mechanisms as predictors of mathematics development. Therefore, in this study, the role of visuospatial short-term memory, visuospatial working memory, verbal short-term memory, and verbal long-term memory was investigated at three key stages of the development of mathematics (5-6 years, 6-7 years, 7-8 years), as well as their interactions across development. The relation between the different memory types and informal and formal mathematics was also studied. The findings of this study provide empirical support for a shift in the relation between different memory types and mathematics achievement over development with: 1) visuospatial short-term memory predicting informal mathematics achievement at the age of 5-6 years; 2) visuospatial working memory predicting informal and formal mathematics achievement at the age of 6-7 years; and 3) verbal short-term memory predicting formal mathematics achievement at the age of 7-8 years. These shifts clearly appear consistent with children's mathematics curriculum content over time and the requirements of mathematics acquisition at specific stages in development. With these findings, the unique role of various forms of memory in the development of mathematics and the timeframe in which they play a crucial part is highlighted, which should be taken into consideration for future research and possible intervention studies in children's mathematics achievement.

The measurement of approximate number system acuity across the lifespan is compromised by congruency effects.

Recent studies have highlighted the influence of visual cues such as dot size and cumulative surface area on the measurement of the approximate number system (ANS). Previous studies assessing ANS acuity in ageing have all applied stimuli generated by the Panamath protocol, which does not control nor measure the influence of convex hull. Crucially, convex hull has recently been identified as an influential visual cue present in dot arrays, with its impact on older adults' ANS acuity yet to be investigated. The current study therefore investigated the manipulation of convex hull by the Panamath protocol, and its effect on the measurement of ANS acuity in younger and older participants. First, analyses of the stimuli generated by Panamath revealed a confound between numerosity ratio and convex hull ratio. Second, although older adults were somewhat less accurate than younger adults on convex hull incongruent trials, ANS acuity was broadly similar between the groups. These findings have implications for the valid measurement of ANS acuity across all ages, and suggest that the Panamath protocol produces stimuli that do not adequately control for the influence of convex hull on numerosity discrimination.

Reduced inter-hemispheric interference in ageing: Evidence from a divided field Stroop paradigm.

One of the most important structural changes that occur in the brain during the course of life relates to the corpus callosum, the largest neural pathway that connects the two cerebral hemispheres. It has been shown that the corpus callosum, and in particular its anterior sections, endures a process of degeneration in ageing. Hence, a primary question is whether such structural changes in the brain of older adults have functional consequences on inter-hemispheric communication. In particular, whether the atrophy of the corpus callosum in ageing may lead to a higher or lower level of inter-hemispheric interference is currently unknown. To investigate this question, we asked young and healthy older adults to perform modified versions of the classic Stroop paradigm in which the target and distracter were spatially separated. Across two experiments, we found that the Stroop effect was significantly reduced in older adults when the two stimuli were distributed in two different hemifields as opposed to the same single hemifield. This new finding suggests that age-related callosal thinning reduces inter-hemispheric interference by facilitating the two hemispheres to process information in parallel.

Dot Display Affects Approximate Number System Acuity and Relationships with Mathematical Achievement and Inhibitory Control.

Much research has investigated the relationship between the Approximate Number System (ANS) and mathematical achievement, with continued debate surrounding the existence of such a link. The use of different stimulus displays may account for discrepancies in the findings. Indeed, closer scrutiny of the literature suggests that studies supporting a link between ANS acuity and mathematical achievement in adults have mostly measured the ANS using spatially intermixed displays (e.g. of blue and yellow dots), whereas those failing to replicate a link have primarily used spatially separated dot displays. The current study directly compared ANS acuity when using intermixed or separate dots, investigating how such methodological variation mediated the relationship between ANS acuity and mathematical achievement. ANS acuity was poorer and less reliable when measured with intermixed displays, with performance during both conditions related to inhibitory control. Crucially, mathematical achievement was significantly related to ANS accuracy difference (accuracy on congruent trials minus accuracy on incongruent trials) when measured with intermixed displays, but not with separate displays. The findings indicate that methodological variation affects ANS acuity outcomes, as well as the apparent relationship between the ANS and mathematical achievement. Moreover, the current study highlights the problem of low reliabilities of ANS measures. Further research is required to construct ANS measures with improved reliability, and to understand which processes may be responsible for the increased likelihood of finding a correlation between the ANS and mathematical achievement when using intermixed displays.

Aging and the number sense: preserved basic non-symbolic numerical processing and enhanced basic symbolic processing.

