Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

From developmental theory to effective training: long-term and transfer effects of promoting the quantity-to-number word linkage in first-graders at risk for mathematical difficulties

Introduction

The model of quantity-to-number word linkage (QNL model) identifies relevant milestones in the process of early numerical acquisition and describes a developmental sequence that can guide the fostering of foundational mathematical abilities in at-risk children. While there is substantial evidence for the predictive value of the quantity-number competencies (QNC) described by the model, evidence supporting the preventive potential of interventions targeting these QNC is so far largely restricted to short-term effects. Findings regarding their long-term preventive impact, especially in terms of transfer to mathematical school achievement, are still limited. This quasi-experimental study aimed to address this gap by evaluating the long-term transfer effects of an intervention program that is strictly derived from the QNL model of mathematical development [QNL training; in German "Mengen, zählen, Zahlen" (MZZ)].

Methods

We assessed the quantity-number competencies of 575 first-graders and identified 119 of them as being at risk for mathematical learning difficulties, who were then assigned to three experimental conditions. Sixty one children received 12 sessions of the QNL training, while 30 underwent training in inductive reasoning. Another 28 children served as a control group, receiving no specific intervention.

Results and Discussion

Multi-level analyses confirmed both significant short-and long-term effects in the specifically trained quantity-number competencies as well as transfer effects on subsequent mathematical school achievement. In accordance with previous findings, transfer effects of the QNL training on mathematical school achievement were not yet evident immediately after the intervention but turned out to be significant after a delay of 6 months and remained stable even 15 months after training. Effect sizes ranged from d = 0.32 to d = 1.12. These findings both underscore the preventive potential of interventions that are strictly driven by developmental theory and, conversely, support the theoretical assumptions of the QNL model.

Psychophysiological evaluation of the Smartick method in children with reading and mathematical difficulties

Introduction

Assistive technologies for learning are aimed at promoting academic skills, such as reading and mathematics. These technologies mainly embrace mobile and web apps addressed to children with learning difficulties. Nevertheless, most applications lack pedagogical foundation. Additionally, the task of selecting suitable technology for educational purposes becomes challenging. Hence, this protocol posits the psychophysiological assessment of an online method for learning (OML) named Smartick. This platform comprises reading and math activities for learning training. In this protocol, individual monitoring of each child is proposed to determine the progress in learning caused by Smartick.

Methods and analysis

One hundred and twelve children aged between 8 and 12 who present reading or math difficulty after a rigorous psychometric evaluation will be recruited. The study comprises four sessions. In sessions 1 and 2, collective and individual psychometric evaluations will be performed, respectively. Reading and mathematical proficiency will be assessed, as well as attentional levels and intellectual quotient. Subsequently, each child will be semi-randomly assigned to either the experimental or control groups. Afterward, a first EEG will be collected for all children in session 3. Then, experimental groups will use Smartick for 3 months, in addition to their traditional learning method. In contrast, control groups will only continue with their traditional learning method. Finally, session 4 will consist of performing a second psychometric evaluation and another EEG, so that psychophysiological parameters can be encountered that indicate learning improvements due to the OML, regardless of the traditional learning method at hand.

Discussion

Currently, few studies have validated learning improvement due to assistive technologies for learning. However, this proposal presents a psychophysiological evaluation addressed to children with reading or math difficulties who will be trained with an OML.

The light side of gaming: creativity and brain plasticity

Could gaming enhance brain plasticity and executive functions (EFs) by fostering creativity? We identify vital benefits from further research exploring the relationship between games, brain plasticity, and creativity. The ongoing progress in neuroscience research in these three disciplines offers many possibilities and prospects for impactful therapy. Therefore, we emphasize the significance of investigating the untapped potentials of using games in creative therapy-our perspective on the often-overlooked neuroscientific aspect of creativity concerning health and wellbeing. One of these potentials is examining games as a therapeutic tool, focusing on their capacity to inspire and engage the imagination and other mental operators shared with creativity. Using a game as a therapeutic approach may boost brain plasticity, which may help them reduce their cognitive impairments by improving their EFs. This review offers a comprehensive outline of the latest advancements in the literature on games that tie to creativity through enhancing brain plasticity and EFs. Communicating this knowledge can furnish countless possibilities to improve our overall health and wellbeing and foster a positive perspective in individuals affected by anxiety.

