Search

Math anxiety results in a drop in performance on various math-related tasks, including the symbolic number ordering task in which participants decide whether a triplet of digits is presented in order (e.g. 3-5-7) or not (e.g. 3-7-5). We investigated whether the strategy repertoire and reaction times during a symbolic ordering task were affected by math anxiety. In study 1, participants performed an untimed symbolic number ordering task and indicated the strategy they used on a trial-by-trial basis. The use of the memory retrieval strategy, based on the immediate recognition of the triplet, decreased with high math anxiety, but disappeared when controlling for general anxiety. In the study 2, participants completed a timed version of the number order task. High math-anxious participants used the decomposition strategy (e.g. 5 is larger than 3 and 7 is larger than 5 to decide whether 3-5-7 is in the correct order) more often, and were slower in responding when both memory- and other decomposition strategies were used. Altogether, both studies demonstrate that high-math anxious participants are not only slower to decide whether a number triplet is in the correct order, but also rely more on procedural strategies.

ispartof: COGNITIVE DEVELOPMENT vol:64 status: accepted

Some number-naming systems are less transparent than others. For example, in Dutch, 49 is named “negen¬enveertig”, which translates to “nine and forty”, i.e., the unit is named first, followed by the decade. This is known as the “inversion property”, where the morpho-syntactic representation of the number name is incongruent with its written Arabic form. Number word inversion can hamper children’s developing mathematical skills. But little is known about its effects on adults’ numeracy, the underlying mechanism and how a person’s bilingual background influences its effects. In the present study, Dutch-English bilingual adults performed an audiovisual matching task, where they heard a number word and simultaneously saw two-digit Arabic symbols and had to determine if these matched in quantity. We experimentally manipulated the morpho-syntactic structure of the number words to alter their phonological (dis)similarities and numerical congruency with the target Arabic two-digit number. Results showed that morpho-syntactic (in)congruency differentially influenced quantity match and non-match decisions. Although participants were faster when hearing traditional non-transparent Dutch number names, they made more accurate decisions when hearing artificial, but morpho-syntactically transparent number words. This pattern was partly influenced by the participants’ bilingual background, i.e., their L2 proficiency in English, which involves more transparent number names. Our findings suggest that, within inversion number-naming systems, multiple associations are formed between two-digit Arabic symbols and number names, which can influence adults’ numerical cognition.

Adaptive educational games provide new opportunities to train early numerical skills. However, empirical evidence for the effectiveness of adaptive educational games is scarce. This study investigated the effectiveness of an adaptive game compared to a nonadaptive game in terms of cognitive, noncognitive and efficiency outcomes. In total, 84 children were randomly assigned to a condition in which children trained early numerical skills with an adaptive version of the Number Sense Game (NSG), or to a condition in which they trained with a nonadaptive version. Early numeracy was evaluated before the training, immediately after the training and 3 weeks after the training. Math anxiety (MA) was assessed before and 3 weeks after the training. The time children practiced with the NSG was used to assess efficiency. Results revealed that children in both conditions improved on early numerical ability, with sustained effects 3 weeks after the training. In both conditions, children’s MA scores were lower after the training. Children in the adaptive condition learned more efficiently compared to the nonadaptive condition, and the interaction between prior knowledge and condition has shown that children with low prior knowledge benefited more from a nonadaptive training while children with high prior knowledge benefited more from an adaptive training in terms of learning efficiency. These results confirm that adaptive educational games can offer solace in terms of the need for differentiation. ispartof: British Journal Of Educational Technology vol:52 issue:1 pages:112-124 status: Published online

Math permeates everyday life, and math skills are linked to general educational attainment, income, career choice, likelihood of full-time employment, and health and financial decision making. Thus, researchers have attempted to understand factors predicting math performance in order to identify ways of supporting math development. Work examining individual differences in math performance typically focuses on either cognitive predictors, including inhibitory control and the approximate number system (ANS; a nonsymbolic numerical comparison system), or affective predictors, like math anxiety. Studies with children suggest that these factors are interrelated, warranting examination of whether and how each uniquely and independently contributes to math performance in adulthood. Here, we examined how inhibitory control, the ANS, and math anxiety predicted college students' math performance (n = 122, mean age = 19.70 years). Using structural equation modeling, we find that although inhibitory control and the ANS were closely related to each other, they did not predict math performance above and beyond the effects of the other while also controlling for math anxiety. Instead, math anxiety was the only unique predictor of math performance. These findings contradict previous results in children and reinforce the need to consider affective factors in our discussions and interventions for supporting math performance in college students. ispartof: Annals Of The New York Academy Of Sciences vol:1511 issue:1 pages:173-190 ispartof: location:United States status: published

