Sensori-motor spatial training of number magnitude representation

Prevalence, comorbidities, and profiles of neurodevelopmental disorders according to the DSM-5-TR in children aged 6 years old in a European region

Background

There are no studies that measure the prevalence and real comorbidities of neurodevelopmental disorders (NDDs) according to the DSM-5-TR in 6-year-old children in population and clinical samples or studies that measure them as a whole. The data on the prevalence of these disorders are usually disparate because of the estimation methods (direct/indirect), the type of sample (population/clinical/school), and the ages studied.

Methods

The initial sample (289 subjects) was representative of 6-year-old children in the entire population of Menorca, obtained from pediatric primary care services (100% of the sample). The patients were divided into two groups based on the criterion of verification of clinical warning signs. One of the groups represented the clinical or experimental sample (EG) (81 subjects) at risk of NDDs; the other group was considered the control sample (CG) (210 subjects), and they were subjects without risk of suffering NDDs. A direct clinical assessment of the clinical sample was carried out, and they were administered the Wechsler Intelligence Scale for Children (WISC-V), the Clinical Evaluation of Language Fundamentals (CELF-5), the Battery for the evaluation of the processes of revised reading (Batería para la evaluación de los procesos de lectura revisada - PROLEC-R), the Test for the Diagnosis of Basic Mathematical Competences, (TEDI-MATH), and the Developmental Coordination Disorder Questionnaire (DCDQ).

Results

A total of 21.5% of the initial sample suffered from an NDD. A total of 2.4% presented autism spectrum disorder (ASD); 14% presented attention-deficit hyperactivity disorder (ADHD); 0.34% presented mild intellectual disability; 9.54% presented communication disorder (CD) (5.8% language disorder, 3.4% phonological disorder, and 0.34% stuttering); 10% presented learning disorder with reading difficulties; 5.8% presented learning disorder with difficulties in writing; 3.11% presented learning disorder with difficulties in mathematics; 1% presented transitory tic disorder; 0.34% presented chronic tic disorder; 1% presented Tourette syndrome; 2% presented motor coordination disorder (MCD); and 0.34% presented stereotypic movement disorders. Male children were more affected than female children in general, with male/female ORs of 0.14/0.92 for the presence of comorbidities, 0.11/0.88 for combined ADHD, 0.06/0.87 for language disorder, 1.02/1.27 for MCD, and 1.39/1.02 for inattentive ADHD.

Conclusion

In disadvantaged contexts, there was a higher prevalence of NDDs and comorbidities, unless the disorder was extreme, in which case only the NDD manifestations were presented. A significant proportion of the sample had not been previously diagnosed (88.6%); therefore, early detection programs are recommended to identify warning signs and develop policies that help and support the most disadvantaged sectors of the population.

Investigating the influence of body movements on children's mental arithmetic performance

Several lines of research have demonstrated spatial-numerical associations in both adults and children, which are thought to be based on a spatial representation of numerical information in the form of a mental number line. The acquisition of increasingly precise mental number line representations is assumed to support arithmetic learning in children. It is further suggested that sensorimotor experiences shape the development of number concepts and arithmetic learning, and that mental arithmetic can be characterized as "motion along a path" and might constitute shifts in attention along the mental number line. The present study investigated whether movements in physical space influence mental arithmetic in primary school children, and whether the expected effect depends on concurrency of body movements and mental arithmetic. After turning their body towards the left or right, 48 children aged 8 to 10 years solved simple subtraction and addition problems. Meanwhile, they either walked or stood still and looked towards the respective direction. We report a congruency effect between body orientation and operation type, i.e., higher performance for the combinations leftward orientation and subtraction and rightward orientation and addition. We found no significant difference between walking and looking conditions. The present results suggest that mental arithmetic in children is influenced by preceding sensorimotor cues and not necessarily by concurrent body movements.

A sensorimotor perspective on numerical cognition

Numbers are present in every part of modern society and the human capacity to use numbers is unparalleled in other species. Understanding the mental and neural representations supporting this capacity is of central interest to cognitive psychology, neuroscience, and education. Embodied numerical cognition theory suggests that beyond the seemingly abstract symbols used to refer to numbers, their underlying meaning is deeply grounded in sensorimotor experiences, and that our specific understanding of numerical information is shaped by actions related to our fingers, egocentric space, and experiences with magnitudes in everyday life. We propose a sensorimotor perspective on numerical cognition in which number comprehension and numerical proficiency emerge from grounding three distinct numerical core concepts: magnitude, ordinality, and cardinality.

Math computerized games in the classroom: A number line training in primary school children

Several studies have shown that the number line can be a useful tool to support early numeracy development. Here, we conducted a school-based training study to evaluate the effectiveness of the software "The Number Line" ("La Linea Dei Numeri"; Tressoldi and Peroni, 2013) in improving children's mathematical skills. We randomly allocated 10 classes of first, second and third graders (N=183) to one of three experimental groups: one group played with The Number Line; the second group played with Labyrinth, a computerized game designed to train attention skills; the third group had no intervention (business-as-usual). At the end of the first training phase, children in The Number Line group completed another training phase playing with Labyrinth, whereas the other two groups played with The Number Line. After playing with The Number Line, all groups displayed more accuracy when placing numbers in the number line task. However, we observed no evident improvement in other mathematical skills. These results suggest that specific training effects emerge even in the school context, although transfer to other numerical skills may be harder to achieve.

