The moderating role of objective and subjective numeracy in attribute framing

Previous research has found that objective numeracy moderates framing effects: People who are less numerate were found to be more susceptible to goal‐framing and attribute‐framing effects than people who are highly numerate. This study examined the possibility that subjective numeracy likewise moderates attribute framing in contexts where participants are presented with percentages of success or failure. The results show that compared with highly numerate participants, less numerate participants were more susceptible to the effect of attribute framing. Interestingly, this moderating effect was revealed only when using objective numeracy measures, and not when subjective numeracy measures were used. Future research is suggested to replicate these findings, to establish the generalizability of numeracy as a moderator of other cognitive biases, and to examine several possible theoretical explanations for the differential moderation of attribute‐framing bias.     

Milestones in the development of infant numeracy

This article deals with the development of numeracy among young children of the four to seven year age group. The research investigation described had two aims: to see how early numeracy develops in children of different ages; and to see whether there are fixed points which might serve as milestones in the development of infant numeracy. The results of this investigation involving 96 children indicate a strong development of numeracy skills during this period. With reference to the literature, it is also shown that certain items of a test previously developed for this purpose may be taken as core items that do indeed represent milestones in the development of infant numeracy.     

Health numeracy and cognitive decline in advanced age

ABSTRACT

The study aimed at investigating health numeracy in cognitively well performing healthy participants aged from 50 to 95 years as well as in participants with cognitive impairment, but no dementia (CIND). In cognitively well performing participants (n = 401), demographic variables and cognitive abilities (executive functions, reading comprehension, mental calculation, vocabulary) were associated with health numeracy. Older age, lower education, female gender as well as lower cognitive functions predicted low health numeracy. The effect of older age was partly mediated by executive functions and calculation abilities. Participants with CIND (n = 51) performed significantly lower than healthy controls in health numeracy. The findings suggest that cognitively well performing old individuals have difficulties in understanding health-related numerical information. The risk of misunderstanding health-related numerical information is increased in persons with CIND. As these population groups are frequently involved in health care decisions, particular attention has to be paid to providing numerical information in comprehensible form.     

The role of procedural memory in grammar and numeracy skills

The objective of this study was to examine the contribution of procedural memory to grammar and numeracy skills, which both involve the manipulation of abstract patterns. Seventy-six typically developing children between 5 and 7 years of age were assessed on grammar with a past tense production task and a sentence comprehension task, on numeracy with a counting task and a calculation task, and on procedural memory with a serial reaction time task. Moderate correlations were found between the measures of grammar and numeracy. Moreover, 4 hierarchical linear regressions indicated that procedural memory was associated with calculation but not with counting or grammar skills when age and working memory were taken into account. These novel findings suggest that procedural memory may have a role to play in the development of some numeracy skills. Several possible explanations for the absence of contribution to grammar are considered.     

Working memory and fine motor skills predict early numeracy performance of children with cerebral palsy

Early numeracy is an important precursor for arithmetic performance, academic proficiency, and work success. Besides their apparent motor difficulties, children with cerebral palsy (CP) often show additional cognitive disturbances. In this study, we examine whether working memory, non-verbal intelligence, linguistic skills, counting and fine motor skills are positively related to the early numeracy performance of 6-year-old children with CP. A total of 56 children (M = 6.0, SD = 0.61, 37 boys) from Dutch special education schools participated in this cross-sectional study. Of the total group, 81% of the children have the spastic type of CP (33% unilateral and 66% bilateral), 9% have been diagnosed as having diskinetic CP, 8% have been diagnosed as having spastic and diskinetic CP and 2% have been diagnosed as having a combination of diskinetic and atactic CP. The children completed standardized tests assessing early numeracy performance, working memory, non-verbal intelligence, sentence understanding and fine motor skills. In addition, an experimental task was administered to examine their basic counting performance. Structural equation modeling showed that working memory and fine motor skills were significantly related to the early numeracy performance of the children (β = .79 and p < .001, β = .41 and p < .001, respectively). Furthermore, counting was a mediating variable between working memory and early numeracy (β = .57, p < .001). Together, these findings highlight the importance of working memory for early numeracy performance in children with CP and they warrant further research into the efficacy of intervention programs aimed at working memory training.     

