Comorbid Word Reading and Mathematics Computation Difficulty at Start of First Grade.

The purpose of this analysis was to describe cognitive processes associated with comorbid difficulty between word reading (WR) and mathematics computation (MC) at the start of first grade among children selected for WR and MC delays. A sample of 234 children (mean age 6.50 years, SD = 0.31) was assessed on WR, MC, core cognitive processes (phonological processing, rapid automatized naming, verbal counting [VC]), and domain-general cognitive processes (working memory, oral language, nonverbal reasoning, attentive behavior). Structural equation modeling was used to predict a latent Comorbidity factor, which modeled shared variance between WR and MC, and to identify processes associated with that Comorbidity factor. Results identified each of the core cognitive processes, especially VC, and each of the domain-general cognitive processes, especially working memory, as explaining shared variance between WR and MC. Implications for understanding comorbid difficulty at the start of first grade and designing coordinated first-grade interventions are discussed.

Developmental profiles of arithmetic fluency skills from grades 1 to 9 and their early identification.

The aim of the present study was to examine the kinds of developmental profiles of arithmetic fluency skills that can be identified across Grades 1-9 (ages 7-16) in a large Finnish sample (n = 2,518). The study also examined whether membership in the developmental profiles could be predicted using a comprehensive set of kindergarten-age factors, including information on cognitive skills; motivational, parental, and home environment factors; and gender. Four profiles of arithmetic fluency skills development were identified using a factor mixture model: persistent arithmetic difficulties (12.23%), precocious onset (50.24%), delayed onset (36.96%), and precocious onset with a Grade 7 drop (.06%). The Cholesky models predicting membership in the three largest profiles suggested that overall, the strongest kindergarten-age predictors were cognitive skills (especially counting, number concepts, spatial relations, rapid automatized naming [RAN], phonological awareness, and letter knowledge), but motivational, parental, and home environment factors were also significant. Membership in the profile with precocious onset was predicted by most of the kindergarten-age measures, suggesting that the strengths in early skills, as well as motivational, parental, and home environment factors, are reflected in the advanced start in arithmetic development at school. The profiles with delayed onset and persistent difficulties were similar in most kindergarten-age measures but differed in task avoidance and four cognitive skills (letter knowledge, counting, number concepts, and RAN), suggesting that these factors predict differential development over the longer term. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Subtypes of mathematical learning disability and their antecedents: A cognitive diagnostic approach.

Using cognitive diagnostic modeling (CDM), this study identified subtypes of mathematics learning disability (MLD) based on children's numerical skills and examined the language and spatial precursors of these subtypes. Participants were 99 MLD children and 420 low achievers identified from 1839 Finnish children (966 boys) who were followed from preschool (age 6) to fourth grade (2007-2011). Five subtypes were identified: the arithmetic fluency deficit only subtype, the counting deficit subtype, the pervasive deficit subtype, the symbolic deficit subtype, and the counting and concept deficit subtype. Different subtypes depended on different constellations of language and spatial deficits. Findings highlight the effectiveness of CDM in identifying MLD subtypes and underscore the importance of understanding the specific deficits and antecedents of the subtypes.

Longitudinal and situational associations between math anxiety and performance among early adolescents.

Studies have found math anxiety and achievement to be related from the beginning of formal schooling, but the knowledge regarding the direction of the relationship is vague. The purpose of the present study was to study this relationship. We investigated math anxiety from two points of view: trait and state anxiety. In the first substudy, we investigated the longitudinal relationship between math anxiety and performance from sixth to seventh grade (n = 848) with cross-lagged modeling. In the second substudy, we investigated the situational relationship of anxiety and performance by giving the participants (n = 149) challenging and nonchallenging math tasks adapted to their skill level, and then examining the association between anxiety and the performance. The results suggest that math anxiety has a small longitudinal effect on performance: High anxiety in sixth grade predicted low performance in seventh grade. Anxiety also had a situational association with performance: when anxiety was aroused, the participants performed more poorly compared to their skill level. The results adduce the two-fold effect of anxiety on achievement: math anxiety seems to have both a real-time association with performance and a long-term effect on the development of basic arithmetic skills.

Benefits of Integrating an Explicit Self-Efficacy Intervention With Calculation Strategy Training for Low-Performing Elementary Students.