Fine motor skills and finger gnosia contribute to preschool children's numerical competencies

Facets of fine motor skills (FMS) and finger gnosia have been reported to predict young children's numerical competencies, possibly by affecting early finger counting experiences. Furthermore, neuronal connections between areas involved in finger motor movement, finger gnosia, and numerical processing have been posited. In this study, FMS and finger gnosia were investigated as predictors for preschool children's performance in numerical tasks. Preschool children (N = 153) completed FMS tasks measuring finger agility and finger dexterity as well as a non-motor finger gnosia task. Furthermore, children completed numerical tasks that involved finger use (i.e., finger counting and finger montring), and tasks that did not (i.e., picture-aided calculation and number line estimation). To control for possible confounding influences of domain general skills, we included measures of reasoning and spatial working memory. We found associations between FMS and both finger counting and calculation, but not finger montring. In contrast, finger gnosia was only associated with finger montring, but not finger counting and calculation. Surprisingly, there were no associations between FMS or finger gnosia with number line estimation. Findings highlight that the relationship between finger gnosia, FMS, and numerical skills is specific to task requirements. Possible implications are discussed.

Combining Numerical Relational and Fundamental Motor Skills to Improve Preschoolers' Early Numeracy: A Pilot Intervention Study

The aim of this pilot study was to examine the immediate and long-term effects of an intervention program that aims to improve preschoolers' (N = 36, M = 4.49 years, SD = 0.35) early numeracy skills by combining the learning of numerical relational skills via story reading with fundamental motor skill practice. The intervention program was piloted with two study designs: a within-subject repeated-measures design with 18 children (study I), and a quasi-experimental study design with 18 children (study II). Children's early numeracy, symbolic magnitude processing, and fundamental motor skills were measured. Results demonstrated that children's early numeracy and especially numerical relational skills improved during the intervention, and the intervention had larger effects on children's early numeracy and numerical relational skills compared to the control period (study I) and control group (study II). Furthermore, the results from the delayed post-test demonstrated that the effects were maintained for 4.5-8 weeks after the intervention. These findings provide preliminary evidence that it is possible to support children's early numeracy skills with combined learning of numerical relational skills via story reading and fundamental motor skills despite the socioeconomic or language background, and narrow the gap between low- and average-performing children.

The effects of motor skill and physical activity interventions on preschoolers' cognitive and academic skills: A systematic review

The present systematic review aimed to investigate the methodological quality and the effects of fundamental motor skills and physical activity interventions on cognitive and academic skills in typically developing 3 to 7-year-old children. The review was conducted and reported in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. A literature search was carried out in April 2020 using seven electronic databases. The methodological quality of the studies was assessed with the Effective Public Health Practice Project (EPHPP) Quality Assessment Tool. Cohen's d effect size calculations and post hoc power analyses were conducted for the included studies. A total of 35 studies, representing 2472 children met the inclusion criteria. Two of the studies demonstrated a strong methodological quality, while 24 were considered as methodologically weak. The majority (71%) of the included studies demonstrated the beneficial effects of the intervention on cognitive and academic skills. The most evidence was found for executive functions, language, and numeracy, and the effects were largest in enhancing memory. The effects were larger on cognitive and academic skills in the combined interventions compared to only fundamental motor skill and physical activity interventions, while fundamental motor skill interventions had larger effects than physical activity interventions. These findings indicate that it may be possible to support typically developing preschoolers' cognitive and academic learning with fundamental motor skill and physical activity interventions. However, most of the studies in this field have a weak methodological quality and thus, the presented evidence was considered weak in nature.

Towards Figurative Expression Enhancement: Effects of the SVVR-Supported Worked Example Approach on the Descriptive Writing of Highly Engaged Students

During the past decades, many researchers have attempted to explore effective teaching methods for developing students’ descriptive writing performance. In this study, the worked example was implemented as an effective way of guiding students to provide step-by-step solutions to learning tasks. Moreover, a spherical video-based virtual reality (SVVR) environment was provided to place students in real-world situations which enabled them to experience the learning contexts in depth. A pretest-posttest quasi experimental study was conducted to explore the influence of the SVVR-supported worked example approach and engagement level on students’ Chinese descriptive writing performance. A total of 79 fourth-grade elementary school students participated in this study. The experimental group used SVVR with worked examples to complete Chinese writing assignments, whereas the control group used videos and worked examples. The results showed no significant effects of the SVVR-supported worked example approach compared with the conventional worked example approach regarding organization, sensory details, or creativity dimensions. As for the figurative expression dimension, students in the SVVR-supported worked example approach condition scored significantly higher. Moreover, high engagement students significantly outperformed low engagement students in all four writing performance dimensions. Additionally, a significant interaction effect between learning approach and engagement level on figurative expression was found.