Previous research has suggested that Event-Related Potentials (ERPs) can index form-, meaning-, and use-related aspects of the second language (L2) vocabulary knowledge, through, respectively, a lexical decision task (LDT, targeting N400), a semantic relatedness task (SEMREL, targeting N400), and a grammatical judgment task (GJT, targeting P600/AN). Yet, those findings were established in the context of either laboratory-based or longitudinal word learning studies. Therefore, this conceptual replication study investigates whether LDT, SEMREL, and GJT could reveal the aforementioned ERP components in the context of an ecologically valid short-term intervention representative of L2 classroom practice. Twenty Dutch-speaking participants performed reading and writing tasks in a computer-assisted learning environment. Target words were 20 real L2 French verbs. ERPs were recorded immediately after the learning sessions. Results showed N400 for form- and meaning-related knowledge and P600 for grammatical use. We conclude that ERPs can index L2 vocabulary knowledge gained through ecologically valid classroom activities.

ispartof: LEARNING AND INDIVIDUAL DIFFERENCES vol:102 status: published

When learning the meaning of symbolic numbers, children learn the numbers up to 4 sequen-tially. A prominent account of this learning process proposes that the increasing sensitivity of the preverbal approximate number system (ANS) allows for reliable discrimination of increasingly large neighboring numbers, which, consequently, leads to the sequential acquisition of the first symbolic numbers. In this work, a more complete quantitative description of this account is provided. This description is based on the mathematical model of the ANS and on additional relevant parameter values reported in the literature. The quantitative description demonstrates that, in the time period during which children learn the meaning of the first number words, the improvement of ANS sensitivity cannot provide the assumed changes in the discriminability of these numbers. The present result challenges the role of the ANS as a leading factor in the acquisition of the first symbolic numbers.

Clarke and Beck (C&B) discuss in their sections on congruency and confounds (sects. 3 and 4) literature that has challenged the claim that the approximate number system (ANS) represents numerical content. We argue that the propositions put forward by these studies aren't that far from the indirect model of number perception suggested by C&B. ispartof: BEHAVIORAL AND BRAIN SCIENCES vol:44 ispartof: location:England status: published

How humans integrate and abstract numerical information across different formats is one of the most debated questions in human cognition. We addressed the neuronal signatures of the numerical integration using an EEG technique tagged at the frequency of visual stimulation. In an oddball design, participants were stimulated with standard sequences of numbers ( 5) was inserted at 1.25 Hz. We observed significant oddball amplitudes for all single notations, showing for the first time using this EEG technique, that the magnitude information is spontaneously and unintentionally abstracted, irrespectively of the numerical format. Significant amplitudes were also observed for digits-number words and number words-dots, but not for digits-dots, suggesting an automatic integration across some numerical formats. These results imply that direct and indirect neuro-cognitive links exist across the different numerical formats. ispartof: SCIENTIFIC REPORTS vol:11 issue:1 ispartof: location:England status: published

Humans can estimate the number of visually displayed items without counting. This capacity of numerosity perception has often been attributed to a dedicated system to estimate numerosity, or alternatively to the exploitation of various stimulus features, such as density, convex hull, the size of items and occupancy area. The distribution of the presented items is usually not varied with eccentricity in the visual field. However, our visual fields are highly asymmetric, and to date, it is unclear how inhomogeneities of the visual field impact numerosity perception. Besides eccentricity, a pronounced asymmetry is the radial-tangential anisotropy. For example, in crowding, radially placed flankers interfere more strongly with target perception than tangentially placed flankers. Similarly, in redundancy masking, the number of perceived items in repeating patterns is reduced when the items are arranged radially but not when they are arranged tangentially. Here, we investigated whether numerosity perception is subject to the radial-tangential anisotropy of spatial vision to shed light on the underlying topology of numerosity perception. Observers were presented with varying numbers of discs and asked to report the perceived number. There were two conditions. Discs were predominantly arranged radially in the “radial” condition and tangentially in the “tangential” condition. Additionally, the spacing between discs was scaled with eccentricity. Physical properties, such as average eccentricity, average spacing, convex hull, and density were kept as similar as possible in the two conditions. Radial arrangements were expected to yield underestimation compared to tangential arrangements. Consistent with the hypothesis, numerosity estimates in the radial condition were lower compared to the tangential condition. Magnitudes of radial alignment (as well as predicted crowding strength) correlated with the observed numerosity estimates. Our results demonstrate a robust radial-tangential anisotropy, suggesting that the topology of spatial vision determines numerosity estimation. We suggest that asymmetries of spatial vision should be taken into account when investigating numerosity estimation.

