Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study

Predicting individual differences in preschoolers' numeracy and geometry knowledge: The role of understanding abstract relations between objects and quantities

Preschoolers' mathematics knowledge develops early and varies substantially. The current study focused on two ontogenetically early emerging cognitive skills that may be important predictors of later math skills (i.e., geometry and numeracy): children's understanding of abstract relations between objects and quantities as evidenced by their patterning skills and the approximate number system (ANS). Children's patterning skills, the ANS, numeracy, geometry, nonverbal intelligence (IQ), and executive functioning (EF) skills were assessed at age 4 years, and their numeracy and geometry knowledge was assessed again a year later at age 5 (N = 113). Above and beyond children's initial knowledge in numeracy and geometry, as well as IQ and EF, patterning skills and the ANS at age 4 uniquely predicted children's geometry knowledge at age 5, but only age 4 patterning uniquely predicted age 5 numeracy. Thus, although patterning and the ANS are related, they differentially explain variation in later geometry and numeracy knowledge. Results are discussed in terms of implications for early mathematics theory and research.

Declarative memory supports children's math skills: A longitudinal study

Substantial progress has been made in understanding the neurocognitive underpinnings of learning math. Building on this work, it has been hypothesized that declarative and procedural memory, two domain-general learning and memory systems, play important roles in acquiring math skills. In a longitudinal study, we tested whether in fact declarative and procedural memory predict children's math skills during elementary school years. A sample of 109 children was tested across grades 2, 3 and 4. Linear mixed-effects regression and structural equation modeling revealed the following. First, learning in declarative but not procedural memory was associated with math skills within each grade. Second, declarative but not procedural memory in each grade was related to math skills in all later grades (e.g., declarative memory in grade 2 was related to math skills in grade 4). Sensitivity analyses showed that the pattern of results was robust, except for the longitudinal prediction of later math skills when accounting for stable inter-individual differences via the inclusion of random intercepts. Our findings highlight the foundational role of early domain-general learning and memory in children's acquisition of math.

The relation between number line performance and mathematics outcomes: Two meta-analyses

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be overestimated because general cognitive ability has not been fully controlled in prior studies. The first of two meta-analyses (162 studies, 33,101 participants) confirmed a relation between performance on whole number (r = 0.33) and fractions number (r = 0.41) lines and overall mathematics performance. These relations were generally consistent across content domains (e.g., algebra and computation) and other moderators. The second (71 studies, 14,543 participants) used meta-analytic structural equation modeling to confirm these relations while controlling general cognitive ability (defined by IQ and working memory measures) and, in one analysis, general mathematics competence. The relation between number line performance and general mathematics competence remained significant but reduced (β = 0.13). Controlling general cognitive ability, whole number line performance consistently predicted competence with fractions but not performance on numeracy or computations measures. The results suggest an understanding of the magnitudes represented by whole numbers might be particularly important for students' fractions learning. RESEARCH HIGHLIGHTS: Two meta-analyses examined the link between the number line and mathematics performance. The first revealed significant relations across domains (e.g., algebra and computation). The second controlled for general cognitive ability and resulted in reduced but still significant relations. The relation between number line and fractions performance was stronger than relations to other domains.

Domain-specific knowledge and domain-general abilities in children's science problem-solving

BACKGROUND

Problem-solving in early and middle childhood is of high relevance for cognitive developmental research and educational support. Previous research on science problem-solving has focussed on the process and strategies of children handling challenging tasks, but less on providing insights into the cognitive network that enables science problem-solving.

AIMS

In this study, we aimed to investigate whether performance in science problem-solving is mainly determined by domain-specific rule knowledge, by domain-general cognitive abilities or both.

METHODS

In our study, 215 6- to 8-year-old children completed a set of three domain-specific rule knowledge tasks and three corresponding problem-solving tasks that were content-coherent, as well as a vocabulary task, and a reasoning task.

RESULTS

Correlational and regression analyses revealed a negligible impact of domain-specific rule knowledge on corresponding problem-solving tasks. In contrast, the associations between problem-solving performance in different domains and the associations between problem-solving performance and domain-general abilities (vocabulary and reasoning) were comparably strong.

CONCLUSIONS

The findings suggest that science problem-solving in primary school children primarily relies on domain-general cognitive abilities. Implications of these findings are discussed with regard to cognitive theories and early science education.

Teaching strategies, cognitive factors and mathematics

Mathematics teaching strategies have a positive impact on learning. However, there is a lack of studies on non-traditional approaches to early mathematics education in the specialized scientific literature. In this theoretical framework, a study to connect teaching methodology with the various cognitive processes implicated in learning has been designed. A total of 114 primary school students aged 74 and 84 months who were taught mathematics either with the method called Open Algorithm Based on Numbers or with the more traditional Closed Algorithm Based on Ciphers, participated in the study. After conducting a thorough examination of cognitive processes and early math performance using well-established assessment instruments, a comparative analysis was undertaken to explore the relationship between cognitive predictors of mathematical performance, while considering the mathematics teaching strategies used. Students were distributed according to their level of mathematical competence and teaching methodology and the type of schools (Charter or Public). The results from the multivariate statistical test showed that the teaching strategy was inconclusive for most of the cognitive factors studied. Significant differences according to mathematical performance were found for fluid intelligence, verbal short-term memory, and visuospatial working memory. Finally, no significant differences were found in the cognitive variables studied when considering the interaction between the teaching approach, school characteristics, and mathematical achievement as a reference.

