Journal of Numerical Cognition (JNC - PsychOpen)
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Reasoning About Fraction and Decimal Magnitudes, Reasoning Proportionally, and Mathematics Achievement in Australia and the United States
No full textThere is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and sixth grade students from two countries which differ in their approach to teaching fractions: Australia and the United States. We gathered data on fraction and decimal magnitude understanding, proportional reasoning, and a standardized mathematics achievement test on whole number computation. Across both countries, reasoning about rational magnitude (either fraction or decimal) was predictive of whole number computation, supporting the central role of rational number learning. However, the precise relation varied, indicating that cross-national differences in rational number instruction can influence the nature of the relation between understanding fraction and decimal magnitude and mathematics achievement. The relation between proportional reasoning and whole number computation was fully mediated by rational magnitude understanding, suggesting that a key mechanism for how reasoning about rational magnitude supports mathematics achievement: proportional reasoning supports the development of an accurate spatial representation of magnitude that can be flexibly and proportionally scaled, which in turn supports children’s mathematics learning. Together, these findings support using measurement models and spatial scaling strategies when teaching fractions and decimals
Distributed Practice and Time Pressure Interact to Affect Learning and Retention of Arithmetic Facts
No full textArithmetic is commonly taught through timed practice and drill, yet little research exists to guide optimal practice structure. This study investigated the effects of distributed practice and time pressure on the acquisition and retention of arithmetic facts. Following a pretest, adult participants (n = 211) were randomly assigned to learn unfamiliar times tables (17 and 19) in one of ten conditions in a 5 (spacing: daily, every other day, weekly, every 10 days, every other week) x 2 (time pressure: timed or untimed) factorial design. After the learning phase, retention tests were given to measure both accuracy and response time immediately, after a ten-day delay, and at the end of semester. Time pressure during learning elevated participants’ perceived stress. It also led to faster response times during testing when learning was spaced daily and every other day, but slower response times for all other spacings. These patterns were reversed in the absence of time pressure during learning. While timed and untimed practice during learning led to similar forgetting of practiced facts over time, untimed practice allowed participants to gradually improve on unpracticed facts and conceptually related facts across test phases. Ultimately, distributed practice and time pressure may interact in complex ways to affect the learning and retention of arithmetic facts, and the effects shown in previous studies using verbal material (e.g., narrative texts, word lists) may not generalize to arithmetic
“We Don’t Have Things for Counting”: An Exploration of Early Numeracy Skills and Home Learning Experiences of Children Growing up in Poverty in South Africa
No full textA child’s home environment has been shown to be related to the development of early numeracy skills in some countries. However, significant relationships between home learning environment and math achievement have not consistently been found, and likely vary across different cultural and socio-political contexts. Here we explored the home environment and early numeracy skills of 243 children (3-5 years), who were not attending preschool programmes in very low-income settings in Cape Town, South Africa. Caregivers completed a questionnaire including information regarding experiences of children in the home; children completed a number identification task, a counting task and the Give-N task. The amount of resources in the home learning environment (e.g. the number of books and toys), frequency of home learning activities caregivers did with their children, and caregiver levels of education and income were not associated with number knowledge. While the home learning environment has been shown to be important for developing early numeracy skills in previous research, this study suggests that factors other than the home learning environment may also be important targets to foster numeracy skills and school readiness in low-income settings in South Africa
Does Spontaneous Attention to Relations Predict Conceptual Knowledge of Negative Numbers?
No full textMastery of mathematics depends on the people’s ability to manipulate and abstract values such as negative numbers. Knowledge of arithmetic principles does not necessarily generalize from positive number arithmetic to arithmetic involving negative numbers (Prather & Alibali, 2008, https://doi.org/10.1080/03640210701864147). In this study, we evaluate the relationship between participant’s knowledge of the Relation to Operands arithmetic principle in both positive and negative numbers and their spontaneous on numerical relations. Additionally, we tested if the feedback that directs attention to relations affects participants’ attention to relation and their arithmetic principle knowledge. This study contributes to our understanding of the specific skills and cognitive processes that are associated with understanding high-level mathematics
Are Approximate Number System Representations Numerical?