Training spatial cognition enhances mathematical learning in a randomized study of 17,000 children

Spatial and mathematical abilities are strongly associated. Here, we analysed data from 17,648 children, aged 6-8 years, who performed 7 weeks of mathematical training together with randomly assigned spatial cognitive training with tasks demanding more spatial manipulation (mental rotation or tangram), maintenance of spatial information (a visuospatial working memory task) or spatial, non-verbal reasoning. We found that the type of cognitive training children performed had a significant impact on mathematical learning, with training of visuospatial working memory and reasoning being the most effective. This large, community-based study shows that spatial cognitive training can result in transfer to academic abilities, and that reasoning ability and maintenance of spatial information is relevant for mathematics learning in young children.

Negative Effects of Embodiment in a Visuo-Spatial Working Memory Task in Children, Young Adults, and Older Adults

Studies examining the effect of embodied cognition have shown that linking one's body movements to a cognitive task can enhance performance. The current study investigated whether concurrent walking while encoding or recalling spatial information improves working memory performance, and whether 10-year-old children, young adults, or older adults (M age = 72 years) are affected differently by embodiment. The goal of the Spatial Memory Task was to encode and recall sequences of increasing length by reproducing positions of target fields in the correct order. The nine targets were positioned in a random configuration on a large square carpet (2.5 m × 2.5 m). During encoding and recall, participants either did not move, or they walked into the target fields. In a within-subjects design, all possible combinations of encoding and recall conditions were tested in counterbalanced order. Contrary to our predictions, moving particularly impaired encoding, but also recall. These negative effects were present in all age groups, but older adults' memory was hampered even more strongly by walking during encoding and recall. Our results indicate that embodiment may not help people to memorize spatial information, but can create a dual-task situation instead.

Grouping strategies in numerosity perception between intrinsic and extrinsic grouping cues

The number of items in an array can be quickly and accurately estimated by dividing the array into subgroups, in a strategy termed "groupitizing." For example, when memorizing a telephone number, it is better to do so by divide the number into several segments. Different forms of visual grouping can affect the precision of the enumeration of a large set of items. Previous studies have found that when groupitizing, enumeration precision is improved by grouping arrays using visual proximity and color similarity. Based on Gestalt theory, Palmer (Cognit Psychol 24:436, 1992) divided perceptual grouping into intrinsic (e.g., proximity, similarity) and extrinsic (e.g., connectedness, common region) principles. Studies have investigated groupitizing effects on intrinsic grouping. However, to the best of our knowledge, no study has explored groupitizing effects for extrinsic grouping cues. Therefore, this study explored whether extrinsic grouping cues differed from intrinsic grouping cues for groupitizing effects in numerosity perception. The results showed that both extrinsic and intrinsic grouping cues improved enumeration precision. However, extrinsic grouping was more accurate in terms of the sensory precision of the numerosity perception.

Resting State EEG Related to Mathematical Improvement After Spatial Training in Children

Spatial cognitive abilities, including mental rotation (MR) and visuo-spatial working memory (vsWM) are correlated with mathematical performance, and several studies have shown that training of these abilities can enhance mathematical performance. Here, we investigated the behavioral and neural correlates of MR and vsWM training combined with number line (NL) training. Fifty-seven children, aged 6–7, performed 25 days of NL training combined with either vsWM or MR and participated in an Electroencephalography (EEG)-session in school to measure resting state activity and steady-state visual evoked potentials during a vsWM task before and after training. Fifty children, aged 6–7, received usual teaching and acted as a control group. Compared to the control group, both training groups improved on a combined measure of mathematics. Cognitive improvement was specific to the training. Significant pre-post changes in resting state-EEG (rs-EEG), common to both training groups, were found for power as well as for coherence, with no significant differences in rs-EEG-changes between the vsWM and MR groups. Two of the common rs-EEG changes were correlated with mathematical improvement: (1) an increase in coherence between the central frontal lobe and the right parietal lobe in frequencies ranging from 16 to 25 Hz, and (2) an increase in coherence between the left frontal lobe and the right parietal lobe ranging from 23 to 25 Hz. These results indicate that changes in fronto-parietal coherence are related to an increase in mathematical performance, which thus might be a useful measure in further investigations of mathematical interventions in children.

Children's spatial-numerical associations on horizontal, vertical, and sagittal axes

There is substantial evidence linking numerical magnitude to the physical properties of space. The most influential support for this connection comes from the SNARC effect (spatial-numerical association of response codes), in which responses to small/large numbers are faster on the left/right side of space, respectively. The SNARC effect has been extensively replicated, and is understood as horizontal mapping of numerical magnitude. However, much less is known about how numbers are represented on the vertical and sagittal axes, and whether spatial-numerical associations on different axes emerge during childhood. To that end, we tested two groups of children, aged 5-7 years and 8 and 9 years, on a single-digit magnitude comparison task with response buttons positioned either upper/lower (vertical), left/right (horizontal) or near/far (sagittal). Our results provide evidence of spatial-numerical mapping on all three axes for both age groups that are similar in strength. This indicates that, even at an early stage of formal education, children can flexibly assign numerical magnitude to any spatial dimension. To examine the contribution of extracorporeal space and spatio-anatomical mapping to the SNARC effect across axes, these sources were pitted against each other by swapping the position of the response hands in Experiment 1b. Switching hand position did not reveal convincing evidence for SNARC effects on any axis. Results are discussed with respect to the utility of three-dimensional mental number lines, and potential avenues for future research are outlined.