Foundations for future math achievement: Early numeracy, home learning environment, and the absence of math anxiety

BACKGROUND

Mathematics achievement is pivotal in shaping children's future prospects. Cognitive skills (numeracy), feelings (anxiety), and the social environment (home learning environment) influence early math development.

METHOD

A longitudinal study involved 85 children (mean age T1 = 6.4 years; T2 = 7.9) to explore these predictors holistically. Data were collected on early numeracy skills, home learning environment, math anxiety, and their impact on various aspects of math.

RESULTS

The study found that early numeracy skills, home learning environment, and math anxiety significantly influenced math school achievement. However, they affected written computation, sequences, and comparisons differently. Early numeracy skills strongly predicted overall achievement and comparison subtest performance.

CONCLUSION

These findings underscore the substantial role of math anxiety and home learning environment in children's math achievement. The study emphasizes the need to consider the selective impacts of these factors in future research, shedding light on the multifaceted nature of mathematics achievement determinants.

Higher level domain specific skills in mathematics; The relationship between algebra, geometry, executive function skills and mathematics achievement

Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms.

Beyond linearity: Using IRT-scaled level models to describe the relation between prior proportional reasoning skills and fraction learning outcomes

Previous research on the role of prior skills like proportional reasoning skills for the development of mathematical concepts offers conclusions such as "more (prior skills) is better (for later learning)." Insights, which prior skill level goes along with which level of learning outcomes, may advance the understanding of the development of mathematical concepts. An exploratory approach is presented based on level models to describe the relation between symbolic proportional reasoning skills and fraction outcomes beyond linearity. Analyses draw on samples of German fourth to sixth graders from a scaling (2017, N = 325, 54.8% female) and longitudinal study (2018/2019, N = 436, 42.7% female). Particularly mastering natural and internal rational ratios in proportional reasoning seems relevant for successful fraction learning.

Exploring academic and cognitive skills impacting retention and acquisition of word-problem knowledge gained during or after intervention

In the present study, we investigated the impact of a word-problem intervention in retention and acquisition of knowledge after the intervention ended. We based analyses upon Grade 4 students experiencing mathematics difficulty (average age at pretest = 8.77) who received one of two variants of a word-problem intervention (with [n = 111] vs. without [n = 110] embedded pre-algebraic reasoning instruction) and students within a business-as-usual condition (BaU [n = 127]) separately. Findings revealed that students who received the intervention not only tended to retain less, but they also showed more active knowledge acquisition after the intervention ended. Furthermore, word-problem intervention altered the contributions of some prior knowledge and skills on both retention and acquisition.

Relative Contributions of g and Basic Domain-Specific Mathematics Skills to Complex Mathematics Competencies

Meta-analytic structural equation modeling was used to estimate the relative contributions of general cognitive ability or g (defined by executive functions, short-term memory, and intelligence) and basic domain-specific mathematical abilities to performance in more complex mathematics domains. The domain-specific abilities included mathematics fluency (e.g., speed of retrieving basic facts), computational skills (i.e., accuracy at solving multi-step arithmetic, algebra, or geometry problems), and word problems (i.e., mathematics problems presented in narrative form). The core analysis included 448 independent samples and 431,344 participants and revealed that g predicted performance in all three mathematics domains. Mathematics fluency contributed to the prediction of computational skills, and both mathematics fluency and computational skills predicted word problem performance, controlling g. The relative contribution of g was consistently larger than basic domain-specific abilities, although the latter may be underestimated. The patterns were similar across younger and older individuals, individuals with and without a disability (e.g., learning disability), concurrent and longitudinal assessments, and family socioeconomic status, and have implications for fostering mathematical development.

Dietary patterns and cognitive achievement among school children in socio-cultural context, a case of Montevideo, Uruguay

PURPOSE

The benefits of a healthy diet on children´s cognition have been described in several studies. However, many previous studies have analyzed the effect on general cognitive domains (e.g. intelligence), used measures based almost exclusively on local examinations, and rarely consider social context.

OBJECTIVE

The objective of the present study was to examine the relationship between two diet patterns and contextualized cognitive performance measures of children aged 6-8 years from low-average income neighborhoods in Montevideo, Uruguay.

