Mojtaba Soltanlou

Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: a longitudinal investigation.

Number facts are commonly assumed to be verbally stored in an associative multiplication fact retrieval network. Prominent evidence for this assumption comes from so-called operand-related errors (e.g., 4 × 6 = 28). However, little is known about the development of this network in children and its relation to verbal and non-verbal memories. In a longitudinal design, we explored elementary school children from grades 3 and 4 in a multiplication verification task with the operand-related and -unrelated distractors. We examined the contribution of multiplicative fact retrieval by verbal and visuo-spatial short-term and working memory (WM). Children in grade 4 showed smaller reaction times in all conditions. However, there was no significant difference in errors between grades. Contribution of verbal and visuo-spatial WM also changed with grade. Multiplication correlated with verbal WM and performance in grade 3 but with visuo-spatial WM and performance in grade 4. We suggest that the relation to verbal WM in grade 3 indicates primary linguistic learning of and access to multiplication in grade 3 which is probably based on verbal repetition of the multiplication table heavily practiced in grades 2 and 3. However, the relation to visuo-spatial semantic WM in grade 4 suggests that there is a shift from verbal to visual and semantic learning in grade 4. This shifting may be induced because later in elementary school, multiplication problems are rather carried out via more written, i.e., visual tasks, which also involve executive functions. More generally, the current data indicates that mathematical development is not generally characterized by a steady progress in performance; rather verbal and non-verbal memory contributions of performance shift over time, probably due to different learning contents.

Increased arithmetic complexity is associated with domain-general but not domain-specific magnitude processing in children: A simultaneous fNIRS-EEG study

The investigation of the neural underpinnings of increased arithmetic complexity in children is essential for developing educational and therapeutic approaches and might provide novel measures to assess the effects of interventions. Although a few studies in adults and children have revealed the activation of bilateral brain regions during more complex calculations, little is known about children. We investigated 24 children undergoing one-digit and two-digit multiplication tasks while simultaneously recording functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG) data. FNIRS data indicated that one-digit multiplication was associated with brain activity in the left superior parietal lobule (SPL) and intraparietal sulcus (IPS) extending to the left motor area, and two-digit multiplication was associated with activity in bilateral SPL, IPS, middle frontal gyrus (MFG), left inferior parietal lobule (IPL), and motor areas. Oscillatory EEG data indicated theta increase and alpha decrease in parieto-occipital sites for both one-digit and two-digit multiplication. The contrast of two-digit versus one-digit multiplication yielded greater activity in right MFG and greater theta increase in frontocentral sites. Activation in frontal areas and theta band data jointly indicate additional domain-general cognitive control and working memory demands for heightened arithmetic complexity in children. The similarity in parietal activation between conditions suggests that children rely on domain-specific magnitude processing not only for two-digit but—in contrast to adults—also for one-digit multiplication problem solving. We conclude that in children, increased arithmetic complexity tested in an ecologically valid setting is associated with domain-general processes but not with alteration of domain-specific magnitude processing.

Planning and Self-Control, but not Working Memory, Directly Predict Multiplication Performance in Adults

Empirical evidence suggests that working memory (WM) is closely related to arithmetic performance. WM, which is the ability to monitor and update recent information, underlies various cognitive processes and behaviors including planning, self-regulation, and self-control. However, only a few studies have examined whether WM uniquely explains variance in arithmetic performance when other WM-related domain-general factors are taken into account. In this study, we examined whether WM explains unique variance in arithmetic performance when planning, self-regulation, and self-control are considered as well. We used the Tower of London task as a measure of planning, self-rated reports as a measure of self-regulation and self-control, and WM measures, to test which of these domain-general functions predicts complex multiplication performance. Results showed that planning predicted multiplication accuracy and self-control predicted response time, while WM and self-regulation did not predict complex multiplication performance. Although WM was not a direct predictor of multiplication performance, it possibly exerted its influence as part of planning ability. We suggest that complex multiplication is not predicted by WM per se, but rather by WM-related general cognitive and behavioral factors, namely self-control and the planning component of executive functions.

Applications of Functional Near-Infrared Spectroscopy (fNIRS) in Studying Cognitive Development: The Case of Mathematics and Language

In this review, we aim to highlight the application of functional near-infrared spectroscopy (fNIRS) as a useful neuroimaging technique for the investigation of cognitive development. We focus on brain activation changes during the development of mathematics and language skills in schoolchildren. We discuss how technical limitations of common neuroimaging techniques such as functional magnetic resonance imaging (fMRI) have resulted in our limited understanding of neural changes during development, while fNIRS would be a suitable and child-friendly method to examine cognitive development. Moreover, this technique enables us to go to schools to collect large samples of data from children in ecologically valid settings. Furthermore, we report findings of fNIRS studies in the fields of mathematics and language, followed by a discussion of the outlook of fNIRS in these fields. We suggest fNIRS as an additional technique to track brain activation changes in the field of educational neuroscience.