What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior

There is an emerging consensus that spatial thinking plays a fundamental role in how people conceive, express, and perform mathematics. However, the underlying nature of this relationship remains elusive. Questions remain as to how, why, and under what conditions spatial skills and mathematics are linked. This review paper addresses this gap. Through a review and synthesis of research in psychology, neuroscience, and education, we examine plausible mechanistic accounts for the oft-reported close, and potentially causal, relations between spatial and mathematical thought. More specifically, this review targets candidate mechanisms that link spatial visualization skills and basic numerical competencies. The four explanatory accounts we describe and critique include the: (1) Spatial representation of numbers account, (2) shared neural processing account, (3) spatial modelling account, and (4) working memory account. We propose that these mechanisms do not operate in isolation from one another, but in concert with one another to give rise to spatial-numerical associations. Moving from the theoretical to the practical, we end our review by considering the extent to which spatial visualization abilities are malleable and transferrable to numerical reasoning. Ultimately, this paper aims to provide a more coherent and mechanistic account of spatial-numerical relations in the hope that this information may (1) afford new insights into the uniquely human ability to learn, perform, and invent abstract mathematics, and (2) on a more practical level, prove useful in the assessment and design of effective mathematics curricula and intervention moving forward.

A Finger-Based Numerical Training Failed to Improve Arithmetic Skills in Kindergarten Children Beyond Effects of an Active Non-numerical Control Training

It is widely accepted that finger and number representations are associated: many correlations (including longitudinal ones) between finger gnosis/counting and numerical/arithmetical abilities have been reported. However, such correlations do not necessarily imply causal influence of early finger-number training; even in longitudinal designs, mediating variables may be underlying such correlations. Therefore, we investigated whether there may be a causal relation by means of an extensive experimental intervention in which the impact of finger-number training on initial arithmetic skills was tested in kindergarteners to see whether they benefit from the intervention even before they start formal schooling. The experimental group received 50 training sessions altogether for 10 weeks on a daily basis. A control group received phonology training of a similar duration and intensity. All children improved in the arithmetic tasks. To our surprise and contrary to most accounts in the literature, the improvement shown by the experimental training group was not superior to that of the active control group. We discuss conceptual and methodological reasons why the finger-number training employed in this study did not increase the initial arithmetic skills beyond the unspecific effects of the control intervention.

Investigating the respective contribution of sensory modalities and spatial disposition in numerical training

Recent studies have suggested that multisensory redundancy may improve cognitive learning. According to this view, information simultaneously available across two or more modalities is highly salient and, therefore, may be learned and remembered better than the same information presented to only one modality. In the current study, we wanted to evaluate whether training arithmetic with a multisensory intervention could induce larger learning improvements than a visual intervention alone. Moreover, because a left-to-right-oriented mental number line was for a long time considered as a core feature of numerical representation, we also wanted to compare left-to-right-organized and randomly organized arithmetic training. Therefore, five training programs were created and called (a) multisensory linear, (b) multisensory random, (c) visual linear, (d) visual random, and (e) control. A total of 85 preschoolers were randomly assigned to one of these five training conditions. Whereas children were trained to solve simple addition and subtraction operations in the first four training conditions, story understanding was the focus of the control training. Several numerical tasks (arithmetic, number-to-position, number comparison, counting, and subitizing) were used as pre- and post-test measures. Although the effect of spatial disposition was not significant, results demonstrated that the multisensory training condition led to a significantly larger performance improvement than the visual training and control conditions. This result was specific to the trained ability (arithmetic) and is discussed in light of the multisensory redundancy hypothesis.

Making Sense of Number Words and Arabic Digits: Does Order Count More?

The ability to choose the larger between two numbers reflects a mature understanding of the magnitude associated with numerical symbols. The present study explores how the knowledge of the number sequence and memory capacity (verbal and visuospatial) relate to number comparison skills while controlling for cardinal knowledge. Preschool children's (N = 140, M_{age-in-months}  = 58.9, range = 41-75) knowledge of the directional property of the counting list as well as the spatial mapping of digits on the visual line were assessed. The ability to order digits on the visual line mediated the relation between memory capacity and number comparison skills while controlling for cardinal knowledge. Beyond cardinality, the knowledge of the (spatial) order of numbers marks the understanding of the magnitude associated with numbers.