METHODS

270 first-grade children with complete data participated in the study. Consumption of foods was determined via two averaged 24-h dietary recalls with the mother. Two dietary patterns were identified via principal component analysis: "processed (high calorie) foods" and "nutrient dense". Children´s cognitive performance, including general cognitive abilities, achievement in mathematics and reading, and discrepancy scores between predicted and actual achievement was assessed with the Woodcock-Muñoz Cognitive and Achievement scales. The association of dietary patterns and cognitive endpoints was analyzed in multilevel models, clustered by children´s school. Sociodemographic and biological variables were used as covariates.

RESULTS

The nutrient dense foods pattern, characterized by higher consumption of dark leafy and red-orange vegetables, eggs, beans & peas, potatoes, was associated with better performance in reading, with beta coefficient 3.28 (95% CI 0.02, 6.54). There was also an association between the nutrient dense foods factor and the Discrepancy in reading, 2.52 (0.17, 4.87). Processed (high calorie) foods pattern, characterized by higher consumption of breads, processed meats, fats and oils, sweetened beverages, and sweetened yogurt/dairy products; reduced intake of milk, pastries and pizza dinners was not associated with cognitive performance.

CONCLUSIONS

Nutrient dense food pattern was positively associated with children's reading achievement. A nutrient-rich diet may benefit written language acquisition at the beginning of schooling.

The importance of domain-specific number abilities and domain-general cognitive abilities for early arithmetic achievement and development

BACKGROUND

Children's numerical and arithmetic skills differ greatly already at an early age. Although research focusing on accounting for these large individual differences clearly demonstrates that mathematical performance draws upon several cognitive abilities, our knowledge concerning key abilities underlying mathematical skill development is still limited.

AIMS

First, to identify key cognitive abilities contributing to children's development of early arithmetic skills. Second, to examine the extent to which early arithmetic performance and early arithmetic development rely on different or similar constellations of domain-specific number abilities and domain-general cognitive abilities.

SAMPLE

In all, 134 Swedish children (Mage  = 6 years and 4 months, SD = 3 months, 74 boys) participated in this study.

METHOD

Verbal and non-verbal logical reasoning, non-symbolic number comparison, counting knowledge, spatial processing, verbal working memory and arithmetic were assessed. Twelve months later, arithmetic skills were reassessed. A latent change score model was computed to determine whether any of the abilities accounted for variations in arithmetic development.

RESULTS

Arithmetic performance was supported by counting knowledge, verbal and non-verbal logical reasoning and spatial processing. Arithmetic skill development was only supported by spatial processing.

CONCLUSIONS

Results show that young children's early arithmetic performance and arithmetic development are supported by different cognitive processes. The findings regarding performance supported Fuchs et al.'s model (Dev Psychol, 46, 2010b, 1731) but the developmental findings did not. The developmental findings align partially to Geary et al.'s (J Educ Psychol, 109, 2017, 680) hypothesis stating that young children's early arithmetic development is more dependent on general cognitive abilities than number abilities.

Understanding the complexities of mathematical cognition: A multi-level framework

Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.

Acquisition of new arithmetic skills based on prior arithmetic skills: A cross-sectional study in primary school from grade 2 to grade 5

BACKGROUND

In several countries, children's math skills have been declining at an alarming rate in recent years and decades, and one of the explanations for this alarming situation is that children have difficulties in establishing the relations between arithmetical operations.

AIM

In order to address this question, our goal was to determine the predictive power of previously taught operations on newly taught ones above general cognitive skills and basic numerical skills.

SAMPLES

More than one hundred children in each school level from Grades 2 to 5 from various socio-cultural environments (N = 435, 229 girls) were tested.

METHODS

Children were assessed on their abilities to solve the four basic arithmetic operations. They were also tested on their general cognitive abilities, including working memory, executive functions (i.e., inhibition and flexibility), visual attention and language. Finally, their basic numerical skills were measured through a matching task between symbolic and nonsymbolic numerosity representations. Additions and subtractions were presented to children from Grade 2, multiplications from Grade 3 and divisions from Grade 4.

RESULTS AND CONCLUSIONS

We show that addition predicts subtraction and multiplication performance in all grades. Moreover, multiplication predicts division performance in both Grades 4 and 5. Finally, addition predicts division in Grade 4 but not in Grade 5 and subtraction and division are not related whatever the school grade. These results are examined considering the existing literature, and their implications in terms of instruction are discussed.

Towards an Integrative Model of Math Cognition: Interactions between Working Memory and Emotions in Explaining Children's Math Performance

Individual variation in mathematical skills can be ascribed to differences in cognitive ability, but also to students' emotional experiences of mathematics, such as enjoyment and anxiety. The current study investigated how the interplay of working memory with math anxiety and enjoyment explains mathematical performance in primary school students. We also explored whether these relations differed with the type of math test and students' age. Using mixed effect models, we reanalyzed data from 4471 Dutch primary school students (grades 2-6) who had completed two computerized working memory tasks, had filled out a questionnaire on math emotions, and had completed two math tests: story problems and speeded arithmetic. Findings showed that working memory, anxiety, and enjoyment were linear (but not curvilinear) predictors of performance on both tests, while some relations were stronger for the math (story)-problem-solving test. Higher math anxiety negatively impacted performance more strongly for students with stronger working memory skills, but only on the arithmetic test. No interaction between working memory and enjoyment was found. The relation between math anxiety and math performance increased with grade level, but no other age-related changes were found. Interpretations and recommendations focus on situated views on learning and emotion.

