Paths to postsecondary education enrollment among adolescents with and without childhood attention-deficit/hyperactivity disorder (ADHD): A longitudinal analysis of symptom and academic trajectories.

We examined developmental trajectories of attention-deficit/hyperactivity disorder (ADHD) symptoms, standardized achievement, and school performance for adolescents with and without ADHD who did and did not enroll in postsecondary education (PSE; N = 749; 79% boys; 63% White, 17% non-Hispanic Black, 10% Hispanic, and 10% other ethnicities). In a multisite study (recruitment based in New York, North Carolina, Pennsylvania, California, and Quebec), participants were originally enrolled between 1994 and 1998 at ages 7 to 9.9 and followed up through 2012 (Mage = 25 at final follow-up). Adolescents who eventually enrolled in PSE had less severe symptoms, but differences were modest and trajectories were similar over time. For all adolescents, standardized achievement trajectories declined up to two thirds of a standard deviation from ages 9 to 17. By the end of high school, the average GPA of adolescents with ADHD was three quarters of a point higher for those who eventually enrolled in PSE compared to those who did not. Overall, school performance mattered more than academic achievement for understanding eventual enrollment of adolescents with ADHD.

Walking another pathway: The inclusion of patterning in the pathways to mathematics model.

According to the Pathways to Mathematics model [LeFevre et al. (2010), Child Development, Vol. 81, pp. 1753-1767], children's cognitive skills in three domains-linguistic, attentional, and quantitative-predict concurrent and future mathematics achievement. We extended this model to include an additional cognitive skill, patterning, as measured by a non-numeric repeating patterning task. Chilean children who attended schools of low or high socioeconomic status (N = 98; 54% girls) completed cognitive measures in kindergarten (Mage = 71 months) and numeracy and mathematics outcomes 1 year later in Grade 1. Patterning and the original three pathways were correlated with the outcomes. Using Bayesian regressions, after including the original pathways and mother's education, we found that patterning skills predicted additional variability in applied problem solving and arithmetic fluency, but not number ordering, in Grade 1. Similarly, patterning skills were included in the best model for applied problem solving and arithmetic fluency, but not for number ordering, in Grade 1. In accord with the hypotheses of the original Pathways to Mathematics model, patterning varied in its unique and relative contributions to later mathematical performance, depending on the demands of the tasks. We conclude that patterning is a useful addition to the Pathways to Mathematics model, providing further insights into the range of cognitive precursors that are related to children's mathematical development.

Divide and conquer: Relations among arithmetic operations and emerging knowledge of fraction notation for Chinese students in Grade 4.

How do whole number arithmetic skills support students' understanding of fraction magnitude during the emerging stages of fraction learning? Chinese students in Grade 4 (N = 1038; Mage = 9.9 years; 55.6% boys) completed assessments of whole number arithmetic skills (i.e., addition, subtraction, multiplication, and division), fraction mapping (i.e., connecting visual fraction representations to fraction notations), and fraction comparison (i.e., comparing magnitudes of fraction symbols). We found that division skills uniquely differentiated students who had a basic understanding of fraction notation (mappers) from students with no understanding of fraction notation (non-mappers). Furthermore, we found that division mediated the relations between all three other arithmetic operations (i.e., addition, subtraction, and multiplication) and fraction mapping performance for the mappers. For fraction comparison, there was evidence of the whole number bias for the majority of students. The current results highlight the importance of the mastery of division skills and its dominance in predicting individual differences in fraction mapping for Chinese students in Grade 4.

Children's Knowledge of Symbolic Number in Grades 1 and 2: Integration of Associations.

How do children develop associations among number symbols? For Grade 1 children (n = 66, M = 78 months), sequence knowledge (i.e., identify missing numbers) and number comparison (i.e., choose larger number) predicted addition, both concurrently and indirectly at the end of Grade 1. Number ordering (i.e., touch numbers in order) did not predict addition but was predicted by number comparison, suggesting that magnitude associations underlie ordering performance. In contrast, for Grade 2 children (n = 80, M = 90 months), number ordering predicted addition concurrently and at the end of Grade 2; number ordering was predicted by number comparison, sequencing, and inhibitory processing. Development of symbolic number competence involves the hierarchical integration of sequence, magnitude, order, and arithmetic associations.