Individual differences influence two-digit number processing, but not their analog magnitude processing : a large-scale online study

Symbolic magnitude comparison is one of the most well-studied cognitive processes in research on numerical cognition. However, while the cognitive mechanisms of symbolic magnitude processing have been intensively studied, previous studies have paid less attention to individual differences influencing symbolic magnitude comparison. Employing a two-digit number comparison task in an online setting, we replicated previous effects, including the distance effect, the unit-decade compatibility effect, and the effect of cognitive control on the adaptation to filler items, in a large-scale study in 452 adults. Additionally, we observed that the most influential individual differences were participants’ first language, time spent playing computer games and gender, followed by reported alcohol consumption, age and mathematical ability. Participants who used a first language with a left-to-right reading/writing direction were faster than those who read and wrote in the right-to-left direction. Reported playing time for computer games was correlated with faster reaction times. Female participants showed slower reaction times and a larger unit-decade compatibility effect than male participants. Participants who reported never consuming alcohol showed overall slower response times than others. Older participants were slower, but more accurate. Finally, higher grades in mathematics were associated with faster reaction times. We conclude that typical experiments on numerical cognition that employ a keyboard as an input device can also be run in an online setting. Moreover, while individual differences have no influence on domain-specific magnitude processing—apart from age, which increases the decade distance effect—they generally influence performance on a two-digit number comparison task.

Behavioral and Neurocognitive Evaluation of a Web-Platform for Game-Based Learning of Orthography and Numeracy

Recent years have seen a considerable increase in informal educational environments complementing formal educational settings such as schools. In this chapter, we will report results on the efficacy of a web-platform for game-based learning of orthography and numeracy. Besides the behavioral assessment of the platform, we focused specifically on neurocognitive changes due to training on the platform. These neurocognitive data are particularly informative to understand how game-based learning leads to performance improvements, and also might help us to develop new instructional designs. Our web-based platform hosts several learning games, aiming at fostering orthography and numeracy skills. Learning games enable individual learning independent from formal learning environments—anytime and anywhere. Behavioral results revealed promising learning effects, particularly for orthography. In the next step, neurocognitive changes during arithmetic learning were assessed. Results indicated that arithmetic learning in our informal environment led to strategy changes, previously reported for the development of arithmetic competencies in formal learning settings for both adults and children. Altogether, the findings suggest that improvements in orthography and numeracy can be achieved in joyful and less stressful informational environments such as our web-platform for game-based learning. We suggest that the additional implementation of adaptivity in such learning games to better meet individual needs should further increase obtained training effects in the future. Instructional implications of these findings and the relevance of neurocognitive data for learning are discussed.

The neural circuits of number and letter copying: an fNIRS study

In our daily lives, we are constantly exposed to numbers and letters. However, it is still under debate how letters and numbers are processed in the brain, while information on this topic would allow for a more comprehensive understanding of, for example, known influences of language on numerical cognition or neural circuits shared by numerical cognition and language processing. Some findings provide evidence for a double dissociation between numbers and letters, with numbers being represented in the right and letters in the left hemisphere, while the opposing view suggests a shared neural network. Since processing may depend on the task, we address the reported inconsistencies in a very basic symbol copying task using functional near-infrared spectroscopy (fNIRS). fNIRS data revealed that both number and letter copying rely on the bilateral middle and left inferior frontal gyri. Only numbers elicited additional activation in the bilateral parietal cortex and in the left superior temporal gyrus. However, no cortical activation difference was observed between copying numbers and letters, and there was Bayesian evidence for common activation in the middle frontal gyri and superior parietal lobules. Therefore, we conclude that basic number and letter processing are based on a largely shared cortical network, at least in a simple task such as copying symbols. This suggests that copying can be used as a control condition for more complex tasks in neuroimaging studies without subtracting stimuli-specific activation.

Time for action versus action in time: time estimation differs between motor preparation and execution

ABSTRACT Theories relating to time perception and motor performance predict very different temporal distortions depending on the synchronisation or succession of temporal processing and motor behaviour. However, our knowledge about the temporal difference between motor preparation and execution is still scarce. In order to expand on prior studies, two different time reproduction tasks were utilised to measure motor preparation and motor execution. We found that motor preparation of a planned action allows participants to complete the time reproduction task more accurately and, in short duration trials, less variably than for motor execution. Furthermore, under-reproduction was found in motor preparation compared to motor execution, which may be caused by increased temporal information processing. According to the attentional gate theory, more attention allocated to time processing and reduced motor distraction leads to less temporal distortion in the motor preparation. The findings are also important for designing to study consciousness, temporal and visual processing.

A Mental Odd-Even Continuum Account: Some Numbers May Be “More Odd” Than Others and Some Numbers May Be “More Even” Than Others

Numerical categories such as parity, i.e., being odd or even, have frequently been shown to influence how particular numbers are processed. Mathematically, number parity is defined categorically. So far, cognitive, and psychological accounts have followed the mathematical definition and defined parity as a categorical psychological representation as well. In this manuscript, we wish to test the alternative account that cognitively, parity is represented in a more gradual manner such that some numbers are represented as “more odd” or “more even” than other odd or even numbers, respectively. Specifically, parity processing might be influenced by more specific properties such as whether a number is a prime, a square number, a power of 2, part of a multiplication table, divisible by 4 or by 5, and many others. We suggest that these properties can influence the psychologically represented parity of a number, making it more or less prototypical for odd- or evenness. In the present study, we tested the influence of these numerical properties in a bimanual parity judgment task with auditorily presented two-digit numbers. Additionally, we further investigated the interaction of these numerical properties with linguistic factors in three language groups (English, German, and Polish). Results show significant effects on reaction times of the congruity of parity status between decade and unit digits, even if numerical magnitude and word frequency are controlled. We also observed other effects of the above specific numerical properties, such as multiplication attributes, which facilitated or interfered with the speed of parity judgment. Based on these effects of specific numerical properties we proposed and elaborated a parity continuum account. However, our cross-lingual study also suggests that parity representation and/or access seem to depend on the linguistic properties of the respective language or education and culture. Overall, the results suggest that the “perceived” parity is not the same as objective parity, and some numbers are more prototypical exemplars of their categories.