Multiple influences of working memory capacity on number comprehension: The interplay with metacognition and number-specific prerequisites

A wide literature has studied the predictors of number comprehension and early math learning by considering both domain-general and number-specific prerequisites. However, a consensus has not been reached regarding the specific contribution of these prerequisites. This study aimed to analyze the contribution and interplay of two domain-general functions, working memory (WM) and metacognitive abilities, and number-specific prerequisites in determining number comprehension. The participants, 126 Italian first-graders, were tested on two WM capacity tasks, an early metacognition questionnaire, five number-specific prerequisites tasks (e.g., quantity and/or size comparison; placement of Arabic numeral), and the Number Knowledge Test for whole-number comprehension. We hypothesized that WM capacity would predict number comprehension both directly and indirectly via metacognition and domain-specific prerequisites. This is because both metacognition and domain-specific prerequisites might place an information load on WM to establish schemes for declarative metamemory and metacognitive monitoring and for emerging counting skills, respectively. The results confirmed these hypotheses. WM capacity was positively associated with number comprehension both directly and via increased metacognition and domain-specific prerequisites. These findings offer a model for interpreting the interplay between domain-general and number-specific predictors of whole-number comprehension, but they also underline the multiple ways in which WM capacity affects it.

The influence of home environmental factors on kindergarten children's addition strategy use

Young children vary widely in their levels of math knowledge, their abilities to solve math problems, and the strategies they use to solve math problems. As much of later math builds on children's early understanding of basic math facts and problem-solving strategies, understanding influences on children's early problem solving is important. Few studies, however, have examined the home environment in relation to children's strategy use during arithmetic problems. We examined how both structural characteristics of children's home environments, such as socioeconomic status (SES), as well as the learning environment, such as engagement in math and literacy activities at home, related to their use of problem-solving strategies for numerical addition problems. Kindergarten children from diverse backgrounds completed a measure of addition problem solving and strategy use, including simple and complex numerical problems. Strategies were coded based on a combination of accuracy and strategy sophistication, with higher scores indicating problems solved correctly with more sophisticated strategies. Parents completed a home activities questionnaire, reporting the frequency with which they and their child had engaged in math and literacy activities at home over the past month. An exploratory factor analysis identified three components of the home activities - a basic activities factor, an advanced math activities factor, and a literacy activities factor. Findings indicated that SES related to children's strategy sophistication, and frequency of engaging in advanced math and literacy activities at home predicted strategy sophistication, however, engaging in activities at home did not moderate the relations between SES and strategy sophistication. This suggests that family engagement in activities at home may promote early arithmetic skills, and that the role of home environmental characteristics should be considered in children's arithmetic strategy use and performance over development.

The Revision and Application of Aurora in China: Based on Successful Intelligence

Aurora Battery is a corresponding test of successful intelligence. This study aims to examine the factorial structure of the Chinese version of Aurora Battery and to investigate its internal consistency and validity, as well as to discover the developmental features of Chinese students. A total number of 2007 students were recruited from 13 schools across eastern, central, and western China, ranging from 4th to 8th grade (mean age = 12.29 years) and among them, 43.9% are girls. Confirmatory factor analysis (CFA) was used to examine the factorial structure. Among the tested models, a second-order factor model, in which the three ability factors serve as indicators of a general factor, provided an acceptable model fit to the data. Moreover, measurement invariance across gender and grades were supported, which suggests the mean scores of analytical, creative, and practical abilities are comparable in this research. The criterion-related validity analysis suggests that the battery and its three subscales have good criterion validity. The scale reliability analysis shows that the Cronbach's alpha and the McDonald's omega value of the whole test were .84 and .87, respectively, indicating the scale's internal reliability is good. For ability differences among grades, students' analytical and practical abilities increase across all grades, while creativity presents an upward trend from grade 4 to 6, followed by a downward trend from grade 6 to 7, and an increase from grade 7 to 8. Female students outperform male students on both analytical and creative ability, while with no obvious difference on practical abilities.

Instructional support in inquiry-based elementary school science classes: how does it relate to students’ science content knowledge and academic language proficiency?

