Dynamic mental number line in simple arithmetic

Spatial attention in mental arithmetic: A literature review and meta-analysis

We review the evidence for the conceptual association between arithmetic and space and quantify the effect size in meta-analyses. We focus on three effects: (a) the operational momentum effect (OME), which has been defined as participants' tendency to overestimate results of addition problems and underestimate results of subtraction problems; (b) the arithmetic cueing effect, in which arithmetic problems serve as spatial cues in target detection or temporal order judgment tasks; and (c) the associations between arithmetic and space observed with eye- and hand-tracking studies. The OME was consistently found in paradigms that provided the participants with numerical response alternatives. The OME shows a large effect size, driven by an underestimation during subtraction while addition was unbiased. In contrast, paradigms in which participants indicated their estimate by transcoding their final estimate to a spatial reference frame revealed no consistent OME. Arithmetic cueing studies show a reliable small to medium effect size, driven by a rightward bias for addition. Finally, eye- and hand-tracking studies point to replicable associations between arithmetic and eye or hand movements. To account for the complexity of the observed pattern, we introduce the Adaptive Pathways in Mental Arithmetic (APiMA) framework. The model accommodates central notions of numerical and arithmetic processing and helps identifying which pathway a given paradigm operates on. It proposes that the divergence between OME and arithmetic cueing studies comes from the predominant use of non-symbolic versus symbolic stimuli, respectively. Overall, our review and findings clearly support an association between arithmetic and spatial processing.

The association between non-symbolic number comparison and mathematical abilities depends on fluency

Numerous studies have explored the correlation between non-symbolic number comparison and mathematical abilities in children, but the results have been inconsistent. The underlying mental processing featuring fluency may affect the correlation. The current study tested the fluency hypothesis that non-symbolic number comparison is associated with mathematical fluency in the development of mathematical ability. Non-symbolic number comparison, arithmetic computation, mathematical reasoning, non-symbolic number estimation, symbolic number comparison, and a series of basic cognitive processing tasks, including mental rotation, non-verbal matrix reasoning, and choice reaction time, were administered to 1072 first- to fourth-grade children. The results show that non-symbolic number comparison (measured via numerosity comparison) was the only independent predictor of arithmetic computation in higher grades, even after controlled for age, gender, basic cognitive processing, non-symbolic number estimation (measured via numerosity estimation), and symbolic number comparison (measured via digit comparison). However, it did not correlate with mathematical reasoning in any grade. These findings support the fluency hypothesis for developmental correlation between non-symbolic number comparison and mathematical abilities. That is, non-symbolic number comparison correlates with mathematical ability featuring fluency.

The perception of subset quantity and items in an environment with distractors in a population with mathematical learning difficulties

OBJECTIVE

People often perceive a quantity of specific objects that appear as part of an overall group of items (a subset). This study investigates this type of perception among a population with mathematical leaning difficulties (MLD).

METHOD

Sixty-two participants (mean age: 26.82) reported the general and subset quantity of items using a subset quantity detection task or a conjunction visual search task.

RESULTS

MLD had difficulties perceiving both the general quantity presented and the subset quantity of items. They also had difficulties preforming a conjunction visual search task, even when the task did not involve numerical processing.

CONCLUSIONS

MLD has spatial difficulties in the form of visual search and subset quantity detection. The current study suggests that MLD might experience greater difficulties in daily tasks, which might be related to those tasks (e.g., detecting the amount of forks among other items of silverware on the table).

Reassessing lateralization in calculation

The role of the left hemisphere in calculation has been unequivocally demonstrated in numerous studies in the last decades. The right hemisphere, on the other hand, had been traditionally considered subsidiary to the left hemisphere functions, although its role was less clearly defined. Recent clinical studies as well as investigations conducted with other methodologies (e.g. neuroimaging, transcranial magnetic stimulation and direct cortical electro-stimulation) leave several unanswered questions about the contribution of the right hemisphere in calculation. In particular, novel clinical studies show that right hemisphere acalculia encompasses a wide variety of symptoms, affecting even simple calculation, which cannot be easily attributed to spatial disorders or to a generic difficulty effect as previously believed. The studies reported here also show how the right hemisphere has its own specific role and that only a bilateral orchestration between the respective functions of each hemisphere guarantees, in fact, precise calculation. Vis-à-vis these data, the traditional wisdom that attributes to the right hemisphere a role mostly confined to spatial aspects of calculation needs to be significantly reshaped. The question for the future is whether it is possible to precisely define the specific contribution of the right hemisphere in several aspects of calculation while highlighting the nature of the cross-talk between the two hemispheres.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

The Time Course of Spatial Attention Shifts in Elementary Arithmetic

It has been proposed that elementary arithmetic induces spatial shifts of attention. However, the timing of this arithmetic-space association remains unknown. Here we investigate this issue with a target detection paradigm. Detecting targets in the right visual field was faster than in the left visual field when preceded by an addition operation, while detecting targets in the left visual field was faster than in the right visual field when preceded by a subtraction operation. The arithmetic-space association was found both at the end of the arithmetic operation and during calculation. In contrast, the processing of operators themselves did not induce spatial biases. Our results suggest that the arithmetic-space association resides in the mental arithmetic operation rather than in the individual numbers or the operators. Moreover, the temporal course of this effect was different in addition and subtraction.

Operational momentum and size ordering in preverbal infants

Recent evidence has shown that, like adults and children, 9-month-old infants manifest an operational momentum (OM) effect during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Here we provide the first evidence that OM occurs for transformations of non-numerical magnitudes (i.e., spatial extent) during ordering operations. Twelve-month-old infants were tested in an ordinal task in which they detected and represented ascension or descension in physical size, and then responded to ordinal sequences that exhibited greater or lesser sizes. Infants displayed longer looking time to the size change whose direction violated the operational momentum experienced during habituation (i.e., the smaller sequence in the ascension condition and the larger sequence in the descension condition). The presence of momentum for ordering size during infancy suggests that continuous quantities are represented spatially during the first year of life.

Ocular drift along the mental number line

We examined the spontaneous association between numbers and space by documenting attention deployment and the time course of associated spatial-numerical mapping with and without overt oculomotor responses. In Experiment 1, participants maintained central fixation while listening to number names. In Experiment 2, they made horizontal target-direct saccades following auditory number presentation. In both experiments, we continuously measured spontaneous ocular drift in horizontal space during and after number presentation. Experiment 2 also measured visual-probe-directed saccades following number presentation. Reliable ocular drift congruent with a horizontal mental number line emerged during and after number presentation in both experiments. Our results provide new evidence for the implicit and automatic nature of the oculomotor resonance effect associated with the horizontal spatial-numerical mapping mechanism.