Number line development of Chilean children from preschool to the end of kindergarten.

Children's performance on number line tasks reflects their developing number system knowledge. Before 5 years of age, most children perform poorly on even the simplest number lines (i.e., 0-10). Our goal was to understand how number line skills develop before formal schooling. Chilean preschoolers attempted a 0-10 number line task three times over 2 years: at the beginning of pre-kindergarten (M = 4:7 [years;months]; Time 1), at the end of pre-kindergarten (M = 5:0; Time 2), and at the end of kindergarten (M = 5:10; Time 3). We used latent class analysis to group children according to their patterns of performance across number targets. At Time 1, 86% of children had error patterns indicating that they randomly placed estimates on the line. At Time 2, 56% of children continued to respond randomly. At Time 3, 56% of children showed competent performance across the number line, 23% were accurate only near the endpoints, and 21% were accurate only for low target numbers near the origin. Latent transition analyses showed that the transition from less to more proficient estimation classes was predicted by children's number identification skills. Thus, number line performance changed dramatically from 4 to 6 years of age as children began to develop the cognitive and numerical skills necessary to accurately estimate numbers on a number line.

The subject matters: relations among types of anxiety, ADHD symptoms, math performance, and literacy performance.

In this study, we extended a model of the relations among ADHD symptoms, anxiety, and academic performance. Undergraduates (N = 515) completed self-report measures of anxiety (i.e. trait, test, math, and literacy) and ADHD symptoms. During the study, they completed math and literacy measures and reported their current (i.e. state) anxiety three times. There were significant correlations among ADHD symptoms and all measures of anxiety. However, neither ADHD symptoms nor trait anxiety were correlated with math or literacy performance. Test-anxious students reported increasing state anxiety as the study progressed. In contrast, math-anxious students reported increased state anxiety following the math tasks but not the literacy tasks and literacy-anxious students reported increased state anxiety following the literacy tasks but not the math tasks. With respect to performance, math-anxious students had worse math performance and literacy-anxious students had worse literacy performance whereas test anxiety was not directly related to performance on either math or literacy tasks. Patterns of relations did not differ for men and women, but, except for literacy anxiety, women reported higher levels of all types of anxiety. These results could help educators understand how affective responses are related to university students' academic performance.

Children's Home Numeracy Environment Predicts Growth of their Early Mathematical Skills in Kindergarten.

This study investigated the longitudinal associations between children's early mathematics and their home numeracy environment (HNE). Chilean children from families who varied widely in socioeconomic status were assessed at the beginning and end of prekindergarten in 2016 (N = 419, Mage  = 4:7 [years:months]), and at the end of kindergarten in 2017 (N = 368, Mage  = 5:10). Children whose parents provided frequent operational numeracy activities (e.g., learning simple sums) at prekindergarten showed better arithmetic performance and growth in nonsymbolic and symbolic number comparison at the end of kindergarten. Parents' knowledge of number-related games predicted children's arithmetic skills and growth in nonsymbolic number comparison. These findings underscore the persistent relations between the HNE and the development of children's mathematical skills.

Refining the quantitative pathway of the Pathways to Mathematics model.

In the current study, we adopted the Pathways to Mathematics model of LeFevre et al. (2010). In this model, there are three cognitive domains--labeled as the quantitative, linguistic, and working memory pathways--that make unique contributions to children's mathematical development. We attempted to refine the quantitative pathway by combining children's (N=141 in Grades 2 and 3) subitizing, counting, and symbolic magnitude comparison skills using principal components analysis. The quantitative pathway was examined in relation to dependent numerical measures (backward counting, arithmetic fluency, calculation, and number system knowledge) and a dependent reading measure, while simultaneously accounting for linguistic and working memory skills. Analyses controlled for processing speed, parental education, and gender. We hypothesized that the quantitative, linguistic, and working memory pathways would account for unique variance in the numerical outcomes; this was the case for backward counting and arithmetic fluency. However, only the quantitative and linguistic pathways (not working memory) accounted for unique variance in calculation and number system knowledge. Not surprisingly, only the linguistic pathway accounted for unique variance in the reading measure. These findings suggest that the relative contributions of quantitative, linguistic, and working memory skills vary depending on the specific cognitive task.