Children Learn From Both Embodied and Passive Pretense: A Replication and Extension

Research suggests that children can learn new information via pretense. However, a fundamental problem with existing studies is that children are passive receivers of the pretense rather than active, engaged participants. This preregistered study replicates previous learning from pretense findings (Sutherland & Friedman, 2012, Child Development), in which children are passive observers of pretense, and extends to two additional conditions that require children to partially (with puppets) or fully (with costumes) embody a character. Children (N = 144, 24-79 months) learned equally well, and better than those in the control condition, from all three play scenarios. At a 2-week follow-up, learning was equally retained across embodiment conditions for older, but not younger, preschoolers. Future research should consider embodiment's role for more complex material.

The effects of risk magnitude training on mapping risks on space

Risk perception has recently been shown to reveal a mental spatial representation, with people responding faster to low-risk items on the left side, and high-risk items on the right side. Subjective risk perception has a stronger spatial representation than objective risk perception; however, both reveal small effect sizes. With risk magnitude being a new domain within spatial mapping literature, we sought to explore its nuances. Following discussion surrounding the relationship between spatial mapping and level of expertise, this study investigated the effect of training an objective risk magnitude sequence on mental spatial representations. Participants (n = 34) used their left and right hands to indicate whether eight risk stimuli were lower or higher risk than a referent activity, both before and after training. Training involved repetitively learning the objectively correct order of the same eight risk stimuli for approximately 15 min. Pre-training results demonstrated the expected spatial representations. Contrary to our predictions, the spatial representation did not get stronger post-training, but instead disappeared. Previous research has demonstrated a loss of spatial-numerical mappings with increased task load. An increase in post-training reaction times could reflect an increase in task load due to a lack of adequate knowledge of risk stimulus order; thus revealing no mental spatial representation. However, failure to find training effects highlights the flexibility of weaker spatial representations, and supports research demonstrating spatial representation flexibility.

Spatial Presentations, but Not Response Formats Influence Spatial-Numerical Associations in Adults

According to theories of embodied numerosity, processing of numerical magnitude is anchored in bodily experiences. In particular, spatial representations of number interact with movement in physical space, but it is still unclear whether the extent of the movement is relevant for this interaction. In this study, we compared spatial-numerical associations over response movements of differing spatial expansion. We expected spatial-numerical effects to increase with the extent of physical response movements. In addition, we hypothesized that these effects should be influenced by whether or not a spatial representation of numbers was presented. Adult participants performed two tasks: a magnitude classification (comparing numbers to the fixed standard 5), from which we calculated the Spatial Numerical Association of Response Codes (SNARC) effect; and a magnitude comparison task (comparing two numbers against each other), from which we calculated a relative numerical congruity effect (NCE), which describes that when two relatively small numbers are compared, responses to the smaller number are faster than responses to the larger number; and vice versa for large numbers. A SNARC effect was observed across all conditions and was not influenced by response movement extent but increased when a number line was presented. In contrast, an NCE was only observed when no number line was presented. This suggests that the SNARC effect and the NCE reflect two different processes. The SNARC effect seems to represent a highly automated classification of numbers as large or small, which is further emphasized by the presentation of a number line. In contrast, the NCE likely results from participants not only classifying numbers as small or large, but also processing their relative size within the relevant section of their mental number line representation. An additional external presentation of a number line might interfere with this process, resulting in overall slower responses. This study follows up on previous spatial-numerical training studies and has implications for future spatial-numerical trainings. Specifically, similar studies with children showed contrasting results, in that response format but not number line presentation influenced spatial-numerical associations. Accordingly, during development, the relative relevance of physical experiences and presentation format for spatial-numerical associations might change.

Differential Development of Children's Understanding of the Cardinality of Small Numbers and Zero

Counting and the understanding of cardinality are important steps in children’s numerical development. Recent studies have indicated that language and visuospatial abilities play an important role in the development of children’s cardinal knowledge of small numbers. However, predictors for the knowledge about zero were usually not considered in these studies. Therefore, the present study investigated whether the acquisition of cardinality knowledge on small numbers and the concept of zero share cross-domain and domain-specific numerical predictors. Particular interest was paid to the question whether visuospatial abilities – in addition to language abilities – were associated with children’s understanding of small numbers and zero. Accordingly, we assessed kindergarteners aged 4 to 5 years in terms of their understanding of small numbers and zero as well as their visuospatial, general language, counting, Arabic number identification abilities, and their finger number knowledge. We observed significant zero-order correlations of vocabulary, number identification, finger knowledge, and counting abilities with children’s knowledge about zero as well as understanding of the cardinality of small numbers. Subsequent regression analyses substantiated the influences of counting abilities on knowledge about zero and the influences of both counting abilities and finger knowledge on children’s understanding of the cardinality of small numbers. No significant influences of cross-domain predictors were observed. In sum, these results indicate that domain-specific numerical precursor skills seem to be more important for children’s development of an understanding of the cardinality of small numbers as well as of the concept of zero than the more proximal cross-domain abilities such as language and visuospatial abilities.