ispartof: British Journal Of Educational Technology vol:52 issue:5 pages:1881-1897 status: published

Understanding whether a sequence is presented in an order or not (i.e., ordinality) is a robust predictor of adults' arithmetic performance, but the mechanisms underlying this skill and its relationship with mathematics remain unclear. In this study, we examined (a) the cognitive strategies involved in ordinality inferred from behavioural effects observed in different types of sequences and (b) whether ordinality is also related to mathematical reasoning besides arithmetic. In Experiment 1, participants performed an arithmetic, a mathematical reasoning test, and an order task, which had balanced trials on the basis of order, direction, regularity, and distance. We observed standard distance effects (DEs) for ordered and non-ordered sequences, which suggest reliance on magnitude comparison strategies. This contradicts past studies that reported reversed distance effects (RDEs) for some types of sequences, which suggest reliance on retrieval strategies. Also, we found that ordinality predicted arithmetic but not mathematical reasoning when controlling for fluid intelligence. In Experiment 2, we investigated whether the aforementioned absence of RDEs was because of our trial list composition. Participants performed two order tasks: in both tasks, no RDE was found demonstrating the fragility of the RDE. In addition, results showed that the strategies used when processing ordinality were modulated by the trial list composition and presentation order of the tasks. Altogether, these findings reveal that ordinality is strongly related to arithmetic and that the strategies used when processing ordinality are highly dependent on the context in which the task is presented. ispartof: QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY vol:74 issue:11 pages:1935-1952 ispartof: location:England status: published

In numerical cognition research, it has traditionally been argued that the processing of symbolic numerals (e.g., digits) is identical to the processing of the non-symbolic numerosities (e.g., dot arrays), because both number formats are represented in one common magnitude system—the Approximate Number System (ANS). In this study, we abandon this deeply rooted assumption and investigate whether the processing of numerals and numerosities can be dissociated, using an audio-visual paradigm in combination with various experimental manipulations. In Experiment 1, participants performed four comparison tasks with large symbolic and non-symbolic numbers: (1) number word–digit (2) tones–dots, (3) number word–dots, (4) tones–digit. In Experiment 2, we manipulated the number range (small vs. large) and the presentation modality (visual–auditory vs. auditory–visual). Results demonstrated ratio effects (i.e., the signature of ANS being addressed) in all tasks containing numerosities, but not in the task containing numerals only. Additionally, a cognitive cost was observed when participants had to integrate symbolic and non-symbolic numbers. Therefore, these results provide robust (i.e., independent of presentation modality or number range) evidence for distinct processing of numerals and numerosities, and argue for the existence of two independent number processing systems. ispartof: Psychological Research-Psychologische Forschung vol:85 issue:2 pages:764-776 ispartof: location:Germany status: published

Two recent studies investigated how children learn to map between digits, number words, and dots (Hurst, Anderson, & Cordes, 2017; Jiménez-Lira, Carver, Douglas, & LeFevre, 2017). In the current study we aimed to replicate these previous findings by examining a much larger sample (N = 195 kindergarteners, aged 2 years 6 months to 5 years 2 months) and taking into account home numeracy activities, that is, daily parent-child interactions with numerical content. In line with previous studies, the results showed that children first learn to map number words onto dots, and number words onto digits, and only afterwards – to map digits onto dots. Furthermore, number words ↔ digits mapping was a better mediator of the relation between digits ↔ dots and the dots ↔ number words mapping tasks, than the dots ↔ number words, suggesting that children rely on their symbolic number knowledge to learn the relation between digits and dots. Finally, both basic and advanced home numeracy activities were positively related to children’s mappings skills. Furthermore, we observed that with increasing the children’s age a shift from basic to advanced activities was present. These results emphasize the importance of tailoring the home numeracy activities according to children’s age. ispartof: Cognitive Development vol:57 pages:1-14 status: published

Math is fundamental to many situations in everyday life such as managing money, preparing food, or making music. Therefore education aims to learn children and adolescents number and math concepts, to enhance math fluency, and to obtain more advanced mathematics. However, a lot of learners have problems with reaching these goals, or even worse, they develop severe difficulties or disorders. This impacts their daily life as they are not able to transfer this knowledge to real-world problems, but it also impedes their future school career and chances on the labor market. Therefore it is crucial to pinpoint which interventions are effective in fostering learners’ number and math performance. For this purpose, we conducted a comprehensive overview of previous reviews and metaanalyses, i.e., a metareview, targeting early numeracy or more advanced mathematics, focusing on both typical and atypical (or at risk) achievers in preschool, primary, or secondary education. Forty-one reviews/metaanalyses were included in this metareview and were analyzed in order to find information that could help us provide an answer on one of the following questions: (1) are math interventions less/more effective in different age groups? (“when”); (2) are math interventions less/more effective for particular math content and does the duration of the intervention moderate effectivity? (“what and how long”); (3) are math interventions less/more effective when they make use of a specific instructional method? (“how”); (4) are math interventions less/more effective for specific samples? (“who”). In addition, all reviews and metaanalyses were also scanned for statements with respect to the quality of interventions. The metareview revealed evidence-based information about the effectiveness of particular interventions and reveals gaps in the literature that may provide challenges for future research.