No full textPrevious research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by amalgamating perceptual features confounded with the set’s cardinality. In this paper, we approach the question of whether ANS representations are numerical by studying the properties they have, rather than how they are formed. Across two pre-registered within-subjects studies, we measured 189 participants’ ability to multiply the numbers between 2 and 8. Participants completed symbolic and nonsymbolic versions of the task. Results showed that participants succeeded at above-chance levels when multiplying nonsymbolic representations within the subitizing range (2-4) but were at chance levels when multiplying numbers within the ANS range (5-8). We conclude that, unlike Object Tracking System (OTS) representations, two ANS representations cannot be multiplied together. We suggest that investigating which numerical properties ANS representations possess may advance the debate over whether the ANS is a genuinely numerical system
Successful Discrimination of Tiny Numerical Differences
No full textAre there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an above-chance rate, this prediction has rarely been empirically tested for any psychological dimension, and never for the domain of number perception. In an experiment with over 400 adults, we find that observers can distinguish which of two collections has more dots from a brief glance. Impressively, observers performed above chance on every numerical comparison tested, even when discriminating a comparison as difficult as 50 versus 51 dots. Thus, we present empirical evidence that numerical discrimination abilities, consistent with SDT, are remarkably fine-grained
Measuring Math Anxiety Through Self-Reports and Physiological Data
No full textMath anxiety (MA) is an important affective factor that contributes to individuals’ math proficiency. While self-reports are commonly used to measure MA, a number of limitations are inherently connected to this measuring method. Physiological responses are considered a promising alternative approach, but research is scarce and the empirical evidence is scattered. Therefore, this paper aimed to (1) investigate whether different types of tasks (i.e., difficulty and topic) result in differences regarding self-reported anxiety and physiological measures, and (2) analyse whether physiological measures can account for differences in self-reported MA. We manipulated the difficulty level of a math and non-math task, so this study had a two-by-two experimental within-subject design. The participants were 44 undergraduate students. In terms of the first research aim, results revealed that the difficult math task elicited more self-reported anxiety compared to the easy math task and the difficult non-math task. However, these differences are barely detected by physiological measures. Regarding the second research aim, results showed that phasic galvanic skin responses and heart coherence ratio significantly predicted the self-reported MA. Our findings point to a possible contribution of using physiological measures to understand the construct of MA, meanwhile warning for a too optimistic use of this measurement method
A Meta-Analysis of Math Anxiety Interventions
No full textThe experience of math anxiety can have detrimental effects on students’ math performance, and researchers have in recent years tried to design interventions aiming at reducing math anxiety. This meta-analysis aimed to examine the effectiveness of math anxiety interventions in reducing math anxiety and improving math performance. The meta-analysis comprised 50 studies and included 75 effect sizes. On average, the effect sizes were moderate (g = -0.467) for reducing math anxiety and improving math performance (g = 0.502). Interventions that focused on Cognitive support or regulating Emotions were effective both in reducing math anxiety and improving math performance. In addition, longer interventions and interventions targeting students older than 12 had the biggest decrease in math anxiety. Study quality was not related to intervention outcomes
The Relation Between Math Anxiety and Play Behaviors in 4- to 6-Year-Old Children
No full textFrom a young age, children’s math achievement is influenced by individual factors, such as math anxiety. While math anxiety has been linked to math avoidance, few studies have explored this link in young children, particularly in the context of play. Because play-based instruction is commonly used for math in early childhood classrooms, understanding the impact of math anxiety on children’s engagement in math-related play may have important implications for children’s early math learning. The current study examined the role of children’s math anxiety in their persistence and exploration during a math toy play task. We observed wide variability in children’s play behaviors, finding that children’s actions during play did not relate to their math anxiety, but their talk related to math while playing with the toy did. There are also age and gender differences in math anxiety, school experience, and reasoning about the toy play task. These results suggest that math anxiety may influence certain aspects of children’s engagement in math-related play, and that more research is needed to consider links between math anxiety and math avoidance in young children
The Real Preschoolers of Orange County: Early Number Learning in a Diverse Group of Children
No full textThe authors assessed a battery of number skills in a sample of over 500 preschoolers, including both monolingual and bilingual/multilingual learners from households at a range of socio-economic levels. Receptive vocabulary was measured in English for all children, and also in Spanish for those who spoke it. The first goal of the study was to describe entailment relations among numeracy skills by analyzing patterns of co-occurrence. Findings indicated that transitive and intransitive counting skills are jointly present when children show understanding of cardinality and that cardinality and knowledge of written number symbols are jointly present when children successfully use number lines. The study’s second goal was to describe relations between symbolic numeracy and language context (i.e., monolingual vs. bilingual contexts), separating these from well-documented socio-economic influences such as household income and parental education: Language context had only a modest effect on numeracy, with no differences detectable on most tasks. However, a difference did appear on the scaffolded number-line task, where bilingual learners performed slightly better than monolinguals. The third goal of the study was to find out whether symbolic number knowledge for one subset of children (Spanish/English bilingual learners from low-income households) differed when tested in their home language (Spanish) vs. their language of preschool instruction (English): Findings indicated that children performed as well or better in English than in Spanish for all measures, even when their receptive vocabulary scores in Spanish were higher than in English