Inquiry-based science instruction has been proposed as an optimal learning environment for language-integrated teaching. While its potential for developing both content knowledge and language skills has been shown for students with limited language proficiency, research focusing on mainstream classrooms has mainly considered domain-specific learning. Despite the effectiveness of inquiry-based science instruction for student outcomes, research on the role of specific aspects of instructional quality is limited. Addressing this research gap, the present study investigates the relationship between teachers’ instructional support during inquiry-based science classes and elementary school students’ learning gains in science content knowledge and academic language proficiency. Multilevel regression analyses are based on data from 459 German elementary school students from Grades 3 and 4 who participated in a longitudinal intervention study that took place over one school year. Our findings indicate a strong impact of students’ prior knowledge on learning outcomes and compositional effects for the language-related measures. Relations between teachers’ instructional support, as measured by the Classroom Assessment Scoring System (CLASS; Pianta et al., 2008), and students’ learning outcomes did not emerge. In interpreting the results, the overall mediocre quality of teachers’ instructional support needs to be considered.

The differential relationship between visual and spatial working memory in children's mathematics performance

BACKGROUND

Previous research suggests that visuospatial working memory (WM) is a unique predictor of mathematics. However, evidence from neuropsychology and cognitive studies suggests dissociations between visual and spatial WM.

PROCEDURE

We examined the differential relationships between visual and spatial WM with mathematics using a new task that 1) utilized the same paradigm across visual and spatial tasks and 2) required executive WM.

MAIN FINDINGS

We found that our new spatial WM task related to mathematics scores while visual WM did not. Spatial WM related to mathematics scores for fourth-graders and not second graders, consistent with previous findings on the relationship between spatial skills and mathematics as mathematics becomes more complex. No relationship was found between spatial WM and reading scores at either grade level.

CONCLUSIONS

Our results highlight the dynamic relationship between WM components and mathematics over the elementary school years and suggest that spatial WM is a unique predictor of mathematics starting from middle childhood.

A sequential model of the contribution of preschool fluid and crystallized cognitive abilities to later school achievement

The present study documented in two distinct population-based samples the contribution of preschool fluid and crystallized cognitive abilities to school achievement in primary school and examined the mediating role of crystallized abilities in this sequence of predictive associations. In both samples, participants were assessed on the same cognitive abilities at 63 months (sample 1, n = 1072), and at 41 and 73 months (sample 2, n = 1583), and then with respect to their school achievement from grade 1 (7 years) to grade 6 (12 years). Preschool crystallized abilities were found to play a key role in predicting school achievement. They contributed substantially to school achievement in the early school years, but more modestly in the later years, due to the strong auto-regression of school achievement. They also mediated the association between fluid abilities and later school achievement in the early grades of school, with the former having modest direct contribution to the latter in the later grades. These findings are discussed regarding their implication for preventive interventions.

Taking a Closer Look: The Relationship between Pre-School Domain General Cognition and School Mathematics Achievement When Controlling for Intelligence

Intelligence, as well as working memory and attention, affect the acquisition of mathematical competencies. This paper aimed to examine the influence of working memory and attention when taking different mathematical skills into account as a function of children’s intellectual ability. Overall, intelligence, working memory, attention and numerical skills were assessed twice in 1868 German pre-school children (t1, t2) and again at 2nd grade (t3). We defined three intellectual ability groups based on the results of intellectual assessment at t1 and t2. Group comparisons revealed significant differences between the three intellectual ability groups. Over time, children with low intellectual ability showed the lowest achievement in domain-general and numerical and mathematical skills compared to children of average intellectual ability. The highest achievement on the aforementioned variables was found for children of high intellectual ability. Additionally, path modelling revealed that, depending on the intellectual ability, different models of varying complexity could be generated. These models differed with regard to the relevance of the predictors (t2) and the future mathematical skills (t3). Causes and conclusions of these findings are discussed.

Using Digital Concept Maps in Conflict Resolution Studies: Implications for Students’ Argumentative Skills, Domain-Specific Knowledge, and Academic Efficacy

While argumentation emerges as one of the major learning skills in the twenty-first century, a somewhat opaque landscape is revealed in terms of identifying its potential in enhancing higher-education students’ domain-specific knowledge. In this study, argumentation-for-learning activity with digital concept mapping (CM) was designed and compared with a traditional teacher-centered activity to determine the former’s effectiveness in promoting students’ domain-specific factual, conceptual, and procedural knowledge. This study also examines how the proposed activity may contribute to students’ academic efficacy and thus promote meaningful learning. A quasi-experimental design was employed by using convenience samples. Two identical courses were selected for this research: the first course with a total of 59 students (the research group), and the second course including a total of 63 students (the control group). Both groups’ domain-specific knowledge was assessed before and after the activity. The designed activity was found to be less effective in fostering factual knowledge and more effective in developing the conceptual and procedural knowledge domains. Another finding demonstrated the benefits of argumentation for learning with CM in facilitating students’ academic efficacy. It can be concluded that engaging students in a deep argumentation learning process may in turn deepen predominantly conceptual and procedural domain-specific knowledge. Limitations and implications are discussed.