Mathlete: an adaptive assistive technology tool for children with dyscalculia

PURPOSE

The use of technology in teaching and learning process for children is gaining importance. Children with specific learning disabilities have shown positive results with assistive technology tools. Dyscalculia is a specific learning disability in which an individual faces problem in mathematical skills. Around 3-7% of the world population is affected with it. The aim of the current research study is to determine the effectiveness of an assistive technology tool, Mathlete on children with dyscalculia's early numeracy skills. Such assistive technology tools can serve as a boon for these children.

METHOD

A total of 40 children with dyscalculia (Mage = 6.8 years) were a part of the study. The group of 40 children were randomly divided into two groups: experiment group using mathlete for improving their learning (30 children) and a control group using only traditional teaching for learning (10 children). The children were screened for dyscalculia using the screening module of mathlete.

RESULTS

The two groups showed no significant difference in terms of their socio-economic status, gender and parents education level. Children in the experiment group showed improvement from pre-test to post-test after using mathlete. Also, there was significant difference in learning of both the groups, children in experiment group could understand the concepts better than the ones in control group.

CONCLUSION

Mathlete helped improve the mathematical learning of children with dyscalculia from pre-test to post-test.

Preschoolers' Mathematics Game Preferences and Learning Performance through Designing a Degree of Freedom for a Tablet Game

Children always have a natural inclination to play, so the purpose of game-based learning is to establish a way for children to acquire knowledge while playing. This study is to discover the relationship between children's play preferences and learning performances toward a mathematics mobile game we designed. The tablet game we designed, "Lily's Closet", is a mathematics game that guides children aged 3-8 to learn "classification". To explore the preferences and learning performances of the games we designed for the preschool children, we put "Lili's Closet" on a children's tablet named Kizpad with over 200 games. We classify and analyze players' behavior data by Data Mining in our designed game to explore children's play behaviors and preferences. We sampled 6,924 children from Taiwan, aged 3-8 years old. In the results, we found that there is a significant difference in the number of ages and achievements in the game. The maturity of the child's age is positively correlated with the achievement of the game, but it is negatively correlated with the number of times of willing to play. As a result, we suggest that to assist learning, we should give children different levels of games according to their ages. The research hopes to resonate with readers and jointly explore the relationship between mobile games.

Effectiveness of digital game-based trainings in children with neurodevelopmental disorders: A meta-analysis

Digital game-based training programs have recently been used to train the cognitive abilities of children with neurodevelopmental disorders (NDDs). However, the effects of training remain controversial. The present meta-analysis explored the effectiveness of digital game-based training in children with NDDs and examined the possible moderators of its effects. Twenty-nine studies with cognitive outcomes in 1535 children were included in the present meta-analysis. The results showed that digital game-based training could significantly enhance the core cognitive abilities of children with each type of NDDs and that training could be used remotely. Meanwhile, task content and game features of digital game-based interventions separately make unique and significant contributions to the training effects, suggesting that the combination of training content and game features could efficiently improve children's cognition. Although the present study revealed that the training benefits could be maintained over a period of time, more studies are needed to explore the retention effects of digital game-based training. The present study provides a comprehensive understanding of the training effects of digital game-based interventions and new insights for future cognitive training design and application.