Aging often leads to general cognitive decline in domains such as memory and attention. The effect of aging on numerical cognition, particularly on foundational numerical skills known as the number sense, is not well-known. Early research focused on the effect of aging on arithmetic. Recent studies have begun to investigate the impact of healthy aging on basic numerical skills, but focused on non-symbolic quantity discrimination alone. Moreover, contradictory findings have emerged. The current study aimed to further investigate the impact of aging on basic non-symbolic and symbolic numerical skills. A group of 25 younger (18-25) and 25 older adults (60-77) participated in non-symbolic and symbolic numerical comparison tasks. Mathematical and spelling abilities were also measured. Results showed that aging had no effect on foundational non-symbolic numerical skills, as both groups performed similarly [RTs, accuracy and Weber fractions (w)]. All participants showed decreased non-symbolic acuity (accuracy and w) in trials requiring inhibition. However, aging appears to be associated with a greater decline in discrimination speed in such trials. Furthermore, aging seems to have a positive impact on mathematical ability and basic symbolic numerical processing, as older participants attained significantly higher mathematical achievement scores, and performed significantly better on the symbolic comparison task than younger participants. The findings suggest that aging and its lifetime exposure to numbers may lead to better mathematical achievement and stronger basic symbolic numerical skills. Our results further support the observation that basic non-symbolic numerical skills are resilient to aging, but that aging may exacerbate poorer performance on trials requiring inhibitory processes. These findings lend further support to the notion that preserved basic numerical skills in aging may reflect the preservation of an innate, primitive, and embedded number sense.

Superior numerical abilities following early visual deprivation.

In numerical cognition vision has been assumed to play a predominant role in the elaboration of the numerical representations and skills. However, this view has been recently challenged by the discovery that people with early visual deprivation not only have a semantic numerical representation that shares the same spatial properties with that in sighted people, but also have better numerical estimation skills. Here, we show that blind people's superior numerical abilities can be found in different numerical contexts, whether they are familiar or more general. In particular, we found that blind participants demonstrated better numerical estimation abilities than sighted participants in both an ecologic footstep and an unfamiliar oral verbal production task. Blind participants also tend to show greater working memory skills compared to sighted participants. These findings support the notion that vision is not necessary in the development of numerical cognition and indicate that early visual deprivation may even lead to a general enhancement in numerical estimation abilities. Moreover, they further suggest that blind people's greater numerical skills might be accounted by enhanced high-level cognitive processes, such as working memory.

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.

Bilateral field advantage in visual enumeration.

A number of recent studies have demonstrated superior visual processing when the information is distributed across the left and right visual fields than if the information is presented in a single hemifield (the bilateral field advantage). This effect is thought to reflect independent attentional resources in the two hemifields and the capacity of the neural responses to the left and right hemifields to process visual information in parallel. Here, we examined whether a bilateral field advantage can also be observed in a high-level visual task that requires the information from both hemifields to be combined. To this end, we used a visual enumeration task--a task that requires the assimilation of separate visual items into a single quantity--where the to-be-enumerated items were either presented in one hemifield or distributed between the two visual fields. We found that enumerating large number (>4 items), but not small number (<4 items), exhibited the bilateral field advantage: enumeration was more accurate when the visual items were split between the left and right hemifields than when they were all presented within the same hemifield. Control experiments further showed that this effect could not be attributed to a horizontal alignment advantage of the items in the visual field, or to a retinal stimulation difference between the unilateral and bilateral displays. These results suggest that a bilateral field advantage can arise when the visual task involves inter-hemispheric integration. This is in line with previous research and theory indicating that, when the visual task is attentionally demanding, parallel processing by the neural responses to the left and right hemifields can expand the capacity of visual information processing.

An electrophysiological measure of visual short-term memory capacity within and across hemifields.

Recent electrophysiological research has identified a specific contralateral correlate of the contents of visual short-term memory (VSTM). This posterior contralateral delay activity (CDA) persists during the retention period, and its amplitude is modulated by the number of items held at any one time. Here we show that, despite the contralateral nature of this activity, its amplitude is modulated by the number of objects from both hemifields. When objects from one side of the visual field are held in memory, CDA activity increased for arrays of one, two, and three objects, but stopped getting larger for arrays of four objects. However, when objects from both sides are memorized at the same time, CDA activity reached its asymptotic limit for arrays of two objects per side. These results suggest that, in spite of being contralaterally organized, VSTM is limited by the number of objects from both hemifields.

Under- and over-estimation: a bi-directional mapping process between symbolic and non-symbolic representations of number?