The Cognitive Profile of Math Difficulties: A Meta-Analysis Based on Clinical Criteria

Math difficulties (MD) manifest across various domain-specific and domain-general abilities. However, the existing cognitive profile of MD is incomplete and thus not applicable in typical settings such as schools or clinics. So far, no review has applied inclusion criteria according to DSM or ICD, summarized domain-specific abilities or examined the validity of response time scores for MD identification. Based upon stringent clinical criteria, the current meta-analysis included 34 studies which compared cognitive performances of a group with MD (n = 680) and a group without MD (n = 1565). Criteria according to DSM and ICD were applied to identify MD (percentile rank ≤ 16, age range 8–12 years, no comorbidities/low IQ). Effect sizes for 22 abilities were estimated and separated by their level and type of scoring (AC = accuracy, RT = response time). A cognitive profile of MD was identified, characterized by distinct weaknesses in: (a) computation (calculation [AC], fact retrieval [AC]), (b) number sense (quantity processing [AC], quantity-number linking [RT], numerical relations [AC]), and (c) visual-spatial short-term storage [AC]. No particular strength was found. Severity of MD, group differences in reading performance and IQ did not significantly moderate the results. Further analyses revealed that (a) effects are larger when dealing with numbers or number words than with quantities, (b) MD is not accompanied by any weakness in abilities typically assigned to reading, and (c) weaknesses in visual-spatial short-term storage emphasize the notion that number and space are interlinked. The need for high-quality studies investigating domain-general abilities is discussed.

Effects of a statewide pre-kindergarten program on children's achievement and behavior through sixth grade

As state-funded pre-kindergarten (pre-K) programs expand, it is critical to investigate their short- and long-term effects. This article presents the results through sixth grade of a longitudinal randomized control study of the effects of a scaled-up, state-supported pre-K program. The analytic sample includes 2,990 children from low-income families who applied to oversubscribed pre-K program sites across the state and were randomly assigned to offers of admission or a wait list control. Data through sixth grade from state education records showed that the children randomly assigned to attend pre-K had lower state achievement test scores in third through sixth grades than control children, with the strongest negative effects in sixth grade. A negative effect was also found for disciplinary infractions, attendance, and receipt of special education services, with null effects on retention. The implications of these findings for pre-K policies and practices are discussed. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Connections between Mathematics and Reading Development: Numerical Cognition Mediates Relations between Foundational Competencies and Later Academic Outcomes

We examined longitudinal relations between 1^st-grade cognitive predictors (early nonverbal reasoning, processing speed, listening comprehension, working memory, calculation skill, word-problem solving, word-reading fluency, attentive behavior, and numerical cognition) and 2^nd-grade academic outcomes (calculations, word-problem solving, and word reading) in 370 children (M _age = 6.55 years, SD _age = 0.33 years at the start of the study) who were identified as at-risk or not-at-risk for mathematics disability. Path analysis mediation models revealed that numerical cognition, assessed at an intermediary timepoint, mediated the effects of processing speed, working memory, calculation skill, word-problem solving, and attentive behavior on all 3 outcomes. Findings indicate that multiple early domain-general cognitive abilities are related to later mathematics and reading outcomes and that numerical cognition processes, which may track ease of forming symbol-concept associations, predict later performance across both academic domains.

Evolution of Self-Awareness and the Cultural Emergence of Academic and Non-academic Self-Concepts

Schooling is ubiquitous in the modern world and academic development is now a critical aspect of preparation for adulthood. A step back in time to pre-modern societies and an examination of life in remaining traditional societies today reveals that universal formal schooling is an historically recent phenomenon. This evolutionary and historical recency has profound implications for understanding academic development, including how instructional practices modify evolved or biological primary abilities (e.g., spoken language) to create evolutionarily novel or biologically secondary academic competencies (e.g., reading). We propose the development of secondary abilities promotes the emergence of academic self-concepts that in turn are supported by evolved systems for self-awareness and self-knowledge. Unlike some forms of self-knowledge (e.g., relative physical abilities) that appear to be universal and central to many people's overall self-concept, the relative importance of academic self-concepts are expected to be dependent on explicit social and cultural supports for their valuation. These culturally contingent self-concepts are contrasted with universal social and physical self-concepts, with implications for understanding variation students' relative valuation of academic competencies and their motivations to engage in academic learning.

Cross- and Within-Domain Associations of Early Reading and Mathematical Skills: Changes Across the Preschool Years

Existing research has mainly examined the role of cognitive correlates of early reading and mathematics from a stationary perspective that does not consider how these skills unfold and interact over time. This approach constraints the interpretation of cross-domain associations and the specificity of domain-specific covariates. In this study, we disentangle the role of these predictors and investigate cross-domain associations between reading, math, and two related domain-specific predictors (phonological awareness and fluency with number sets) over the kindergarten years (n=512, Mage=54months, SDage=3.5, 52% females). Results reveal that the overlap between reading and math skills changes over development. Reciprocal associations between reading and math abilities are observed at earlier stages; then, reading abilities become the lead force. Findings also show that phonological awareness and fluency with number sets are domain-specific predictors that do not contribute to cross-domain gains in academic skills. Indeed, there is a trend for domain-specific skills to be more strongly related to achievement at the beginning of formal education than at the beginning of kindergarten, which suggests an increasing differentiation of domains over the kindergarten years. Such findings have implications for the timing and nature of interventions that aim to support children's reading and mathematical development.