Clock Walking and Gender: How Circular Movements Influence Arithmetic Calculations

Starting from a rich body of evidence on the strict bidirectional relationship between numerical cognition and action processes, the present study aims at deepening the existing knowledge of the influence of body movement on arithmetic calculation. Numerous studies have shown that moving the body along the vertical or the horizontal axis could facilitate calculations such as additions and subtractions. More specifically, results showed an effect of congruence between the type of operation (additions vs. subtractions) and the direction of the movement performed (up/right or down/left). While this congruence effect is present for both additions and subtractions when the axis of action is vertical, when the axis of action is horizontal, the effect appears only for additions. The purpose of this study is to investigate the influence of circular motion, which has so far not been explored, on counting. Participants were asked to count by adding or subtracting “three,” while performing a circular motion (i.e., a clockwise or counterclockwise movement), in an active (i.e., walking) or passive mode (i.e., being pushed on a wheelchair). Results showed a congruence effect for additions calculated in the active modality and only for male participants. Implications of the results for theories of embodied cognition and for the debate on gender differences in mathematical skills are discussed in this paper.

On the genesis of spatial-numerical associations: Evolutionary and cultural factors co-construct the mental number line

Mapping numbers onto space is a common cognitive representation that has been explored in both behavioral and neuroimaging contexts. Empirical work probing the diverse nature of these spatial-numerical associations (SNAs) has led researchers to question 1) how the human brain links numbers with space, and 2) whether this link is biologically vs. culturally determined. We review the existing literature on the development of SNAs and situate that empirical work within cognitive and neuroscientific theoretical frameworks. We propose that an evolutionarily-ancient frontal-parietal circuit broadly tuned to multiple magnitude dimensions provides the phylogenetic substrate for SNAs, while enculturation and sensorimotor experience shape their specific profiles. We then use this perspective to discuss educational implications and highlight promising avenues for future research.

Counting and Number Line Trainings in Kindergarten: Effects on Arithmetic Performance and Number Sense

Children’s early numerical capacities form the building blocks for later arithmetic proficiency. Linear number placements and counting skills are indicative of mapping, as an important precursor to arithmetic skills, and have been suggested to be of vital importance to arithmetic development. The current study investigated whether fostering mapping skills is more efficient through a counting or a number line training program. Effects of both programs were compared through a quasi-experimental design, and moderation effects of age and socio-economic status (SES) were investigated. Ninety kindergartners were divided into three conditions: a counting, a number line, and a control condition. Pretests and posttests included an arithmetic (addition) task and a battery of number sense tasks (comparison, number lines, and counting). Results showed significantly greater gains in arithmetic, counting, and symbolic number lines in the counting training group than in the control group. The number line training group did not make significantly greater gains than the control group. Training gains were moderated by age, but not SES. We concluded that counting training improved numerical capacities effectively, whereas no such improvements could be found for the number line training. This suggests that only a counting approach is effective for fostering number sense and early arithmetic skills in kindergarten. Future research should elaborate on the parameters of training programs and the consequences of variation in these parameters.

Transcranial random noise stimulation and cognitive training to improve learning and cognition of the atypically developing brain: A pilot study

Learning disabilities that affect about 10% of human population are linked to atypical neurodevelopment, but predominantly treated by behavioural interventions. Behavioural interventions alone have shown little efficacy, indicating limited success in modulating neuroplasticity, especially in brains with neural atypicalities. Even in healthy adults, weeks of cognitive training alone led to inconsistent generalisable training gains, or "transfer effects" to non-trained materials. Meanwhile, transcranial random noise stimulation (tRNS), a painless and more direct neuromodulation method was shown to further promote cognitive training and transfer effects in healthy adults without harmful effects. It is unknown whether tRNS on the atypically developing brain might promote greater learning and transfer outcomes than training alone. Here, we show that tRNS over the bilateral dorsolateral prefrontal cortices (dlPFCs) improved learning and performance of children with mathematical learning disabilities (MLD) during arithmetic training compared to those who received sham (placebo) tRNS. Training gains correlated positively with improvement on a standardized mathematical diagnostic test, and this effect was strengthened by tRNS. These findings mirror those in healthy adults, and encourage replications using larger cohorts. Overall, this study offers insights into the concept of combining tRNS and cognitive training for improving learning and cognition of children with learning disabilities.

Learning from where 'eye' remotely look or point: Impact on number line estimation error in adults

In this article, we present an investigation into the use of visual cues during number line estimation and their influence on cognitive processes for reducing number line estimation error. Participants completed a 0-1000 number line estimation task before and after a brief intervention in which they observed static-visual or dynamic-visual cues (control, anchor, gaze cursor, mouse cursor) and also made estimation marks to test effective number-target estimation. Results indicated that a significant pre-test to post-test reduction in estimation error was present for dynamic-visual cues of modelled eye-gaze and mouse cursor. However, there was no significant performance difference between pre- and post-test for the control or static anchor conditions. Findings are discussed in relation to the extent to which anchor points alone are meaningful in promoting successful segmentation of the number line and whether dynamic cues promote the utility of these locations in reducing error through attentional guidance.