Over the last 30 years, numerical estimation has been largely studied. Recently, Castronovo and Seron (2007) proposed the bi-directional mapping hypothesis in order to account for the finding that dependent on the type of estimation task (perception vs. production of numerosities), reverse patterns of performance are found (i.e., under- and over-estimation, respectively). Here, we further investigated this hypothesis by submitting adult participants to three types of numerical estimation task: (1) a perception task, in which participants had to estimate the numerosity of a non-symbolic collection; (2) a production task, in which participants had to approximately produce the numerosity of a symbolic numerical input; and (3) a reproduction task, in which participants had to reproduce the numerosity of a non-symbolic numerical input. Our results gave further support to the finding that different patterns of performance are found according to the type of estimation task: (1) under-estimation in the perception task; (2) over-estimation in the production task; and (3) accurate estimation in the reproduction task. Moreover, correlation analyses revealed that the more a participant under-estimated in the perception task, the more he/she over-estimated in the production task. We discussed these empirical data by showing how they can be accounted by the bi-directional mapping hypothesis (Castronovo & Seron, 2007).

Subitizing in congenitally blind adults.

We investigated the role of vision in tactile enumeration within and outside the subitizing range. Congenitally blind and sighted (blindfolded) participants were asked to enumerate quickly and accurately the number of fingers stimulated. Both groups of participants enumerated one to three fingers quickly and accurately but were much slower and less accurate with four to nine fingers. Within the subitizing range, blind participants performed no differently from both sighted (blindfolded) and sighted-seeing participants. Outside of the subitizing range, blind and sighted-seeing participants showed better performance than did sighted-blindfolded participants, suggesting that lack of access to the predominant sensory modality does affect performance. Together, these findings further support the claim that subitizing is a general perceptual mechanism and demonstrate that vision is not necessary for the development of the subitizing mechanism.

Numerical estimation in blind subjects: evidence of the impact of blindness and its following experience.

Vision was for a long time considered to be essential in the elaboration of the semantic numerical representation. However, early visual deprivation does not seem to preclude the development of a spatial continuum oriented from left to right to represent numbers (J. Castronovo & X. Seron, 2007; D. Szücs & V. Csépe, 2005). The authors investigated the impact of blindness and its following experience on a 3rd property of the mental number line: its obedience to Weber's law. A group of blind subjects and a group of sighted subjects were submitted to 2 numerical estimation tasks: (a) a keypress estimation task and (b) an auditory events estimation task. Blind and sighted subjects' performance obeyed Weber's law. However, blind subjects demonstrated better numerical estimation abilities than did sighted subjects, especially in contexts involving proprioception, indicating the existence of better mapping abilities between the symbolic representations of numbers and their corresponding magnitude representations, obeying Weber's law (e.g., J. S. Lipton & E. Spelke, 2005). These findings suggest that blindness and its following experience with numbers might result in better accuracy in numerical processing.

Semantic numerical representation in blind subjects: the role of vision in the spatial format of the mental number line.

Does vision play a role in the elaboration of the semantic representation of small and large numerosities, notably in its spatial format? To investigate this issue, we decided to compare in the auditory modality the performance of congenitally and early blind people with that of a sighted control group, in two number comparison tasks (to 5 and to 55) and in one parity judgement task. Blind and sighted participants presented exactly the same distance and SNARC (Spatial Numerical Association of Response Codes) effects, indicating that they share the same semantic numerical representation. In consequence, our results suggest that the spatial dimension of the numerical representation is not necessarily attributable to the visual modality and that the absence of vision does not preclude the elaboration of this representation for 1-digit (Experiment 1) and 2-digit numerosities (Experiment 2). Moreover, as classical semantic numerical effects were observed in the auditory modality, the postulate of the amodal nature of the mental number line for both small and large magnitudes was reinforced.

Evaluation of cognitive functioning in 101 patients before opiate detoxification: implications in setting up therapeutic strategies.

Many studies have brought to light the facts that repeated use of drugs significantly influences one's cognitive functions, and that cognitive problems could interfere directly with one's capacity to participate in a rehabilitation program. In this research, we used the Global Deterioration Scale (GDS) to assess the cognitive status of 101 hospitalized patients in an opiate detoxification program. The results reveal that a majority of the tested patients present cognitive abnormalities to varying degrees of severity. Furthermore, these cognitive deficits are correlated with four Addiction Severity Index (ASI) scales (medical, alcohol use, drug use, and psychiatry, respectively). Considering the results, because cognition is a major issue in detoxification and rehabilitation programs, simple cognitive screening (as with the GDS) coupled with a particular interest in some aspects of a patient's anamnesis could lead to better management of opiate-dependent patients.