The Benefits of an Interdisciplinary Approach to Mathematics Education on Issues Around Computation in School

We present arguments in favor of an interdisciplinary approach in mathematics education. As an instance, we briefly recall how cognitive neuropsychologists promoted intense finger gnosis acquisition, i.e., acquiring the ability to mentally represent one’s fingers, at an early age. Mathematics educators definitely recommended the development of finger gnosis but examined its limits. They also presented arguments in favor of developing flexible mental calculation as a goal of arithmetical instruction in elementary school. In this context we describe the training of “Zahlenblick” as a way to foster flexible mental calculation and connect it with concepts from the theory of metacognition. We illustrate how precisely this branch of metacognition demands further interdisciplinary research. In our analysis, “Zahlenblick” extends to acquiring an eye for proportions, beyond just whole numbers. We illustrate how useful it would be to better understand the neural underpinnings responsible for the advantages of so-called natural frequencies, compared with percentages or probabilities, and of icon arrays for representing them. Such natural frequencies are adequate formats for the early confrontation with decision-making under risk.

Increased structural covariance in brain regions for number processing and memory in children with developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability associated with deficits in processing numerical and mathematical information. Several studies demonstrated functional network alterations in DD. Yet, there are no studies, which examined the structural network integrity in DD. We compared whole‐brain maps of volume based structural covariance between 19 (4 males) children with DD and 18 (4 males) typically developing children. We found elevated structural covariance in the DD group between the anterior intraparietal sulcus to the middle temporal and frontal gyrus (p < 0.05, corrected). A hippocampus subfield analysis showed higher structural covariance in the DD group for area CA3 to the parahippocampal and calcarine sulcus, angular gyrus and anterior part of the intraparietal sulcus as well as to the lingual gyrus. Lower structural covariance in this group was seen for the subiculum to orbitofrontal gyrus, anterior insula and middle frontal gyrus. In contrast, the primary motor cortex (control region) revealed no difference in structural covariance between groups. Our results extend functional magnetic resonance studies by revealing abnormal gray matter integrity in children with DD. These findings thus indicate that the pathophysiology of DD is mediated by both structural and functional abnormalities in a network involved in number processing and memory function.

Approximate arithmetic training does not improve symbolic math in third and fourth grade children

BACKGROUND

Prior studies reported that practice playing an approximate arithmetic game improved symbolic math performance relative to active control groups in adults and preschool children (e.g. Park & Brannon, 2013, 2014; Park et al., 2016; Szkudlarek & Brannon, 2018). However, Szkudlarek, Park and Brannon (2021) recently failed to replicate those findings in adults. Here we test whether approximate arithmetic training yields benefits in elementary school children who have intermediate knowledge of arithmetic.

METHOD

We conducted a randomized controlled trial with a pre and post-test design to compare the effects of approximate arithmetic training and visuo-spatial working memory training on standardized math performance in third and fourth grade children.

RESULTS

We found that approximate arithmetic training did not yield any significant gains on standardized measures of symbolic math performance.

CONCLUSION

A Bayesian analysis supports the conclusion that approximate arithmetic provides no benefits for symbolic math performance.

Failure to replicate the benefit of approximate arithmetic training for symbolic arithmetic fluency in adults

Previous research reported that college students’ symbolic addition and subtraction fluency improved after training with non-symbolic, approximate addition and subtraction. These findings were widely interpreted as strong support for the hypothesis that the Approximate Number System (ANS) plays a causal role in symbolic mathematics, and that this relation holds into adulthood. Here we report four experiments that fail to find evidence for this causal relation. Experiment 1 examined whether the approximate arithmetic training effect exists within a shorter training period than originally reported (2 vs 6 days of training). Experiment 2 attempted to replicate and compare the approximate arithmetic training effect to a control training condition matched in working memory load. Experiments 3 and 4 replicated the original approximate arithmetic training experiments with a larger sample size. Across all four experiments (N = 318) approximate arithmetic training was no more effective at improving the arithmetic fluency of adults than training with control tasks. Results call into question any causal relationship between approximate, non-symbolic arithmetic and precise symbolic arithmetic.

Efficacy of a Computer-Based Learning Program in Children With Developmental Dyscalculia. What Influences Individual Responsiveness?