Continuity and change in the home literacy environment as predictors of growth in vocabulary and reading.

One hundred and ten English-speaking children schooled in French were followed from kindergarten to Grade 2 (Mage : T1 = 5;6, T2 = 6;4, T3 = 6;11, T4 = 7;11). The findings provided strong support for the Home Literacy Model (Sénéchal & LeFevre, ) because in this sample the home language was independent of the language of instruction. The informal literacy environment at home predicted growth in English receptive vocabulary from kindergarten to Grade 1, whereas parent reports of the formal literacy environment in kindergarten predicted growth in children's English early literacy between kindergarten and Grade 1 and growth in English word reading during Grade 1. Furthermore, 76% of parents adjusted their formal literacy practices according to the reading performance of their child, in support of the presence of a responsive home literacy curriculum among middle-class parents.

Formal and informal home learning activities in relation to children's early numeracy and literacy skills: the development of a home numeracy model.

The purpose of this study was to propose and test a model of children's home numeracy experience based on Sénéchal and LeFevre's home literacy model (Child Development, 73 (2002) 445-460). Parents of 183 children starting kindergarten in the fall (median child age=58 months) completed an early home learning experiences questionnaire. Most of the children whose parents completed the questionnaire were recruited for numeracy and literacy testing 1 year later (along with 32 children from the inner city). Confirmatory factor analyses were used to reduce survey items, and hierarchical regression analyses were used to predict the relation among parents' attitudes, academic expectations for their children, reports of formal and informal numeracy, and literacy home practices on children's test scores. Parental reports of formal home numeracy practices (e.g., practicing simple sums) predicted children's symbolic number system knowledge, whereas reports of informal exposure to games with numerical content (measured indirectly through parents' knowledge of children's games) predicted children's non-symbolic arithmetic, as did numeracy attitudes (e.g., parents' enjoyment of numeracy). The home literacy results replicated past findings; parental reports of formal literacy practices (e.g., helping their children to read words) predicted children's word reading, whereas reports of informal experiences (i.e., frequency of shared reading measured indirectly through parents' storybook knowledge) predicted children's vocabulary. These findings support a multifaceted model of children's early numeracy environment, with different types of early home experiences (formal and informal) predicting different numeracy outcomes.

Forty years of research on mathematical cognition: Summing it up.

In this article, I describe my academic journey as a Canadian researcher in the field of mathematical cognition. The article is a version of the talk I gave when I was presented with the Donald O. Hebb Award from the Canadian Society for Brain, Behaviour and Cognitive Science in July 2023 at the University of Guelph. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Transcoding of French numbers for first- and second-language learners in third grade.

Transcoding is the process of translating between spoken and written numbers, and it is correlated with other mathematical skills. In the present study, we investigated the link between French number writing of 49 students in the third grade (aged 7-9 years) and their language skills. Transcoding in French is of particular interest because the spoken number language system does not completely correspond to that of the written digits (e.g., quatre-vingt-dix [four-twenty-ten] and 90). We hypothesised that the complex linguistic structure of spoken numbers in French would be challenging for students who are learning to transcode. First and second French-language learners' accuracy and errors were recorded during a writing task of 3- to 7-digit numbers. Children also completed linguistic tests (e.g., receptive vocabulary, receptive syntax). Results showed that first- and second-language learners did not differ in their transcoding accuracy. Number size, decade complexity of stimulus number words in French (i.e., numbers containing a complex decade, operationalized as a number between soixante-dix, 70, and quatre-vingt-dix-neuf, 99), and receptive vocabulary predicted children's French transcoding skills. Students were more likely to produce errors (e.g., 68 or 6018 for 78) when they transcoded complex decade numbers compared with simple decade numbers. When an error was made on the complex decade portion of a number, it was likely a lexical error. In conclusion, third graders, both first- and second-language learners, found complex decade numbers challenging and their performance was related to their general vocabulary skills.

Cognition in early relapsing-remitting multiple sclerosis: consequences may be relative to working memory.