Cognitive control is crucial to resolve conflict in tasks such as the flanker task. Reactive control is used when conflict is rare, whereas proactive control is more efficient in situations where conflict is frequent. Macizo and Herrera (Psychological Research, 2013, Vol. 77, pp. 651–658) found that these two control processes can also underlie two-digit number comparison in adults. Specifically, they observed that the unit–decade compatibility effect decreased in a block containing many conflict trials as compared with a block containing few conflict trials (i.e., a list-wide proportion congruency effect). In the current study, we assessed whether this finding also applies to children (7-, 9-, and 11-year-olds). Participants performed a flanker task and a two-digit number comparison task. In both tasks, the proportion of conflict was manipulated (80% vs. 20%). Results from the flanker task showed a typical list-wide proportion congruency effect in reaction times in all participating age groups. In the number comparison task, we observed list-wide proportion congruency effects in both reaction times and error rates, which did not interact with age. Our findings support the assumption that children as young as 7 years can effectively use proactive and reactive control strategies. We showed that this effect is not limited to standardized artificial laboratory tasks, such as the flanker task, but also underlies more daily life tasks, such as the processing of Arabic numbers.

Background Many children with developmental coordination disorder (DCD) have mathematical problems which are more pronounced for mathematical skills that also require executive functions. Although empirical evidence is missing, math and special education need teachers of children with DCD report difficulties with mathematical word problem solving that can be remediated by providing the children with scaffolds cueing the intermediate steps. Aims This study aims to find empirical evidence for the effectivity of such additional support. In addition, we want to investigate whether the difficulties are due to inefficient arithmetic or executive functioning skills. Methods and Procedures A DCD and a control group solved word problems with and without scaffolds and conducted a series of tasks measuring calculation and executive skills. Outcomes and Results Performance improves when scaffolds are presented to children with DCD. Children with DCD and control children differ on executive functioning tasks but perform similarly on arithmetic tests. Conclusions and Implications Providing scaffolds for word problem solving is effective in children with DCD. Scaffolds possibly reduce the required cognitive load, making the problem solvable for DCD children that have reduced executive functioning skills.

Digital educational games play an increasingly important role in education. However, multiple questions about the effectiveness of educational games with respect to cognitive and non-cognitive effects remain unclear. The current study, a longitudinal, quasi-experiment with 336 first graders, examined the effects of two digital educational games, Number Sense Game (NSG) and Reading Game (RG). The NSG trained early numerical skills, the RG supported emergent reading. Children were pseudo-randomly assigned to either an experimental condition, comprising eight weeks of intensive game-based training, or a control condition in which they took part in regular education without game-based practice. A pretest-posttest design was used to examine the effects of the intervention on cognitive (digit comparison, number line estimation, letter knowledge, math and reading competence) and non-cognitive outcomes (math and reading anxiety). Delayed cognitive effects on math and reading competence were also investigated two months after the intervention. Furthermore, we examined variances of the impact of the training on cognitive outcomes as a consequence of differences in children's prior knowledge, prior affect and socio-economic status. For cognitive outcomes, results revealed that children who played a game performed better on number line estimation and reading competence, whereas no significant differences were observed for digit comparison, letter knowledge and math competence. Also, children who played a game showed better scores in the delayed reading posttest, but not in the delayed math posttest. For non-cognitive outcomes, game training did not affect math or reading anxiety. Regarding individual differences, children with less prior knowledge in the game play condition performed better on the number line estimation posttest compared to children in the control condition. Children with more prior knowledge in the game play condition still scored better on this test compared to the control condition, but the difference between the conditions was smaller.

ispartof: Journal Of Computer Assisted Learning vol:2020 issue:4 pages:1-12 status: Published online

