You can count on your fingers: Finger-based intervention improves first-graders' arithmetic learning.

The question of whether finger use should be encouraged or discouraged in early mathematics instruction remains a topic of debate. Scientific evidence on this matter is scarce due to the limited number of systematic intervention studies. Accordingly, we conducted an intervention study in which first-graders (Mage = 6.48 years, SD = 0.35) completed a finger-based training (18 sessions of âˆ¼ 30 min each) over the course of the first school year. The training was integrated into standard mathematics instruction in schools and compared with business-as-usual curriculum teaching. At the end of first grade and in a follow-up test 9 months later in second grade, children who received the finger training (n = 119) outperformed the control group (n = 123) in written addition and subtraction. No group differences were observed for number line estimation tasks. These results suggest that finger-based numerical strategies can enhance arithmetic learning, supporting the idea of an embodied representation of numbers, and challenge the prevailing skepticism about finger use in primary mathematics education.

Finger counting, finger number gesturing, and basic numerical skills: A cross-sectional study in 3- to 5-year-olds.

Recent evidence suggests that using finger-based strategies is beneficial for the acquisition of basic numerical skills. There are basically two finger-based strategies to be distinguished: (a) finger counting (i.e., extending single fingers successively) and (b) finger number gesturing (i.e., extending fingers simultaneously to represent magnitudes). In this study, we investigated both spontaneous and prompted finger counting and finger number gesturing as well as their contribution to basic numerical skills in 3- to 5-year-olds (N = 156). Results revealed that only 6% of children spontaneously used their fingers for counting when asked to name a specific number of animals, whereas 59% applied finger number gesturing to show their age. This indicates that the spontaneous use of finger-based strategies depends heavily on the specific context. Moreover, children performed significantly better in prompted finger counting than in finger number gesturing, suggesting that both strategies build on each other. Finally, both prompted finger counting and finger number gesturing significantly and individually predicted counting, cardinal number knowledge, and basic arithmetic. These results indicate that finger counting and finger number gesturing follow and positively relate to numerical development.

Concepts of order: Why is ordinality processed slower and less accurately for non-consecutive sequences?

Both adults and children are slower at judging the ordinality of non-consecutive sequences (e.g., 1-3-5) than consecutive sequences (e.g., 1-2-3). It has been suggested that the processing of non-consecutive sequences is slower because it conflicts with the intuition that only count-list sequences are correctly ordered. An alternative explanation, however, may be that people simply find it difficult to switch between consecutive and non-consecutive concepts of order during order judgement tasks. Therefore, in adult participants, we tested whether presenting consecutive and non-consecutive sequences separately would eliminate this switching demand and thus improve performance. In contrast with this prediction, however, we observed similar patterns of response times independent of whether sequences were presented separately or together (Experiment 1). Furthermore, this pattern of results remained even when we doubled the number of trials and made participants explicitly aware when consecutive and non-consecutive sequences were presented separately (Experiment 2). Overall, these results suggest slower response times for non-consecutive sequences do not result from a cognitive demand of switching between consecutive and non-consecutive concepts of order, at least not in adults.

Engaging learners with games-Insights from functional near-infrared spectroscopy.

The use of game elements in learning tasks is thought to facilitate emotional and behavioral responses as well as learner engagement. So far, however, little is known about the underlying neural mechanisms of game-based learning. In the current study, we added game elements to a number line estimation task assessing fraction understanding and compared brain activation patterns to a non-game-based task version. Forty-one participants performed both task versions in counterbalanced order while frontal brain activation patterns were assessed using near-infrared spectroscopy (within-subject, cross-sectional study design). Additionally, heart rate, subjective user experience, and task performance were recorded. Task performance, mood, flow experience, as well as heart rate did not differ between task versions. However, the game-based task-version was rated as more attractive, stimulating and novel compared to the non-game-based task version. Additionally, completing the game-based task version was associated with stronger activation in frontal brain areas generally involved in emotional and reward processing as well as attentional processes. These results provide new neurofunctional evidence substantiating that game elements in learning tasks seem to facilitate learning through emotional and cognitive engagement.

