Journal of Numerical Cognition (JNC - PsychOpen)
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The Nature of Math Anxiety in Adults: Prevalence and Correlates
No full textIt is important to understand the nature of math anxiety in the general adult population, as the importance of math skills does not end when one leaves school. To this end, we present a well-powered, preregistered study of English-speaking U.S. adults describing the nature of math anxiety in this population. 1000 participants were recruited online. Math anxiety was approximately normally distributed, with the mean between “some” and “moderate”. Math anxiety was significantly negatively correlated with probability knowledge and math fluency, and significantly positively correlated with general anxiety and test anxiety. Women reported higher math anxiety than did men. Participants who had completed graduate school or had a STEM career had significantly lower levels of math anxiety than did those with less education, or non-STEM careers. Thus, we see evidence for math anxiety in U.S. adults and that it correlates with factors also reported in previous studies using younger and student populations
Utilizing Analogical Reasoning to Aid Children’s Proportional Reasoning Understanding
No full textProportional reasoning is an important skill that relates to fraction learning and math achievement. Because both proportional and analogical reasoning involve comparing relations, we hypothesized that supports for analogical reasoning (multiple exemplars and labels) would help children match discrete proportions. Fourth and 5th graders (N = 119) completed a 16-item proportional equivalence choice task in a 2 (exemplars: one, two) x 3 (script type: juice mixing narrative, novel adjectives, no labels) x 2 (trial type: part-foil, whole-foil) mixed-effects design. The juice mixing script included common labels and a story paradigm, whereas the novel adjectives script only utilized common labels. The least-informative no-labels script served as a baseline. Results showed a significant three-way interaction between exemplars, script type, and trial type. Viewing two exemplars led to no significant differences across the other factors. However, when viewing one exemplar, children exhibited a part-matching bias with novel adjectives and no labels, but not the juice narrative. In sum, multiple exemplars and the juice narrative reduced children’s part-matching bias; we conclude that supports for analogical reasoning can aid proportional reasoning as well
Adaptive Number Knowledge in Secondary School Students: Profiles and Antecedents
No full textThe present study aims to examine inter-individual differences in adaptive number knowledge in secondary school students. Adaptive number knowledge is defined as a well-connected network of knowledge of numerical characteristics and arithmetic relations. Substantial and relevant qualitative differences in the strategies and expression of adaptive number knowledge have been found in primary school students still in the process of learning arithmetic. We present a study involving 879 seventh-grade students that examines the structure of individual differences in adaptive number knowledge with students who have completed one year of algebra instruction. Results of a latent profile analysis reveal a model that is similar than was previously found in primary school students. As well, arithmetic fluency and the development of arithmetic fluency are strong predictors of adaptive number knowledge latent profile membership. These results suggest that adaptive number knowledge may be characteristic of high-level performance extending into secondary school, even after formal instruction with arithmetic concludes
Verbal Working Memory Load Dissociates Common Indices of the Numerical Distance Effect: Implications for the Study of Numerical Cognition
No full textIn four experiments, we explore the role that verbal WM plays in numerical comparison. Experiment 1 demonstrates that verbal WM load differentially impacts the two most common variants of numerical comparison tasks, evidenced by distinct modulation of the size of the numerical distance effect (NDE). Specifically, when comparing one Arabic digit to a standard, the size of the NDE increases as a function of increased verbal WM load; however, when comparing two simultaneously presented Arabic digits, the size of the NDE decreases (and here is eliminated) as a function of an increased verbal WM load. Experiment 2, using the same task structure but different stimuli (physical size judgments), provides support for the notion that this pattern of results is unique to tasks employing numerical stimuli. Experiment 3 demonstrates that the patterns observed in Experiment 1 are not an artifact of the stimulus pairs used. Experiment 4 provides evidence that the differing pattern of results observed between Experiment 1 and Experiment 2 are due to differences in stimuli (numerical vs. non-numerical) rather than to other differences between tasks. These results are discussed in terms of current theories of numerical comparison
Is the Long-Term Association Between Symbolic Numerical Magnitude Processing and Arithmetic Bi-Directional?