The Relative Consequence Model proposes multiple sclerosis (MS) patients have a fundamental deficit in processing speed that compromises other cognitive functions. The present study examined the mediating role of processing speed,as well as working memory, in the MS-related effects on other cognitive functions for early relapsing-remitting patients. Seventy relapsing-remitting MS patients with disease duration not greater than 10 years and 72 controls completed tasks assessing processing speed, working memory, learning, and executive functioning. The possible mediating roles of speed and working memory in the MS-related effects on other cognitive functions were evaluated using structural equation modeling. Processing speed was not significantly related to group membership and could not have a mediating role. Working memory was related to group membership and functioned as a mediating/intervening factor. The results do not support the Relative Consequence Model in this sample and they challenge the notion that working memory impairment only emerges at later disease stages. The results do support a mediating/intervening role of working memory. These results were obtained for early relapsing-remitting MS patients and should not be generalized to the broader MS population. Instead, future research should examine the relations that exist at other disease stages.

The role of executive attention in the acquisition of mathematical skills for children in Grades 2 through 4.

We examined the role of executive attention, which encompasses the common aspects of executive function and executive working memory, in children's acquisition of two aspects of mathematical skill: (a) knowledge of the number system (e.g., place value) and of arithmetic procedures (e.g., multi-digit addition) and (b) arithmetic fluency (i.e., speed of solutions to simple equations such as 3+4 and 8-5). Children in Grades 2 and 3 (N=157) completed executive attention and mathematical tasks. They repeated the mathematical tasks 1 year later. We used structural equation modeling to examine the relations between executive attention and (a) concurrent measures of mathematical knowledge and arithmetic fluency and (b) growth in performance on these measures 1 year later. Executive attention was concurrently predictive of both knowledge and fluency but predicted growth in performance only for fluency. A composite language measure predicted growth in knowledge from Grade 2 to Grade 3. The results support an important role for executive attention in children's acquisition of novel procedures and the development of automatic access to arithmetic facts.

The hierarchical relations among mathematical competencies: From fundamental numeracy to complex mathematical skills.

Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students (N = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Fraction mapping and fraction comparison skills among grade 4 Chinese students: An error analysis.

BACKGROUND: Mapping fraction symbols to magnitudes is easier for students to master than comparing fraction magnitudes. Fraction mapping assesses students' understanding of part-whole interpretations of fractions; fractions represent the parts of an object or set of objects. Fraction comparison assesses students' understanding of measurement interpretations of fractions; a fraction is a single numerical quantity, not a combination of two whole numbers. AIM: To examine and compare the types of errors made by emergent fraction learners on fraction mapping and comparison tasks. SAMPLE: Grade 4 Chinese students (N = 1036; 577 boys; Mage  = 9.9 years). METHOD: We examined performance and identified errors on fraction mapping and comparison tasks. For mapping, students converted pictorial representations into fraction notation. For comparison, they chose the larger of two symbolic fractions. RESULTS: Consistent with curriculum expectations, most students successfully mapped pictorial representations to fraction notation. In contrast, few students were able to accurately compare fraction magnitudes. Within each task, students' errors were consistent across trials, suggesting that they applied systematic but incorrect procedures. However, errors were not consistent between tasks and the correlation between mapping and comparison performance was weak. CONCLUSION: Emergent fraction learners can acquire part-whole knowledge of fractions without acquiring measurement interpretations of fractions. Moreover, misconceptions about different interpretations of fractions need not overlap. Awareness of the types of errors that students make can assist educators in identifying misconceptions early so that students do not build their fraction knowledge on erroneous beliefs.

The symbol digit modalities test and the paced auditory serial addition test involve more than processing speed.