Performance increases in mathematics during COVID-19 pandemic distance learning in Austria: Evidence from an intelligent tutoring system for mathematics.

BACKGROUND: In 2020, school closures during the COVID-19 pandemic forced students all over the world to promptly alter their learning routines from in-person to distance learning. However, so far, only a limited number of studies from a few countries investigated whether school closures affected students' performance within intelligent tutoring system-such as intelligent tutoring systems. METHOD: In this study, we investigated the effect of school closures in Austria by evaluating data (n = 168 students) derived from an intelligent tutoring system for learning mathematics, which students used before and during the first period of school closures. RESULTS: We found that students' performance increased in mathematics in the intelligent tutoring system during the period of school closures compared to the same period in previous years. CONCLUSION: Our results indicate that intelligent tutoring systems were a valuable tool for continuing education and maintaining student learning during school closures in Austria.

A potential dissociation between perception and production version for bounded but not unbounded number line estimation.

BACKGROUND: What, exactly, do number line estimation (NLE) tasks measure? Different versions of the task were observed to have different effects on performance. METHOD: We investigated associations between the production (indicating the location) and perception version (indicating the number) of the bounded and unbounded NLE task and their relationship to arithmetic. RESULTS: A stronger correlation was observed between the production and perception version of the unbounded than the bounded NLE task, indicating that both versions of the unbounded-but not the bounded-NLE task measure the same construct. Moreover, overall low but significant associations between NLE performance and arithmetic were only observed for the production version of the bounded NLE task. CONCLUSION: These results substantiate that the production version of bounded NLE seems to rely on proportion judgment strategies, whereas both unbounded versions and the perception version of the bounded NLE task may rely more on magnitude estimation.

Assignment strategies modulate students' academic performance in an online learning environment during the first and second COVID-19 related school closures.

A growing number of studies seek to evaluate the impact of school closures during the ongoing COVID-19 pandemic. While most studies reported severe learning losses in students, some studies found positive effects of school closures on academic performance. However, it is still unclear which factors contribute to the differential effects observed in these studies. In this article, we examine the impact of assignment strategies for problem sets on the academic performance of students (n ≈ 16,000 from grades 4-10 who calculated ≈ 170,000 problem sets) in an online learning environment for mathematics, during the first and second period of pandemic-related school closures in Germany. We observed that, if teachers repeatedly assigned single problem sets (i.e., a small chunk of on average eight mathematical problems) to their class, students' performance increased significantly during both periods of school closures compared to the same periods in the previous year (without school closures). In contrast, our analyses also indicated that, if teachers assigned bundles of problem sets (i.e., large chunks) or when students self-selected problem sets, students' performance did not increase significantly. Moreover, students' performance was generally higher when single problem sets were assigned, compared to the other two assignment types. Taken together, our results imply that teachers' way of assigning problem sets in online learning environments can have a positive effect on students' performance in mathematics.

Combining virtual reality and tactile stimulation to investigate embodied finger-based numerical representations.

Finger-based representation of numbers is a high-level cognitive strategy to assist numerical and arithmetic processing in children and adults. It is unclear whether this paradigm builds on simple perceptual features or comprises several attributes through embodiment. Here we describe the development and initial testing of an experimental setup to study embodiment during a finger-based numerical task using Virtual Reality (VR) and a low-cost tactile stimulator that is easy to build. Using VR allows us to create new ways to study finger-based numerical representation using a virtual hand that can be manipulated in ways our hand cannot, such as decoupling tactile and visual stimuli. The goal is to present a new methodology that can allow researchers to study embodiment through this new approach, maybe shedding new light on the cognitive strategy behind the finger-based representation of numbers. In this case, a critical methodological requirement is delivering precisely targeted sensory stimuli to specific effectors while simultaneously recording their behavior and engaging the participant in a simulated experience. We tested the device's capability by stimulating users in different experimental configurations. Results indicate that our device delivers reliable tactile stimulation to all fingers of a participant's hand without losing motion tracking quality during an ongoing task. This is reflected by an accuracy of over 95% in participants detecting stimulation of a single finger or multiple fingers in sequential stimulation as indicated by experiments with sixteen participants. We discuss possible application scenarios, explain how to apply our methodology to study the embodiment of finger-based numerical representations and other high-level cognitive functions, and discuss potential further developments of the device based on the data obtained in our testing.