This study examined the malleability of math self-efficacy (SE) among children with poor calculation fluency via an intervention that targeted four sources of SE (mastery experiences, vicarious experiences, social persuasions, and emotional and physiological states). The effect of pure strategy training was contrasted with an intervention that integrated strategy training and explicit SE support. Moreover, the changes in SE source experiences and their relation with math SE, as well as the relation between math-SE profiles and calculation fluency development, were examined. In a quasi-experimental design, 60 Finnish children with calculation fluency problems in Grades 2 to 4 participated in strategy training (N = 38) or in an intervention that integrated SE support with strategy training (N = 32) for 12 weeks. The results showed that the explicit SE intervention integrated with strategy training enhanced math SE among children with poor calculation fluency and low SE (effect size, r = 0.61). Changes in mastery experiences and social persuasions were positively associated with changes in math SE among children who received the explicit SE intervention. An initially high math-SE profile and a profile indicating an increase from low to high math SE were related to growth in calculation fluency that approached the children's average age level during the interventions. In conclusion, an integrated approach that combined skill training and SE intervention was especially beneficial for children with poor calculation fluency and low math SE.

Cognitive Correlates of the Covariance in Reading and Arithmetic Fluency: Importance of Serial Retrieval Fluency.

This study examines the core predictors of the covariance in reading and arithmetic fluency and the domain-general cognitive skills that explain the core predictors and covariance. Seven-year-old Finnish children (N = 200) were assessed on rapid automatized naming (RAN), phonological awareness, letter knowledge, verbal counting, number writing, number comparison, memory skills, and processing and articulation speed in the spring of Grade 1 and on reading and arithmetic fluency in the fall of Grade 2. RAN and verbal counting were strongly associated, and a constructed latent factor, serial retrieval fluency (SRF), was the strongest unique predictor of the shared variance. Other unique predictors were phonological awareness, number comparison, and processing speed. Findings highlight the importance of SRF in clarifying the relation between reading and arithmetic fluency.

Early Cognitive Precursors of Children's Mathematics Learning Disability and Persistent Low Achievement: A 5-Year Longitudinal Study.

Mathematical difficulties have been distinguished as mathematics learning disability (MLD) and persistent low achievement (LA). Based on 1,880 Finnish children who were followed from kindergarten (age 6) to fourth grade, this study examined the early risk factors for MLD and LA. Distinct groups of MLD (6.0% of the sample) and LA (25.7%) children were identified on the basis of their mathematics performance between first and fourth grades with latent class growth modeling. Impairment in the same set of cognitive skills, including language, spatial, and counting skills, was found to underlie MLD and LA. The finding highlights the importance of monitoring mathematical development across the early grades and identifying early cognitive precursors of MLD and LA for screening and intervention efforts.

Individuality in the Early Number Skill Components Underlying Basic Arithmetic Skills.

Early number skills underlie success in basic arithmetic. However, very little is known about the skill profiles among children in preprimary education and how the potential profiles are related to arithmetic development. This longitudinal study of 440 Finnish children in preprimary education (mean age: 75 months) modeled latent performance-level profile groups for the early number skill components that are proposed to be key predictors of arithmetic (symbolic number comparison, mapping, and verbal counting skills). Based on three assessment time points (September, January, and May), four profile groups were found: the poorest-performing (6%), low-performing (16%), near-average-performing (33%), and high-average-performing children (45%). Although the differences between the groups were statistically significant in all three number skill components and in basic arithmetic, the poorest-performing children seemed to have serious difficulties in accessing the semantic meaning of symbolic numbers that was required in the number comparison and mapping tasks in this study. Interestingly, the tasks demanding processing between quantities and symbols also most differentiated the poorest-performing children from the low-performing children. Due to remarkable and stable individual differences in early number skill components, the findings suggest systematic support and progress monitoring practices in preeducational settings to diminish and avoid potential difficulties in arithmetic and mathematics in general.

Does Multi-Component Strategy Training Improve Calculation Fluency Among Poor Performing Elementary School Children?

The aim of the present study was to extend the previous intervention research in math by examining whether elementary school children with poor calculation fluency benefit from strategy training focusing on derived fact strategies and following an integrative framework, i.e., integrating factual, conceptual, and procedural arithmetic knowledge. It was also examined what kind of changes can be found in frequency of using different strategies. A quasi-experimental design was applied, and the study was carried out within the context of the school and its schedules and resources. Twenty schools in Finland volunteered to participate, and 1376 children were screened in for calculation fluency problems. Children from second to fourth grades were recruited for the math intervention study. Children with low performance (below the 20th percentile) were selected for individual assessment, and indications of using counting-based strategies were the inclusion criteria. Altogether, 69 children participated in calculation training for 12 weeks. Children participated in a group based strategy training twice a week for 45 min. In addition, they had two short weekly sessions for practicing basic addition skills. Along with pre- and post-intervention assessments, a 5-month follow-up assessment was conducted to exam the long-term effects of the intervention. The results showed that children with dysfluent calculation skills participating in the intervention improved significantly in their addition fluency during the intervention period, showing greater positive change than business-as-usual or reading intervention controls. They also maintained the reached fluency level during the 5-month follow-up but did not continue to develop in addition fluency after the end of the intensive training program. There was an increase in fact retrieval and derived fact/decomposition as the preferred strategies in math intervention children and a decrease of the use of counting-based strategies, which were the most common strategies for them before the intervention. No transfer effect was found for subtraction fluency.