Right-wing adherence and objective numeracy as predictors of minority group size perceptions and size threat reactions

Racial, ethnic, religious, and sexual minority populations are growing rapidly in the West. We investigate predictors and consequences of threat responses to perceived minority group size, and perceptions of minority group size itself. Study 1 (N = 274) finds that right-wing adherence predicts greater size threat, whereas lower numerical ability predicts larger perceived group size (confirmed in Studies 2–3). Study 2 (Sample 1, N = 124; Sample 2, N = 263) finds that the relation between right-wing adherence and prejudice toward minorities exhibits an indirect effect via group size threat (but not perceived size), explaining 35–66% of this relation. Study 3 (N = 310) finds a comparable indirect effect explaining 27–40% of this relation, even after statistically controlling for indirect effects of realistic, symbolic, and terroristic threat. These findings provide novel insights into psychological processes surrounding perceived minority group size, identifying size threat as especially crucial in understanding intergroup relations.     

How representations of number and numeracy predict decision paradoxes: A fuzzy-trace theory approach

Higher numeracy has been associated with decision biases in some numerical judgment-and-decision problems. According to fuzzy-trace theory, understanding such paradoxes involves broadening the concept of numeracy to include processing the gist of numbers—their categorical and ordinal relations—in addition to objective (verbatim) knowledge about numbers. We assess multiple representations of gist, as well as numeracy, and use them to better understand and predict systematic paradoxes in judgment and decision-making. In two samples (Ns = 978 and 957), we assessed categorical (some vs. none) and ordinal gist representations of numbers (higher vs. lower, as in relative magnitude judgment, estimation, approximation, and simple ratio comparison), objective numeracy, and a nonverbal, nonnumeric measure of fluid intelligence in predicting: (a) decision preferences exhibiting the Allais paradox and (b) attractiveness ratings of bets with and without a small loss in which the loss bet is rated higher than the objectively superior no-loss bet. Categorical and ordinal gist tasks predicted unique variance in paradoxical decisions and judgments, beyond objective numeracy and intelligence. Whereas objective numeracy predicted choosing or rating according to literal numerical superiority, appreciating the categorical and ordinal gist of numbers was pivotal in predicting paradoxes. These results bring important paradoxes under the same explanatory umbrella, which assumes three types of representations of numbers—categorical gist, ordinal gist, and objective (verbatim)—that vary in their strength across individuals.     

Early literacy and early numeracy: the value of including early literacy skills in the prediction of numeracy development

The purpose of this study was to examine whether early literacy skills uniquely predict early numeracy skills development. During the first year of the study, 69 3- to 5-year-old preschoolers were assessed on the Preschool Early Numeracy Skills (PENS) test and the Test of Preschool Early Literacy Skills (TOPEL). Participants were assessed again a year later on the PENS test and on the Applied Problems and Calculation subtests of the Woodcock–Johnson III Tests of Achievement. Three mixed effect regressions were conducted using Time 2 PENS, Applied Problems, and Calculation as the dependent variables. Print Knowledge and Vocabulary accounted for unique variance in the prediction of Time 2 numeracy scores. Phonological Awareness did not uniquely predict any of the mathematics domains. The findings of this study identify an important link between early literacy and early numeracy development.     

Confirmatory factor analysis of the Early Arithmetic,Reading, and Learning Indicators (EARLI)

Despite growing interest in early intervention, there are few measures available to monitor the progress of early academic skills in preschoolers. The Early Arithmetic, Reading, and Learning Indicators (EARLI; DiPerna, Morgan, & Lei, 2007) were developed as brief assessments of critical early literacy and numeracy skills. The purpose of the current study was to examine the factor structure of the EARLI probes via confirmatory factor analysis (CFA) in a sample of Head Start preschoolers (N = 289). A two-factor model with correlated error terms and a bifactor model provided comparable fit to the data, although there were some structural problems with the latter model. The utility of the bifactor model for explaining the structure of early academic skills as well as the utility of the EARLI probes as measures of literacy and numeracy skills in preschool are discussed.     

Making Numbers Come to Life: Two Scoring Methods for Creativity in Aurora's Cartoon Numbers

Although creativity has long been recognized as an important aspect of mathematical thinking, both for the advancement of the field and in students' developing expertise in mathematics, assessments of student creativity in that domain have been limited in number and focus. This article presents an assessment developed for creativity that provides a score for mathematical creativity (MaC) in addition to a score for general creativity in the numeric domain, or what we might call numerical creativity (NuC). We developed different rating scales for each and then explored how each scoring method accounts for the students' mathematical/numerical and creative skills. The psychometric properties for both scoring approaches were examined. Each method was shown to reflect different relationships with other performance tests. In addition, it is proposed that MaC may provide useful insight into students' levels of adaptive expertise in mathematics, as reflected by their ability to apply mathematical knowledge (i.e., language, operations, concepts) to novel situations, representing an informative supplement to performance indicators of math achievement.     