The relation between working memory, number sense, and mathematics throughout primary education in children with and without mathematical difficulties

Number sense and working memory contribute to mathematical development throughout primary school. However, it is still unclear how the contributions of each of these predictors may change across development and whether the cognitive contribution is the same for children with and without mathematical difficulties. The aim of the two studies in this paper was to shed light on these topics. In a cross-sectional design, a typically developing group of children (study 1; N = 459, Grades 1-4) and a group with mathematical difficulties (study 2; N = 61, Grades 4-6) completed a battery of number sense and working memory tests, as well as a measure of arithmetic competence. Results of study 1 indicated that number sense was important in first grade, while working memory gained importance in second grade, before predictive value of both predictors waned. Number sense and working memory supported mathematics development independently from one another from Grade 1. Analysis of task demands showed that typically developing children rely on comprehension and visualization of quantity-to-number associations in early development. Later in development, pupils rely on comparing larger numerals and working memory until automatization. Children with mathematical difficulties were less able to employ number sense during mathematical operations, and thus might remain dependent on their working memory resources during arithmetic tasks. This suggests that children with mathematical difficulties need aid to employ working memory for mathematics from an early age to be able to automatize mathematical abilities later in development.

Boys' visuospatial abilities compensate for their relatively poor in-class attentive behavior in learning mathematics

The mathematics and reading achievement of 322 adolescents (159 boys) was assessed in seventh and eighth grades, as were their intelligence, working memory, and spatial abilities. Their seventh- and eighth-grade mathematics and English language arts teachers reported on their in-class attentive behavior. The latter emerged as an important predictor of achievement, but more so for mathematics than for reading. Boy were less attentive in classroom settings than girls (d = -.34) and performed better than expected in mathematics given their level of engagement in the classroom. Boys' better-than-expected mathematics achievement was related to advantages on visuospatial measures (ds = .28-.56), which fully mediated a sex difference in mathematics (ds = .27-.28) but not in reading achievement, with control of in-class attentive behavior. The results suggest that boys' advantages in visuospatial skills compensate for lower levels of classroom engagement in the learning of mathematics but not in reading competencies.

In-Class Attention, Spatial Ability, and Mathematics Anxiety Predict Across-Grade Gains in Adolescents' Mathematics Achievement

Identifying meaningful cognitive and non-cognitive predictors of mathematical competence is critical for developing targeted interventions for students struggling with mathematics. Here, 317 students' short-term verbal memory, verbal and visuospatial working memory, complex spatial abilities, intelligence, and mathematics attitudes and anxiety were assessed, and their teachers reported on their attentive-behavior in seventh-grade mathematics classrooms. Bayesian regression models revealed that complex spatial abilities and in-class attention were the most plausible predictors of seventh-grade mathematics, but not word reading, achievement, controlling for prior achievement. These results were confirmed with multilevel models that revealed interactions between these factors and prior achievement. The largest gains were among students with strong mathematical competencies in sixth-grade, and average or better in-class attention in seventh-grade as well as above average spatial abilities. High mathematics anxiety was associated with lower attention and through this indirectly influenced achievement gains. These results have implications for how to best target interventions for students at risk for long-term difficulties with mathematics.

Mathematics Clusters Reveal Strengths and Weaknesses in Adolescents' Mathematical Competencies, Spatial Abilities, and Mathematics Attitudes

Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders (n = 1,926), including whole number and fractions arithmetic, conceptual understanding of equality and fractions magnitudes, and the fractions number line. The goal was to determine if there were clusters of students with similar patterns of pre-algebra strengths and weaknesses and if variation between clusters was related to mathematics attitudes, anxiety, or for a subsample (n = 342) some combination of intelligence, working memory, or spatial abilities. Critically, strengths and weaknesses were not uniform across the three identified clusters. Lower-performing students had pronounced deficits in their understanding of mathematical equality, fractions magnitudes, and the fractions number line. Higher-performing students had particular advantages in whole number and fractions arithmetic, and the fractions number line. Students could be reliably placed into clusters based on their mathematics self-efficacy and a combination of intelligence and spatial abilities. The results contribute to our understanding of key aspects of students' mathematical development, highlight areas in need of intervention for at-risk students, and identify cognitive areas in which scaffolds might be incorporated into these interventions.

Emerging neurodevelopmental perspectives on mathematical learning

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.