No full textBy analyzing longitudinal data from the start to the end of primary education, we aimed to investigate whether symbolic numerical magnitude processing at the start of primary education predicted arithmetic at the end, and whether arithmetic at the start of primary education predicted later symbolic numerical magnitude processing skills at the end. In the first grade (start) and sixth grade (end) of primary education, the same group of children’s symbolic numerical magnitude processing skills and arithmetic competence were assessed. We were particularly interested in exploring the direction of the association between symbolic numerical magnitude processing and arithmetic and observed that this association was bi-directional across primary education. Symbolic numerical magnitude processing skills in first grade predicted arithmetic in sixth grade; but also the reversed direction turned out significant: Early arithmetic predicted later symbolic numerical magnitude processing skills. Both directions remained significant after controlling for motor speed and nonverbal reasoning. Critically, when controlling for auto-regressive effects of prior abilities, the symbolic comparison-arithmetic association was no longer significant, the reversed direction became marginally significant. This suggests that children’s arithmetic development across primary education to some extent strengthens their ability to process the numerical meaning of Arabic digits
Spatial Skills First: The Importance of Mental Rotation for Arithmetic Skill Acquisition
No full textConsidering the importance of arithmetic in school curricula, it is crucial to understand the cognitive processes underlying its successful acquisition. Previous research suggests the involvement of spatial skills, especially during arithmetic skill acquisition. We assessed the predictive effect of mental rotation on different arithmetic components in children halfway through elementary school. At this stage, additions and subtractions are already well mastered, while multiplications and divisions are newly acquired. Although mental rotation positively correlated with arithmetic performances regardless of operation, only multiplication, division and completion performances were significantly predicted by mental rotation when controlling for age, gender as well as domain-specific symbolic number skills and visuospatial short-term memory. This highlights the differential effects of mental rotation on arithmetic and suggests a particular importance for newly acquired arithmetic material. These findings extend previous research on the relation between spatial skills and arithmetic and yield practical information for mathematical education and instruction
Narrowing the Early Mathematics Gap: A Play-Based Intervention to Promote Low-Income Preschoolers’ Number Skills
No full textPreschoolers from low-income households lag behind preschoolers from middle-income households on numerical skills that underlie later mathematics achievement. However, it is unknown whether these gaps exist on parallel measures of symbolic and non-symbolic numerical skills. Experiment 1 indicated preschoolers from low-income backgrounds were less accurate than peers from middle-income backgrounds on a measure of symbolic magnitude comparison, but they performed equivalently on a measure of non-symbolic magnitude comparison. This suggests activities linking non-symbolic and symbolic number representations may be used to support children’s numerical knowledge. Experiment 2 randomly assigned low-income preschoolers (Mean Age = 4.7 years) to play either a numerical magnitude comparison or a numerical matching card game across four 15 min sessions over a 3-week period. The magnitude comparison card game led to significant improvements in participants’ symbolic magnitude comparison skills in an immediate posttest assessment. Following the intervention, low-income participants performed equivalently to an age- and gender-matched sample of middle-income preschoolers in symbolic magnitude comparison. These results suggest a brief intervention that combines non-symbolic and symbolic magnitude representations can support low-income preschoolers’ early numerical knowledge
Exploring the Influence of Basic Cognitive Skills on the Relation Between Math Performance and Math Anxiety
No full textWhat causes math anxiety? According to a cognitive deficits view, early weaknesses in basic number and spatial skills lead to poor performance and hence negative affect. A strong version of this view suggests that the relation between math anxiety and math performance among adults will be explained by deficits in spatial and basic number skills. In the present research, we tested a model to account for the relations among math anxiety, math performance, and cognitive skills (i.e., working memory, basic number and spatial skills) among adults (N = 90). We replicated the modest correlations observed between math anxiety and these cognitive skills. However, we did not find a direct link between basic number and spatial skills and math anxiety; instead, these relations were mediated by complex math performance. We conclude by rejecting the hypothesis that math anxiety in adults is linked directly to individual differences in spatial and basic numerical skills and suggest instead that the present results are consistent with the alternative view in which even basic numerical tasks, under certain conditions may evoke an anxiety response and mask skill proficiency. Finally, we note that caution should be applied when extrapolating correlational results to make causal claims about whether cognitive skills may be precursors in the development of math anxiety
Norms and Validation of the Online and Paper-and-Pencil Versions of the Abbreviated Math Anxiety Scale (AMAS) For Polish Adolescents and Adults
No full textThe Abbreviated Math Anxiety Scale (AMAS) is one of the most popular instruments measuring math anxiety (MA). It has been validated across several linguistic and cultural contexts. In this study, we investigated the extent of administration method invariance of the AMAS by comparing results (average scores, reliabilities, factorial structure) obtained online with those from paper-and-pencil. We administered the online version of the AMAS to Polish students. Results indicate that psychometric properties of the AMAS do not differ between online and paper-and-pencil administration. Additionally, average scores of the AMAS did not differ considerably between administration forms, contrary to previous results showing that computerized measurement of MA leads to higher scores. Therefore, our results provide evidence for the usefulness of the AMAS as a reliable and valid MA measurement tool for online research and online screening purposes across cultures and also large similarity between administration forms outside an American-English linguistic and cultural context. Finally, we provide percentile and standard norms for the AMAS for adolescents and adults (in the latter case for both online and paper-and-pencil administration) as well as critical differences for the comparison of both subscales in an individual participant for practical diagnostic purposes