Different aspects of fraction understanding are associated selectively with performance on a fraction learning game.

Fraction understanding seems a double-edged sword. On the one hand, it is an important predictor of later mathematical achievement. On the other hand, it is also one of the topics students struggle most in secondary math education. To complement traditional instruction, digital learning games were developed and found to successfully foster fraction understanding. However, so far, it is not known to what degree different aspects of fraction understanding (e.g., part-whole relations, fraction magnitude, fraction arithmetic) may be conveyed by such games. The current study evaluated selective associations of in-game performance of the fraction learning game Semideus with specific aspects of fraction understanding assessed using a comprehensive paper-pencil test. In Semideus, seventh graders (Mage=12.3years) from academic track secondary schools in Germany estimated the location of fractions on a number line and compared fractions according to their magnitude. Results replicated previous findings showing that in-game performance was significantly associated with mathematics achievement (i.e., math grades) and basic, whole number arithmetic skills. Moreover, we observed significant associations for aspects of fraction understanding closely matching mechanics of the learning game such as fraction number line estimation, fraction magnitude comparison and fraction ordering. These associations were observed for accuracy on the game's fraction learning tasks (e.g., estimation accuracy on the number line) but also generalized to game-based metrics such as virtual incentives (i.e., stars awarded in the game). This implies that the actual game mechanic may help to convey aspects of fraction understanding, substantiating ideas of intrinsic integration in game design.

The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data.

Recent research indicated that fraction understanding is an important predictor of later mathematical achievement. In the current study we investigated associations between basic numerical skills and students' fraction processing. We analyzed data of 939 German secondary school students (age range = 11.92 to 18.00 years) and evaluated the determinants of fraction processing considering basic numerical skills as predictors (i.e., number line estimation, basic arithmetic operations, non-symbolic magnitude comparison, etc.). Additionally, we controlled for general cognitive ability, grade level, and sex. We found that multiplication, subtraction, conceptual knowledge, number line estimation, and basic geometry were significantly associated with fraction processing beyond significant associations of general cognitive ability and sex. Moreover, relative weight analysis revealed that addition and approximate arithmetic should also be considered as relevant predictors for fraction processing. The current results provide food for thought that further research should focus on investigating whether recapitulating basic numerical content in secondary school mathematics education can be beneficial for acquiring more complex mathematical concepts such as fractions.

Influences of cognitive control on number processing: New evidence from switching between two numerical tasks.

A growing body of research suggests that basic numerical abilities such as number magnitude and number parity processing are influenced by cognitive control. So far, however, evidence for number processing being influenced by cognitive control came primarily from observed adaptations to stimulus set characteristics (e.g., ratio or order of specific stimulus types) and switches between a numerical and non-numerical task. Complementing this previous research, the present study employed a task switching paradigm exclusively involving numerical tasks (i.e., magnitude comparisons and parity judgements) to examine how cognitive control processes influence number processing. Participants were presented with a single-digit number and had to either judge its parity or compare its magnitude with a standard of 5, depending on a preceding cue. Based on previous results, we expected the numerical distance effect and the spatial-numerical association of response codes (SNARC) effect to be modulated in switch trials requiring the exertion of cognitive control. Partly in line with our expectations, the numerical distance effect was reduced in switch trials. However, no modulation of the SNARC effect was observed. The results pattern suggests that number processing is influenced by cognitive control, depending on task requirements and the type of numerical information (i.e., numerical magnitude vs spatial association of numbers) that is processed. To reconcile the present and previous results, we propose an information prioritisation account, suggesting that cognitive control primarily influences the processing of the information type that requires the most explicit processing.