This study presents the evaluation of a computer-based learning program for children with developmental dyscalculia and focuses on factors affecting individual responsiveness. The adaptive training program Calcularis 2.0 has been developed according to current neuro-cognitive theory of numerical cognition. It aims to automatize number representations, supports the formation and access to the mental number line and trains arithmetic operations as well as arithmetic fact knowledge in expanding number ranges. Sixty-seven children with developmental dyscalculia from second to fifth grade (mean age 8.96 years) were randomly assigned to one of two groups (Calcularis group, waiting control group). Training duration comprised a minimum of 42 training sessions à 20 min within a maximum period of 13 weeks. Compared to the waiting control group, children of the Calcularis group demonstrated a higher benefit in arithmetic operations and number line estimation. These improvements were shown to be stable after a 3-months post training interval. In addition, this study examines which predictors accounted for training improvements. Results indicate that this self-directed training was especially beneficial for children with low math anxiety scores and without an additional reading and/or spelling disorder. In conclusion, Calcularis 2.0 supports children with developmental dyscalculia to improve their arithmetical abilities and their mental number line representation. However, it is relevant to further adapt the setting to the individual circumstances.

Data and supplemental material of the paper "Effectiveness of digital-based interventions for children with mathematical learning difficulties: A meta-analysis"

Data and supplement material of the article "Effectiveness of digital-based interventions for children with mathematical learning difficulties: A meta-analysis" (Benavides-Varela et al.) [1] are presented. Data were collected from studies included in the meta-analysis to evaluate the effects of digital-based interventions for children with mathematical learning difficulties compared to control conditions in group-designed randomized controlled trials. Literature search, inclusion criteria and coding procedure are described. PRISMA flow-chart is reported to summarize the literature search and coding of all the relevant characteristics of the primary studies is made available. This allows other researchers to easily access to the information needed to evaluate the studies and to use these data in future meta-analyses. However, researchers are highly recommended to refer to the original papers in order to check studies suitability to their own criteria. Moreover, in the supplemental material all the information needed to reproduce the meta-analysis results is reported together with the R code syntax. Data and supplemental material are available online (https://osf.io/ajdnv/).

Number Magnitude Processing and Verbal Working Memory in Children with Mild Intellectual Disabilities

This study examined if children (M_age = 14.60) with Mild Intellectual Disabilities (MID) display weaknesses in number processing and verbal working memory. An age-matched and mental age-matched (MA, M_age = 6.17) design extended by a group of 9-10-year-olds, and a group of 11-12-year-olds were used. The MID children's working memory was equal to the MA group but poorer than the other groups. On number tasks, the MID group was faster than the MA group but slower than the other groups. All groups obtained equal Weber fraction scores and distance effects on the number comparison tasks. The MID group performed subitizing and counting faster than the MA group, but slower than the 11-12-year-olds. The results demonstrate that number processing and working memory in children with MID is characterized by a developmental delay, not a deficit. Their main problem is to access the quantitative meaning of Arabic numerals. The development of different types of cognitive abilities is differently affected by educational experience and intellectual ability. The innate number system appears to be unaffected by intellectual capacity or educational experience, while the innate working memory ability is affected by intellectual capacity but not by educational experience. Culturally acquired symbolic number abilities are strongly affected by educational experience.

Effectiveness of Computerized Cognitive Training Programs (CCTP) with Game-like Features in Children with or without Neuropsychological Disorders: a Meta-Analytic Investigation

Computerized cognitive training programs (CCTP) are based on the assumption that cognitive abilities may be boosted by repetitively performing challenging tasks. The integration of game-like features in these programs, associated with the goal of amusing or rewarding participants, may contribute to generate cognitive benefits. Indeed, reinforcement contingencies have been reported to produce positive effects on performance and motivation, especially in children. This meta-analysis was aimed at providing a quantitative summary of the effectiveness of CCTP with game-like features in school-aged children with typical and atypical development. A total of 24 studies, with the cognitive and behavioral outcome data of 1547 participants, were selected for inclusion in the meta-analysis. Subgroup analyses were performed to identify the sources of the observed methodological heterogeneity. A robust variance estimation model, after removal of study outliers, yielded a small-to-moderate significant effect size. Final results pointed out smaller but more precise estimate effect sizes according to methodological aspects related to cognitive domain of outcomes, standardization of measures and type of control applied. Alongside supporting the use of CCTP for rehabilitating cognitive functions, the present results shed light on how different methodological choices are able to shape research findings in the field of children's cognitive rehabilitation.