Development of Cognitive Functions and Academic Skills in 9- to 10-year-old Children with Borderline Intellectual Functioning

This longitudinal study examined whether the cognitive and academic development of children (M_age = 10.52 years) with Borderline Intellectual Functioning (BIF), is characterized by developmental delay or atypical development. Cognitive tasks, arithmetic tasks, and reading tasks were administrated during three succeeding years to the BIF group and a Chronological Age-Matched Comparison (CAMC) group. The BIF children displayed weaknesses in relation to all tasks, and slower developmental rates on four arithmetic tasks and word reading. The results provide evidence in support of the developmental delay model as the BIF children overall displayed similar developmental growth and trends as the CAMC group.

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

In the field of mathematics education, one of the main questions remaining under debate is whether students' development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students' math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students' performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students' learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension.

Comorbid Learning Difficulties in Reading and Mathematics: The Role of Intelligence and In-Class Attentive Behavior

The goal was to identify the domain-general cognitive abilities and academic attitudes that are common and unique to reading and mathematics learning difficulties that in turn will have implications for intervention development. Across seventh and eighth grade, 315 (155 boys) adolescents (M age = 12.75 years) were administered intelligence, verbal short-term and working memory, and visuospatial memory, attention, and ability measures, along with measures of English and mathematics attitudes and mathematics anxiety. Teachers reported on students' in-class attentive behavior. A combination of Bayesian and multi-level models revealed that intelligence and in-class attentive behavior were common predictors of reading accuracy, reading fluency, and mathematics achievement. Verbal short-term memory was more critical for reading accuracy and fluency, whereas spatial ability and mathematics self-efficacy were more critical for mathematics achievement. The combination of intelligence and in-class attentive behavior discriminated typically achieving students from students with comorbid (D = 2.44) or mathematics (D = 1.59) learning difficulties, whereas intelligence, visuospatial attention, and verbal short-term memory discriminated typically achieving students from students with reading disability (D = 1.08). The combination of in-class attentive behavior, verbal short-term memory, and mathematics self-efficacy discriminated students with mathematics difficulties from their peers with reading difficulties (D = 1.16). Given the consistent importance of in-class attentive behavior, we conducted post hoc follow-up analyses. The results suggested that students with poor in-class attentive behavior were disengaging from academic learning which in turn contributed to their risk of learning difficulties.

Boys' advantage on the fractions number line is mediated by visuospatial attention: Evidence for a parietal-spatial contribution to number line learning

The study tested the hypotheses that boys will have an advantage learning the fractions number line and this advantage will be mediated by spatial abilities. Fractions number line and, as a contrast, fractions arithmetic performance were assessed for 342 adolescents, as was their intelligence, working memory, and various spatial abilities. Boys showed smaller placement errors on the fractions number line (d = -0.22) and correctly solved more fractions arithmetic problems (d = 0.23) than girls. Working memory and intelligence predicted performance on both fractions measures, and a measure of visuospatial attention uniquely predicted number line performance and fully mediated the sex difference. Visuospatial working memory uniquely predicted fractions arithmetic performance and fully mediated the sex difference. The results help to clarify the nuanced relations between spatial abilities and formal mathematics learning and the sex differences that often emerge in mathematical domains that have a visuospatial component.

Maintenance in Mathematics for Individuals with Intellectual Disability: A Systematic Review of Literature

Despite the growing attention being paid to teaching mathematics for students with disabilities, the existing research tends to focus on mathematical skill acquisition, but not on skill maintenance. The researchers in this study reviewed all studies from 1975 to 2018 that involved teaching mathematics to individuals with intellectual disability. A total of 135 studies met inclusion criteria, but only 53 studies involved a maintenance phase (39.2%). Among the 53 studies, only 22 were included for the final analysis, after evaluating their methodological rigor. In those 22 studies, there was no consensus among researchers on the standards for conducting a maintenance phase (i.e., latency between intervention and maintenance phases, length of maintenance phase, number of maintenance sessions). Further, in the studies which included a maintenance phase, the most widely taught mathematical content was numbers and operations. All studies employed intervention packages which included more than one instructional method and/or materials and the most widely used instructional method was prompting while the most widely used instructional materials were visual supports and manipulatives. The results suggest that prompting is an evidence-based practice for individuals with intellectual disability in supporting maintenance, while explicit instruction, time delay, feedback, and instructional sequence (e.g., the virtual-representational-abstract instructional sequence) are potentially evidence-based practice for individuals with intellectual disability.

Using working memory performance to predict mathematics performance 2 years on

A number of previous studies have used working memory components to predict mathematical performance in a variety of ways; however, there is no consideration of the contributions of the subcomponents of visuospatial working memory to this prediction. In this paper we conducted a 2-year follow-up to the data presented in Allen et al. (Q J Exp Psychol 73(2):239–248, 2020b) to ascertain how these subcomponents of visuospatial working memory related to later mathematical performance. 159 children (M age = 115.48 months) completed the maths test for this second wave of the study. Results show a shift from spatial–simultaneous influence to spatial–sequential influence, whilst verbal involvement remained relatively stable. Results are discussed in terms of their potential for education and future research.