Children's spatial language skills predict their verbal number skills: A longitudinal study.

The process of number symbolization is assumed to be critically influenced by the acquisition of so-called verbal number skills (e.g., verbally reciting the number chain and naming Arabic numerals). For the acquisition of these verbal number skills, verbal and visuospatial skills are discussed as contributing factors. In this context, children's verbal number skills have been found to be associated with their concurrent spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind). In a longitudinal study with three measurement times (T1, T2, T3) at an interval of about 6 months, we evaluated the predictive role of preschool children's (mean age at T1: 3 years and 10 months) spatial language skills for the acquisition of verbal number skills. Children's spatial language skills at T2 significantly predicted their verbal number skills at T3, when controlling for influences of important covariates such as vocabulary knowledge. In addition, further analyses replicated previous results indicating that children's spatial language skills at T2 were associated with their verbal number skills at T2. Exploratory analyses further revealed that children's verbal number skills at T1 predict their spatial language at T2. Results suggests that better spatial language skills at the age of 4 years facilitate the future acquisition of verbal number skills.

Body experience influences lexical-semantic knowledge of body parts in children with hemiplegic cerebral palsy.

Background: Disorders in different levels of body representation (i.e., body schema, body structural description, and body image) are present in hemiplegic cerebral palsy (HCP). However, it remains unclear whether the body image develops from aspects of body schema and body structural description, and how this occurs in children with HCP. Objective and methods: In a cross-sectional study, we investigated 53 children with HCP (mean age about 10 years) and 204 typically developing (TD) control children to qualitatively evaluate whether and how body schema (related sensorimotor experiences) and body structural description (related visuospatial experiences) affect the development of children's body image and whether this development is delayed through HCP. Graph analysis was used to create a lexical-semantic map of body representation from data of a semantic word fluency task. Results: Results indicated a similar qualitative pattern of influences of sensorimotor and visuospatial experiences on lexical-semantic knowledge of body parts, with a delayed developmental course in children with HCP compared to TD children. Conclusion: These findings suggest that children's body image seemed to be influenced by body schema and body structural descriptions as indicated by poorer lexical-semantic knowledge of body parts in children with HCP due to missing physical experiences of the affected body parts. This might imply that "body talk" may beneficially complement physical therapy for children with HCP to promote body image development.

Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding.

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old's spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children's absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children's spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children's SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers' relative understanding of numerical magnitude.

MAOA-LPR polymorphism and math anxiety: A marker of genetic susceptibility to social influences in girls?

Math anxiety (MA) seems to result from an interaction of genetic vulnerability with negative experiences learning mathematics. Although mathematics achievement does not substantially differ between the sexes, MA levels are usually higher in girls. Molecular genetic markers of MA vulnerability have been seldom explored. This article examines the contribution of the monoamine oxidase A gene (MAOA) to MA and to sex differences in MA. Five hundred and sixty-eight third to fifth graders were genotyped for the MAOA-LPR polymorphism (a repetitive element in MAOA promoter that has been associated with MAOA enzymatic activity), and assessed on general cognitive ability, mathematics achievement, and the cognitive and affective dimensions of MA. MAOA-LPR genotypes were classified as high (MAOA-H) or low (MAOA-L) according to their predicted enzymatic activity. Mixed models controlling for effects of school, sex, general cognitive ability, and mathematics achievement were evaluated. The best fitting model included school, math achievement, sex, MAOA-LPR, and the MAOA-LPR by sex interaction. This indicated that under the MAOA-H dominant model, anxiety toward mathematics interacted with the MAOA genotype: girls with an MAOA-L genotype exhibited higher levels of MA, with a small but significant effect. The association between MAOA-L genotype and MA in girls may represent an example of developmental plasticity.

Finger-Based Numerical Training Increases Sensorimotor Activation for Arithmetic in Children-An fNIRS Study.