Computer-assisted intervention for children with low numeracy skills

We present results of a computer-assisted intervention (CAI) study on number skills in kindergarten children. Children with low numeracy skill (n = 30) were randomly allocated to two treatment groups. The first group played a computer game (The Number Race) which emphasized numerical comparison and was designed to train number sense, while the other group played a game (Graphogame-Math) which emphasized small sets of exact numerosities by training matching of verbal labels to visual patterns and number symbols. Both groups participated in a daily intervention session for three weeks. Children's performance in verbal counting, number comparison, object counting, arithmetic, and a control task (rapid serial naming) were measured before and after the intervention. Both interventions improved children's skills in number comparison, compared to a group of typically performing children (n = 30), but not in other areas of number skills. These findings, together with a review of earlier computer-assisted intervention studies, provide guidance for future work on CAI aiming to boost numeracy development of low performing children.     

Breaking the structuralist barrier. Literacy and numeracy with fluency.

Behavior analysis is an example of a selection science, and behavioral programs that follow the tenets of selectionism, long advocated by B. F. Skinner, can have a large impact on social problems. This article describes the characteristics of selection sciences and their application in the Morningside Model of Generative Instruction, which addresses both adult literacy and children's learning and attention problems. School curricula are analyzed for their key component elements and underlying tool skills. Teaching procedures then establish and build these key components to fluency. New and complex repertoires then emerge with little or no instruction, producing curriculum leaps that allow students to make rapid academic advancement. Children typically gain more than two grade levels per school year, and adults advance two grades per month.     

Numeracy skills in young children as predictors of mathematical competence

As mathematical competence is linked to educational success, professional achievement, and even a country's economic growth, researchers have been interested in early predictors for quite some time. Although there have been numerous studies on domain-specific numerical abilities predicting later mathematical competence in preschool children, research in toddlers is scarce, especially regarding additional influential aspects, such as domain-general cognitive abilities and the children's social background. Using a large-scale dataset, the present study examined predictive effects of numeracy skills in 17-month-olds for later mathematical achievement. We found small, positive effects, even when controlling for child-related variables (i.e., age and sex) and the children's social background (i.e., maternal education and household language). Additionally, we compared results with a domain-general categorization task and found no distinct effect on mathematical competence. The present results are discussed with regard to the specificities of the dataset, as well as implications for future studies on predictors of mathematical competence.     

Working memory resources in young children with mathematical difficulties

Kyttälä, M., Aunio, P. & Hautamäki, J. (2010). Working memory resources in young children with mathematical difficulties. Scandinavian Journal of Psychology, 51 , 1–15.
Working memory (WM) ( Baddeley, 1986, 1997 ) is argued to be one of the most important cognitive resources underlying mathematical competence ( Geary, 2004 ). Research has established close links between WM deficits and mathematical difficulties. This study investigated the possible deficits in WM, language and fluid intelligence that seem to characterize 4- to 6-year-old children with poor early mathematical skills before formal mathematics education. Children with early mathematical difficulties showed poor performance in both verbal and visuospatial WM tasks as well as on language tests and a fluid intelligence test indicating a thoroughly lower cognitive base. Poor WM performance was not moderated by fluid intelligence, but the extent of WM deficits was related to language skills. The educational implications are discussed.     

Working memory and early numeracy training in preschool children

Many factors influence children’s performance in mathematical achievement, including both domain-specific and domain-general factors. This study aimed to verify and compare the effects of two types of training on early numerical skills. One type of training focused on the enhancement of working memory, a domain-general precursor, while the other focused on the enhancement of early numeracy, a domain-specific precursor. The participants were 48 five-year-old preschool children. Both the working memory and early numeracy training programs were implemented for 5 weeks. The results showed that the early numeracy intervention specifically improved early numeracy abilities in preschool children, whereas working memory intervention improved not only working memory abilities but also early numeracy abilities. These findings stress the importance of performing activities designed to train working memory abilities, in addition to activities aimed to enhance more specific skills, in the early prevention of learning difficulties during preschool years.