BACKGROUND: Slowed processing speed is the most frequently reported cognitive deficit for people with multiple sclerosis (MS). However, measures used to assess processing speed may also recruit other cognitive abilities. The present objective was to determine the contributions of different cognitive functions to performance on two commonly used processing speed measures: the Symbol Digit Modalities Test (SDMT) and the Paced Auditory Serial Addition Test (PASAT). METHODS: Adults with relapsing-remitting MS (n = 70) and controls (n = 72) completed the SDMT, PASAT, and multiple measures assessing processing speed, working memory, and learning. Hierarchical regression analyses were used to examine the contributions of MS, processing speed, working memory, learning, and all possible interactions among factors to SDMT and PASAT scores. RESULTS: Processing speed and working memory generally contributed to performance on the SDMT and PASAT, with learning additionally contributing to SDMT performance. However, significant interactions revealed processing speed did not influence PASAT performance for individuals with high working memory ability whereas processing speed became increasingly more important as working memory declined to average and low levels. Further, processing speed was associated with SDMT performance for patients with MS but not controls. CONCLUSIONS: These findings support a multifactorial interpretation of the SDMT and PASAT, which facilitates their usefulness as screening measures for cognitive decline but prevents them from identifying which specific cognitive functions are affected.

With a little help from our pediatrician: An intervention to promote mathematics-related home activities through regular well-child visits.

Introduction: Children's involvement in mathematics-related activities in the home environment is associated with the development of their early numeracy over the preschool years. Intervention studies to promote parents' awareness and provision of mathematics-related home activities are however scant. In this study we developed and tested the effectiveness of a non-intensive intervention program delivered by community pediatricians to promote mathematics-related activities in the home environment. Methods: Parents of 204 Italian children were invited to report on the frequency of mathematics-related home activities when children attended the first preschool year (3 years, 8 months of age on average) and, subsequently, the third preschool year (5 years, 6 months of age on average). At both waves, children were also assessed on their early numeracy. In occasion of the routine well-child visit at age 5, parents who were randomly allocated to the intervention condition (vs. a business-as-usual control condition) received guidance on age-appropriate home mathematics-related practices to sustain children's numerical development. Results: Results revealed that parents in the intervention group improved their provision of home mathematics-related activities at the post-intervention assessment (relative to baseline) to a greater extent than parents in the control condition. No effect was observed on children's early numeracy. Discussion: Overall, results are promising in suggesting that community pediatricians may be a resource to promote home mathematics-related activities though non-intensive low-cost interventions.

Fixated in more familiar territory: Providing an explicit midpoint for typical and atypical number lines.

Does providing an explicit midpoint affect adults' performance differently for typical and atypical number line tasks? Participants (N = 29) estimated the location of target numbers on typical (i.e., 0-10,000) and atypical (i.e., 0-7,000) number lines with either an explicitly labelled midpoint or no midpoint. For the typical number line, estimation accuracy did not differ for the explicit- and implicit-midpoint conditions. For the atypical number line, participants in the explicit-midpoint condition were more accurate than those in the implicit-midpoint condition and their pattern of error was similar to that seen for typical number lines (i.e., M-shaped). In contrast, for participants in the implicit-midpoint condition, the pattern of error on the atypical line was tent-shaped, with less accurate estimates around the midpoint and quartiles than the endpoints. Eye-tracking data showed that, for all number lines, participants used the middle of the line to guide their estimates, but participants in the explicit-midpoint condition were more likely to make their first fixation around the true midpoint than those in the implicit-midpoint condition. We conclude that adults have difficulty in estimating on atypical number lines because they incorrectly calculate the numerical value of the midpoint.

Home Learning Environments of Children in Mexico in Relation to Socioeconomic Status.

We explored the home learning environments of 173 Mexican preschool children (aged 3-6 years) in relation to their numeracy performance. Parents indicated the frequency of their formal home numeracy and literacy activities, and their academic expectations for children's numeracy and literacy performance. Children completed measures of early numeracy skills. Mexican parent-child dyads from families with either high- or low-socioeconomic status (SES) participated. Low-SES parents (n = 99) reported higher numeracy expectations than high-SES parents (n = 74), but similar frequency of home numeracy activities. In contrast, high-SES parents reported higher frequency of literacy activities. Path analyses showed that operational (i.e., advanced) numeracy activities were positively related to children's numeracy skills in the high- but not in the low-SES group. These findings improve the understanding of the role of the home environment in different contexts and provide some insights into the sources of the variable patterns of relations between home learning activities and children's numeracy outcomes. They also suggest that SES is a critical factor to consider in research on children's home numeracy experiences.