Most children use their fingers when learning to count and calculate. These sensorimotor experiences were argued to underlie reported behavioral associations of finger gnosis and counting with mathematical skills. On the neural level, associations were assumed to originate from overlapping neural representations of fingers and numbers. This study explored whether finger-based training in children would lead to specific neural activation in the sensorimotor cortex, associated with finger movements, as well as the parietal cortex, associated with number processing, during mental arithmetic. Following finger-based training during the first year of school, trained children showed finger-related arithmetic effects accompanied by activation in the sensorimotor cortex potentially associated with implicit finger movements. This indicates embodied finger-based numerical representations after training. Results for differences in neural activation between trained children and a control group in the IPS were less conclusive. This study provides the first evidence for training-induced sensorimotor plasticity in brain development potentially driven by the explicit use of fingers for initial arithmetic, supporting an embodied perspective on the representation of numbers.

Sex differences in the association of math achievement with visual-spatial and verbal working memory: Does the type of math test matter?

Previous research on sex differences in mathematical achievement shows mixed findings, which have been argued to depend on types of math tests used and the type of solution strategies (i.e., verbal versus visual-spatial) these tests evoke. The current study evaluated sex differences in (a) performance (development) on two types of math tests in primary schools and (b) the predictive value of verbal and visual-spatial working memory on math achievement. Children (N = 3175) from grades 2 through five participated. Visual-spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed five times during two school years using a speeded arithmetic test (math fluency) and a word problem test (math problem solving). Results from Multilevel Multigroup Latent Growth Modeling, showed that sex differences in level and growth of math performance were mixed and very small. Sex differences in the predictive value of verbal and visual-spatial working memory for math performance suggested that boys seemed to rely more on verbal strategies than girls. Explanations focus on cognitive and emotional factors and how these may interact to possibly amplify sex differences as children grow older.

The structure of early numeracy: Evidence from multi-factorial models.

BACKGROUND: Despite the relevance of basic numerical skills to later mathematical outcomes, there remains little consensus on which skills comprise the construct of early numeracy. PROCEDURE: Here, we evaluate recent studies that investigated this construct using various approaches. MAIN FINDINGS: Findings from these studies indicated broad consensus in considering skills such as counting, number relations, and basic arithmetic, as central aspects of early numeracy. However, both the number and contents of identified factors varied considerably across studies. CONCLUSIONS: Although this review substantiated the critical relevance of certain basic numerical skills, it also highlights a need for future research to evaluate the structure of early numeracy in a more systematic and coordinated way to increase comparability and coherence across studies.

The association of basic numerical abilities and math achievement: The mediating role of visuospatial and arithmetical abilities.

Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. The results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithmetical abilities as well as basic numerical abilities such as number line estimation (i.e., the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement.

Neuromotor examination in unilateral cerebral palsy: Bilateral impairments in different levels of motor integration.

Unilateral cerebral palsy (UCP) usually results in damage to the unilateral pyramidal system. However, the clinical presentation of neuromotor deficits also suggests lesions to the extrapyramidal and cerebellar systems bilaterally. In this study, we developed and tested a behavioral neuromotor examination protocol assessing impairments at three levels of motor integration for children with UCP, also considering impairments of the non-paretic upper limb as well as the influences of the laterality of the lesion. We included 30 children with UCP (10.79 ± 2.61 years) and 60 healthy children (8.27 ± 1.57 years) in the study. All children were assessed on general cognitive ability and classified according to the manual ability classification system (MACS). Our neuromotor examination protocol incorporated specific tasks for each level of motor integration: pyramidal, extrapyramidal and cerebellar. Children with UCP and controls did not differ with respect to general cognitive abilities and sex but children with UCP were significantly older. Controls performed significantly better than children with UCP on neuromotor tasks at all levels of motor integration. Additionally, performance of the non-plegine hand in children with UCP was significantly inferior to controls. With the exception of fine motor skills (pyramidal level), children with right and left UCP did not differ. Our behavioral neuromotor examination was sensitive to reveal impairments at all three levels of motor integration bilaterally in children with UCP-although more subtle for the non-paretic limb.