Think3d!: Improving mathematics learning through embodied spatial training

Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a foundational cognitive skill. The present research examined the impact of an embodied spatial training program on elementary students’ spatial and mathematical thinking. Students in rural elementary schools completed spatial and math assessments prior to and after participating in an origami and pop-up paper engineering-based program, called Think3d!. Think3d! uses embodied tasks, such as folding and cutting paper, to train two-dimensional to three-dimensional spatial thinking. Analyses explored spatial thinking gains, mathematics gains – specifically for problem types expected to show gains from spatial training – and factors predicting mathematics gains. Results showed spatial thinking gains in two assessments. Using a math categorization to target problems more and less likely to be impacted by spatial training, we found that all students improved on real-world math problems and older students improved on visual and spatial math problems. Further, the results are suggestive of developmental time points for implementing embodied spatial training related to applying spatial thinking to math. Finally, the spatial thinking assessment that was most highly related to training activities also predicted math performance gains. Future research should explore developmental issues related to how embodied spatial training might support STEM learning and outcomes.

Support of mathematical thinking through embodied cognition: Nondigital and digital approaches

Research on mathematics education has shown that learners’ actions can influence how they think and vice versa. Much of this work has been rooted in the use of manipulatives, gestures, and body movements. Our article dissects the mechanisms that underscore the impact of embodied activities and applies this lens to explore how to harness the affordances of new technology to enhance mathematical thinking. This is especially crucial given the increasing accessibility of technology—such as digital touch devices, 3D printers, and location sensors—for constructing embodied experiences. Providing guidance for incorporating those tools, we focus on the role that embodied cognition can play in communicating mathematical concepts as well as in allowing learners to experiment and evolve their ideas. To inspire future integration of theory in the development of technologically enhanced embodied mathematics experiences, we provide examples of how this can be done. Finally, we outline future directions in the areas of design, implementation, and assessment of embodied learning of mathematics.

Touchscreen Tablets: Coordinating Action and Perception for Mathematical Cognition

Proportional reasoning is important and yet difficult for many students, who often use additive strategies, where multiplicative strategies are better suited. In our research we explore the potential of an interactive touchscreen tablet application to promote proportional reasoning by creating conditions that steer students toward multiplicative strategies. The design of this application (Mathematical Imagery Trainer) was inspired by arguments from embodied-cognition theory that mathematical understanding is grounded in sensorimotor schemes. This study draws on a corpus of previously treated data of 9-11 year-old students, who participated individually in semi-structured clinical interviews, in which they solved a manipulation task that required moving two vertical bars at a constant ratio of heights (1:2). Qualitative analyses revealed the frequent emergence of visual attention to the screen location halfway along the bar that was twice as high as the short bar. The hypothesis arose that students used so-called "attentional anchors" (AAs)-psychological constructions of new perceptual structures in the environment that people invent spontaneously as their heuristic means of guiding effective manual actions for managing an otherwise overwhelming task, in this case keeping vertical bars at the same proportion while moving them. We assumed that students' AAs on the mathematically relevant points were crucial in progressing from additive to multiplicative strategies. Here we seek farther to promote this line of research by reanalyzing data from 38 students (aged 9-11). We ask: (1) What quantitative evidence is there for the emergence of AAs?; and (2) How does the transition from additive to multiplicative reasoning take place when solving embodied proportions tasks in interaction with the touchscreen tablet app? We found that: (a) AAs appeared for all students; (b) the AA-types were few across the students; (c) the AAs were mathematically relevant (top of the bars and halfway along the tall bar); (d) interacting with the tablet was crucial for the AAs' emergence; and (e) the vast majority of students progressed from additive to multiplicative strategies (as corroborated with oral utterances). We conclude that touchscreen applications have the potential to create interaction conditions for coordinating action and perception into mathematical cognition.

Making sense of movement in embodied design for mathematics learning

Embodiment perspectives from the cognitive sciences offer a rethinking of the role of sensorimotor activity in human learning, knowing, and reasoning. Educational researchers have been evaluating whether and how these perspectives might inform the theory and practice of STEM instruction. Some of these researchers have created technological systems, where students solve sensorimotor interaction problems as cognitive entry into curricular content. However, the field has yet to agree on a conceptually coherent and empirically validated design framework, inspired by embodiment perspectives, for developing these instructional resources. A stumbling block toward such consensus, we propose, is an implicit disagreement among educational researchers on the relation between physical movement and conceptual learning. This hypothesized disagreement could explain the contrasting choices we witness among current designs for learning with respect to instructional methodology for cultivating new physical actions – whereas some researchers use an approach of direct instruction, such as explicit teaching of gestures, others use an indirect approach, where students must discover effective movements to solve a task. Prior to comparing these approaches, it may help first to clarify key constructs. In this theoretical essay we draw on embodiment and systems literature as well as findings from our design research so as to offer the following taxonomy that may facilitate discourse about movement in STEM learning: (1) distal movement is the technologically extended effect of physical movement on the environment; (2) proximal movement is the physical movements themselves; and (3) sensorimotor schemes are the routinized patterns of cognitive activity that become enacted through proximal movement by orienting on so-called attentional anchors. Attentional anchors are goal-oriented phenomenological objects or enactive perceptions (“sensori-”) that organize proximal movement to effect distal movement (“-motor”). All three facets of movement must be considered in analyzing embodied learning processes. We demonstrate that indirect movement instruction enables students to develop new sensorimotor schemes including attentional anchors as idiosyncratic solutions to physical interaction problems. These schemes are, by necessity, grounded in students’ own agentive relation to the world while also grounding target content such as mathematical notions.