Home numeracy has been defined as the parent-child interactions that include experiences with numerical content in daily-life settings. Previous studies have commonly operationalized home numeracy either via questionnaires or via observational methods. These studies have shown that both types of measures are positively related to variability in children's mathematical skills. This study investigated whether these distinctive data collection methods index the same aspect of home numeracy. The frequencies of home numeracy activities and parents' opinions about their children's mathematics education were assessed via a questionnaire. The amount of home numeracy talk was observed via two semi-structured videotaped parent-child activity sessions (Lego building and book reading). Children's mathematical skills were examined with two calculation subtests. We observed that parents' reports and number of observed numeracy interactions were not related to each other. Interestingly, parents' reports of numeracy activities were positively related to children's calculation abilities, whereas the observed home numeracy talk was negatively related to children's calculation abilities. These results indicate that these two methods tap on different aspects of home numeracy. Statement of contribution What is already known on this subject? Home numeracy, that is, parent-child interactions that include experiences with numerical content, is supposed to have a positive impact on calculation or mathematical ability in general. Despite many positive results, some studies have failed to find such an association. Home numeracy has been assessed with questionnaires on the frequency of numerical experiences and observations of parent-child interactions; however, those two measures of home numeracy have never been compared directly. What does this study add? This study assessed home numeracy through questionnaires and observations in the 44 parent-child dyads and showed that home numeracy measures derived from questionnaires and observations are not related. Moreover, the relation between the reported frequency of home numeracy activities and calculation on the one hand, and parent-child number talk (derived from observations) and calculation on the other hand is in opposite directions; the frequency of activities is positively related to calculation performance; and the amount of number talk is negatively related to calculation. This study shows that both measures tap into different aspects of home numeracy and can be an important factor explaining inconsistencies in literature.

Digit order processing is highly related to individual differences in arithmetic performance. To examine whether serial scanning or associative mechanisms underlie order processing, order tasks (i.e. deciding whether three digits were presented in an order or not) were administered in two experiments. In the first experiment, digits were presented in different directions namely ascending, descending and non-ordered. For each direction, close and far distance sequences were presented. Results revealed reversed distance effects for ordered sequences, but ascending sequences elicited faster performance and stronger reversed distance effects than descending sequences, suggesting that associative mechanisms underlie order processing. In the second experiment, it was examined to which extent the relation between order processing and arithmetic is number-specific by presenting order tasks with digits, letters and months. In all order tasks similar distance effects were observed and similar relations with arithmetic were found, suggesting that both general associative mechanisms and number-specific mechanisms contribute to arithmetic., SCOPUS: ar.j, info:eu-repo/semantics/published

Children's intuitive understanding of number, i.e. number sense, is associated with individual differences in mathematics achievement. To investigate the causal association between number sense, traditionally assessed with comparison or number line estimation tasks, and mathematics achievement, often assessed with an arithmetic test, an intervention study was conducted that aimed at training either comparison or number line estimation skills. We contrasted a comparison and number line estimation training. By doing so, we wanted to address the question which intervention had the largest effect on arithmetic. In addition, such a direct comparison between comparison and number line estimation trainings would allow us to get more insight in the association between both tasks. Participants were 151 five-year-olds that were randomly allocated to either an experimental condition (i.e. comparison or number line estimation) or one of the two control conditions (i.e., active control condition and empty control condition) in a pretest-posttest design measuring number knowledge, (non-)symbolic comparison and number line estimation and arithmetic. The results showed that both comparison and number line estimation trainings had a positive effect on arithmetic. However, the absence of transfer effects from one task to another, also suggested that comparison and number line estimation rely on different mechanisms and probably influence arithmetic through different mechanisms.

Three theoretical accounts have been put forward for the development of children‟s response patterns on number line estimation (NLE) tasks: the log-to-linear representational shift, the two-linear-to-linear transformation and the proportion judgment account. Despite the ongoing debate, it remains to date unclear which of these three developmental accounts reflects best how children‟s NLE performance evolve through development. The present study is the first which contrasted these three accounts in both symbolic and non-symbolic NLE performance of children at different ages, cross-sectionally as well as longitudinally: In Experiment 1, first, second and sixth graders were examined. In Experiment 2, first and second graders were tested again one year later. In case of symbolic estimations, the proportion judgment account described the data best. Most young children‟s non-symbolic estimation patterns were best described by a logarithmic model (within the log-to-lin account), whereas those of most older children were best described by the simple power model (within the proportion judgment account). Together, in line with the integrative account proposed by Dackermann et al. (2015), these data suggest that the development of children‟s symbolic and non-symbolic NLE patterns does not reflect a developmental change in their mental representations of number per se, but rather the trajectory of when they start using (advanced) cognitive strategies on those number representations – a process that might be modulated by their numerical knowledge. ispartof: Psychologica Belgica vol:56 issue:4 pages:382-405 ispartof: location:England status: published