Persistent Effects of Musical Training on Mathematical Skills of Children With Developmental Dyscalculia

Musical training (MT) is perceived as a multi-sensory program that simultaneously integrates visual, aural, oral, and kinesthetic senses. Furthermore, MT stimulates cognitive functions in a ludic way instead of tapping straight into the traditional context of school learning, including mathematics. Nevertheless, the efficacy of MT over mathematics remains understudied, especially concerning longstanding effects. For this reason, this longitudinal study explored the impact of MT on numerical cognition and abstract visual reasoning using a double-blind and quasi-experimental design. We assessed two groups of children from primary schools, namely one with developmental dyscalculia [DD; n = 22] and another comprising typically developing children [TD; n = 22], who concomitantly underwent MT. Numerical cognition measurement was carried out at four different time points: Baseline (pre-MT assessment), mid-test (after 7 weeks of MT), post-test (after 14 weeks of MT), and follow-up (10 weeks after the end of MT). Significant interactions were found between time and group for numerical cognition performance, in which the DD group showed higher scores in number comprehension, number production at mid-test, and calculation at post-test compared to baseline. A key finding was that number production, number comprehension, and calculation effects were time-resistant for the DD group since changes remained on follow-up. Moreover, no significant differences over time were found for abstract visual reasoning for both groups. In conclusion, the findings of this study showed that MT appears to be a useful tool for compensatory remediation of DD.

Neurostructural correlate of math anxiety in the brain of children

Adequate mathematical competencies are currently indispensable in professional and social life. However, mathematics is often associated with stress and frustration and the confrontation with tasks that require mathematical knowledge triggers anxiety in many children. We examined if there is a relationship between math anxiety and changes in brain structure in children with and without developmental dyscalculia. Our findings showed that math anxiety is related to altered brain structure. In particular, the right amygdala volume was reduced in individuals with higher math anxiety. In conclusion, math anxiety not only hinders children in arithmetic development, but it is associated with altered brain structure in areas related to fear processing. This emphasizes the far-reaching outcome emotional factors in mathematical cognition can have and encourages educators and researchers alike to consider math anxiety to prevent detrimental long-term consequences on school achievement and quality of life, especially in children with developmental dyscalculia.

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.

Functional hyperconnectivity vanishes in children with developmental dyscalculia after numerical intervention

Developmental dyscalculia (DD) is a developmental learning disability associated with deficits in processing numerical and mathematical information. Although behavioural training can reduce these deficits, it is unclear which neuronal resources show a functional reorganization due to training. We examined typically developing (TD) children (N = 16, mean age: 9.5 years) and age-, gender-, and handedness-matched children with DD (N = 15, mean age: 9.5 years) during the performance of a numerical order task with fMRI and functional connectivity before and after 5-weeks of number line training. Using the intraparietal sulcus (IPS) as seed region, DD showed hyperconnectivity in parietal, frontal, visual, and temporal regions before the training controlling for age and IQ. Hyperconnectivity disappeared after training, whereas math abilities improved. Multivariate classification analysis of task-related fMRI data corroborated the connectivity results as the same group of TD could be discriminated from DD before but not after number line training (86.4 vs. 38.9%, respectively). Our results indicate that abnormally high functional connectivity in DD can be normalized on the neuronal level by intensive number line training. As functional connectivity in DD was indistinguishable to TD’s connectivity after training, we conclude that training lead to a re-organization of inter-regional task engagement.

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.

Evaluation of a Computer-Based Training Program for Enhancing Arithmetic Skills and Spatial Number Representation in Primary School Children

Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6-8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation.