Journal of Numerical Cognition (JNC - PsychOpen)
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Money Talks! The Role of Parents’ Discussion of Money for Preschoolers’ Math Knowledge
No full textChildren’s participation in cultural, everyday practices and social interactions involving math and money can contribute to the development of their knowledge and skills in these domains. Further work is needed to uncover what features of these activities, such as aspects of the conversations that may occur (e.g., number and money talk), facilitate and/or are shaped by children’s understanding of money concepts and skills. The present study examined the extent to which parents engaged in conversations about numbers and money with their four-year-old children during pretend grocery play and the relations to children’s math skills. We found that talk about price labeling and exchanging currency or goods occurred most frequently and that money and number talk were not significantly related to children’s broader math skills. However, parents’ money talk was positively associated with children’s money-related math skills, and this association was driven by the co-occurrence of talk about money and numbers. Our results suggest that parent-child conversations in familiar contexts such as grocery shopping provide rich opportunities to discuss culturally relevant practices surrounding money and practice math skills in the context of monetary exchanges. Thus, it is critical to consider how existing family practices and everyday contexts support children’s early math learning
Parental Math Anxiety Is Associated With Negative Emotional Activation During Hypothetical Health Decision Making
No full textDealing with numbers is an inherent aspect of interpreting health statistics, and negative emotions may interfere with medical decision making. One emotionally charged decision-making context is parents making medical decisions for their children. Knowing which factors–such as anxiety specific to math contexts–are associated with parents’ negative emotions during the decision-making process may inform ways to better support families as they make critical medical decisions. The current study involved secondary data analyses of an experiment with 249 parents. Participants were randomly assigned to make hypothetical health decisions for themselves, their child, or a stranger. We examined which domain-specific math (e.g., math anxiety), domain general (i.e., need for cognition), and demographic variables (e.g., parents’ health-care coverage) were associated with ratings of negative emotional activation immediately after making the decisions. Results indicated that two factors were significantly associated with parents’ ratings of negative emotional activation: (1) the person they were making decisions about (i.e., higher negative emotion activation if they were randomly assigned to make hypothetical health decisions about their child versus themselves or a stranger), and (2) parents’ ratings of their own math anxiety (i.e., parents with higher self-reported math anxiety also reported higher negative emotional activation). Future research may further consider the joint roles of emotional activation and math anxiety in how parents make health decisions for their children. Further, understanding how much math anxiety causally contributes to people’s overall negative emotional activation could lead to a more nuanced understanding of negative emotional activation in health decision making
Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions
No full textStudents often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order of precedence (the order of operations). Research has shown that the syntactic structure of problems, and students’ perceptual processes, are involved in mathematics performance and developing fluency with precedence. We examined 837 U.S. middle schoolers’ propensity for precedence errors on six problems in an online mathematics game. We included an algebra knowledge assessment, math anxiety measure, and a perceptual math equivalence task measuring quick detection of equivalent expressions as predictors of students’ precedence errors. We found that students made more precedence errors when the leftmost operation was invalid (addition followed by multiplication). Individual difference analyses revealed that students varied in propensity for precedence errors, which was better predicted by students’ performance on the perceptual math equivalence task than by their algebra knowledge or math anxiety. Students’ performance on the perceptual task and interactive game provide rich insights into their real-time understanding of precedence and the role of perceptual processes in equation solving
A Brief, Multiple-Choice Assessment of Mature Number Sense Is Strongly Correlated With More Resource-Intensive Measures
No full textStudents who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of strategy usage. Yet, the lack of an efficient, rigorously developed measure has made it difficult to collect systematic, replicable evidence on students’ mature number sense. To address this, we developed a brief assessment of mature number sense. The present study provides additional convergent evidence of validity for this measure with US students in grades 3-8 (8–14 years old). We compared middle school (N = 40) and upper elementary school (N = 41) scores from the brief assessment with an established, time-intensive measure (Yang, 2019, https://doi.org/10.1007/s10649-018-9874-8) and an in-depth interview of student strategy usage (Markovits & Sowder, 1994, https://doi.org/10.2307/749290). We found strong correlations (r > 0.7) across all three measures, and this held even when controlling for students’ arithmetic scores (pr > 0.6). Researchers and educators can now use the brief assessment to investigate students’ mathematical thinking and advance knowledge of a key aspect of mathematical cognition
Routine and Adaptive Experts: Individual Characteristics and Their Impact on Multidigit Arithmetic Strategy Flexibility and Mathematics Achievement
No full textMotivated by a curriculum privileging number-based strategies but national tests highlighting students’ reliance on standard algorithms, this study analyses 2,216 Danish Grade 3, 6 and 8 students’ solutions to various multidigit arithmetic tasks, each designed to elicit shortcut strategies, against background variables including sex, ethnicity and familial socio-economic status (SES), and outcomes including strategy flexibility, and national tests for both mathematics and reading. Students offering multiple solutions to a task were defined as flexible, while arithmetic experts (defined by accuracy) were distinguished by their use of shortcut strategies; routine experts never used them, while adaptive experts used them in at least one third of all tasks. With respect to mathematics achievement, experts scored 0.86 SD-units higher than non-experts, and within the former, adaptive experts scored 0.49 SD-units higher than routine experts. With respect to reading, experts achieved 0.57 SD-units higher than non-experts, while adaptive experts achieved 0.19 SD-units higher than routine experts. Boys were significantly more adaptive and flexible than girls. The proportion of experts increased from Grade 3 to Grade 8, whereas the proportion of adaptive experts increased from Grade 3 to 6 but then remained constant. Familial SES was significantly higher for experts than for non-experts but not for adaptive experts in relation to routine. Neither quarter of birth nor the existence of older siblings influenced any outcomes, although the proportion of experts was higher for children with Western backgrounds than for children with non-western background. The results suggest a relationship between adaptive expertise, strategy flexibility, and achievement
Understanding the Role of Working Memory and Phonological Memory in Mathematics and Response to Intervention for Emergent Bilingual Kindergartners
No full textThis study explores how kindergarten students from a multilingual sample (n = 131) representing 23 different languages differ in response to intervention, based on their skill in mathematics and domain general cognitive skills. Analyses for this study indicate significant correlations between initial math skill, phonological memory, working memory, and language proficiency. There was no statistically significant relationship demonstrated between gains in mathematics and phonological memory, working memory, and language proficiency. No moderation effect was found between domain general skills and response to math intervention. Implications of this work will inform development and delivery of math interventions for multilingual students in kindergarten
Do Errors on Classic Decision Biases Happen Fast or Slow? Numeracy and Decision Time Predict Probability Matching, Sample Size Neglect, and Ratio Bias
No full textHigher numeracy is associated with better comprehension and use of numeric information as well as reduced susceptibility to some decision biases. We extended this line of work by showing that increased numeracy predicted probability maximizing (versus matching) as well as a better appreciation of large sample sizes. At the same time, we replicated the findings that the more numerate were less susceptible to the ratio bias and base rate neglect phenomena. Decision time predicted accuracy for the ratio bias, probability matching, and sample size scenarios, but not the base rate scenarios. Interestingly, this relationship between decision time and accuracy was positive for the ratio bias problems, but negative for the probability matching and sample size scenarios. Implications for research on cognitive ability and decision biases are discussed
Below Zero? Universal Distance Effect and Situated Space and Size Associations in Negative Numbers
No full textWhile some researchers place negative numbers on a so-called extended mental number line to the left of positive numbers, others claim that negative numbers do not have mental representations but are processed through positive numbers combined with transformation rules. We measured spatial associations of negative numbers with a modified implicit association task that avoids spatial confounds present in most previous studies. In two lab-based magnitude classification experiments (each including 24 participants) and two online replications (with 74 and 77 participants, respectively), positive and negative numbers were combined with two spatial contexts: either directional symbols (left- or right-pointing arrows) or rectangles of varying sizes. In all experiments, we found a robust distance effect for negative numbers. However, there were no consistent associations of negative numbers with directional or size contexts. In the context of directional symbols, holistic processing was prevalent only in the small negative number range (-9, -8, -7, -6) when ensured by the stimulus set, supporting an extended mental number line. In the context of rectangles, however, large negative numbers from -4 to -1 were perceived as small, thus supporting rule-based processing. For negative number processing in the context of size, we further suggest the Semantic-Perceptual Size Congruity Cuing model (SPeSiCC model). We show that associations of size with negative numbers underly more complex processing mechanisms than mere recruitment of a transformation rule. In general, we conclude that associations of negative numbers with space and size are situated in the context, as they depend on the presented number range and differ for spatial direction and size
Consumers With Math Anxiety, a Financially Vulnerable Group? Unpacking the Negative Relation Between Math Anxiety and Performance on a Price Comparison Task
No full textComparison shopping is good financial practice, but situations involving numbers and computations are challenging for consumers with math anxiety. We asked North Americans (N = 256) to select the better deal between two products differing in volume and price. As predicted, math anxiety was negatively related to performance on this Price Comparison Task. We then explored the mechanism underlying this relation by testing math competency, price calculation ability, need for cognition, and cognitive reflection as potential mediators. The results from a competing mediator analysis indicated that all factors, apart from need for cognition, served as significant independent mediators between math anxiety and performance on our Price Comparison Task. This study has important implications for how–and why–math anxiety relates to a person’s ability to accurately compare product prices. These data suggest that consumers higher in math anxiety may represent a financially vulnerable population, particularly in the context of financial tasks that are inherently mathematical
The Link Between Math Anxiety and Math Achievement: The Role of Afterschool Learning
No full textThe present study tested the learning avoidance model by examining the degree to which learning avoidance in various afterschool settings mediated the negative association between math anxiety and math achievement. Participants consisted of 207 third to sixth graders. Using a path model, findings showed that students’ math anxiety was negatively associated with both standardized math achievement test scores and parent-reported math school grades. Additionally, higher math anxiety was associated with more negative homework behaviors and less frequent participation in math-related extracurricular activities. Finally, the association between math anxiety and math achievement was partially mediated by negative math homework behaviors and participation in math extracurricular activities. Effort in math exam preparation did not contribute to explaining the association between math anxiety and math achievement. Overall, these findings support the learning avoidance model and suggest that avoidance behaviors in everyday learning in the afterschool setting may contribute to explaining the undesired math achievement among highly math anxious students