Experimental But Not Sex Differences of a Mental Rotation Training Program on Adolescents

Given the importance of visuospatial processing in areas related to the STEM (Science, Technology, Engineering, and Mathematics) disciplines, where there is still a considerable gap in the area of sex differences, the interest in the effects of visuospatial skills training continues to grow. Therefore, we have evaluated the visuospatial improvement of adolescents after performing a computerized mental rotation training program, as well as the relationship of this visuospatial ability with other cognitive, emotional factors and those factors based on the experience with videogames. The study, which was performed on students aged 14 and 15 years old, showed a significant improvement in this visuospatial skill for a training group (n = 21) compared to a control group (n = 24). Furthermore, no significant sex differences were obtained for spatial ability or for any of the other tasks evaluated, either before or after training. Regarding the relationship between skills, a significant correlation between experience with video games and spatial ability was found, as well as between mathematical reasoning and intelligence and with spatial ability in the initial phase for the total sample. These findings are discussed from a cognitive point of view and within the current sociocultural context, where the equal use of new technologies could help reduce the visuospatial gap between sexes.

Behavior and neuroimaging at baseline predict individual response to combined mathematical and working memory training in children

Mathematical performance is highly correlated with several general cognitive abilities, including working memory (WM) capacity. Here we investigated the effect of numerical training using a number-line (NLT), WM training (WMT), or the combination of the two on a composite score of mathematical ability. The aim was to investigate if the combination contributed to the outcome, and determine if baseline performance or neuroimaging predict the magnitude of improvement.

We randomly assigned 308, 6-year-old children to WMT, NLT, WMT + NLT or a control intervention. Overall, there was a significant effect of NLT but not WMT. The WMT + NLT was the only group that improved significantly more than the controls, although the interaction NLTxWM was non-significant. Higher WM and maths performance predicted larger benefits for WMT and NLT, respectively. Neuroimaging at baseline also contributed significant information about training gain. Different individuals showed as much as a three-fold difference in their responses to the same intervention.

These results show that the impact of an intervention is highly dependent on individual characteristics of the child. If differences in responses could be used to optimize the intervention for each child, future interventions could be substantially more effective.

Bewegtes Lernen numerischer Kompetenzen

Zusammenfassung. Nicht nur in Konzepten wie der Bewegten Schule ist körperliche Bewegung zur Unterstützung des Lernens von großer Bedeutung. Inzwischen liegen erste empirische Befunde zum positiven Einfluss spezifischer körperlicher Bewegungen vor, wie zum Beispiel dem Einsatz der Finger beim Erstrechnen oder dem Laufen entlang eines Zahlenstrahls. Diese aktuellen Studien deuten darauf hin, dass Bewegung den Erwerb numerischer Konzepte unterstützen kann. Neue bewegungssensitive Eingabemedien (z. B. Tanzmatte, Kinect Sensor) ermöglichen nicht nur solche Bewegungen in der Interaktion mit einer Lernumgebung, sondern machen diese mess- und damit spezifisch nutzbar. Dadurch können Trainings realisiert werden, die gezielt den Zusammenhang von Zahlen und Raum und damit für die Ausprägung des mentalen Zahlenstrahls relevante Prozesse trainieren. Die Entwicklung solcher Trainings ist von besonderer Bedeutung, weil der mentale Zahlenstrahl wichtig für eine erfolgreiche numerisch-mathematische Entwicklung zu sein scheint. In diesem Artikel stellen wir neben den theoretischen Grundlagen eine Zusammenfassung der Ergebnisse verschiedener eigener Arbeiten zu verkörperlichten numerischen Trainings vor.

A Matter of Balance: Motor Control is Related to Children's Spatial and Proportional Reasoning Skills

Recent research has shown close links between spatial and mathematical thinking and between spatial abilities and motor skills. However, longitudinal research examining the relations between motor, spatial, and mathematical skills is rare, and the nature of these relations remains unclear. The present study thus investigated the relation between children's motor control and their spatial and proportional reasoning. We measured 6-year-olds' spatial scaling (i.e., the ability to reason about different-sized spaces), their mental transformation skills, and their ability to balance on one leg as an index for motor control. One year later (N = 126), we tested the same children's understanding of proportions. We also assessed several control variables (verbal IQ and socio-economic status) as well as inhibitory control, visuo-spatial and verbal working memory. Stepwise hierarchical regressions showed that, after accounting for effects of control variables, children's balance skills significantly increased the explained variance in their spatial performance and proportional reasoning. Our results suggest specific relations between balance skills and spatial as well as proportional reasoning skills that cannot be explained by general differences in executive functioning or intelligence.