Response-To-Intervention in Finland and the United States: Mathematics Learning Support as an Example.

Response to Intervention (RTI) was accepted in the early 2000s as a new framework for identifying learning difficulties (LD) in the U.S. In Finland, a similar multi-tiered framework has existed since 2010. In the present study, these frameworks are presented from the viewpoint of the role of assessment and instruction as expressed in documents that describe the frameworks, as it seems that these two components of RTI are the most disparate between the U.S. and Finland. We present a suggestion for the Finnish framework as an example of support in mathematics learning that incorporates principles of RTI (such as systematized assessment and instruction, cyclic support, and modifiable instruction). Finally, recommendations are presented for further refining and developing assessment and instruction policies in the two countries.

Knowing, applying, and reasoning about arithmetic: Roles of domain-general and numerical skills in multiple domains of arithmetic learning.

The longitudinal relations of domain-general and numerical skills at ages 6-7 years to 3 cognitive domains of arithmetic learning, namely knowing (written computation), applying (arithmetic word problems), and reasoning (arithmetic reasoning) at age 11, were examined for a representative sample of 378 Finnish children. The results showed that domain-general skills, including spatial visualization, language, rapid automatized naming, and working memory, contributed independently to arithmetic learning. These relations were mostly mediated via basic number competence (i.e., counting sequence and number system knowledge), although spatial visualization remained predictive of arithmetic outcomes. The findings underscore a similar developmental course of arithmetic learning across different cognitive domains where domain-general skills build a launchpad for advanced arithmetic via enhancing basic number competence. (PsycINFO Database Record

Math anxiety and its relationship with basic arithmetic skills among primary school children.

BACKGROUND: Children have been found to report and demonstrate math anxiety as early as the first grade. However, previous results concerning the relationship between math anxiety and performance are contradictory, with some studies establishing a correlation between them while others do not. These contradictory results might be related to varying operationalizations of math anxiety. AIMS: In this study, we aimed to examine the prevalence of math anxiety and its relationship with basic arithmetic skills in primary school children, with explicit focus on two aspects of math anxiety: anxiety about failure in mathematics and anxiety in math-related situations. SAMPLE: The participants comprised 1,327 children at grades 2-5. METHODS: Math anxiety was assessed using six items, and basic arithmetic skills were assessed using three assessment tasks. RESULTS: Around one-third of the participants reported anxiety about being unable to do math, one-fifth about having to answer teachers' questions, and one tenth about having to do math. Confirmatory factor analysis indicated that anxiety about math-related situations and anxiety about failure in mathematics are separable aspects of math anxiety. Structural equation modelling suggested that anxiety about math-related situations was more strongly associated with arithmetic fluency than anxiety about failure. Anxiety about math-related situations was most common among second graders and least common among fifth graders. CONCLUSIONS: As math anxiety, particularly about math-related situations, was related to arithmetic fluency even as early as the second grade, children's negative feelings and math anxiety should be identified and addressed from the early primary school years.

A pilot study of the effects of RightStart instruction on early numeracy skills of children with specific language impairment.

This pilot study investigated the effects of an early numeracy program, RightStart Mathematics (RS), on Finnish kindergartners with specific language impairment (SLI). The study applied a pre-test-instruction-post-test design. The children with SLI (n=9, Mage=82.11 months) received RS instruction two to three times a week for 40 min over seven months, which replaced their business-as-usual mathematics instruction. Mathematical skill development among children with SLI was examined at the individual and group levels, and compared to the performance of normal language-achieving age peers (n=32, Mage=74.16 months) who received business-as-usual kindergarten mathematics instruction. The children with SLI began kindergarten with significantly weaker early numeracy skills compared to their peers. Immediately after the instruction phase, there was no significant difference between the groups in counting skills. In Grade 1, the children with SLI performed similarly to their peers in addition and subtraction skills (accuracy) and multi-digit number comparison, but showed weaker skills in arithmetical reasoning and in matching spoken and printed multi-digit numbers. Our pilot study showed encouraging signs that the early numeracy skills of children with SLI can be improved successfully in a kindergarten small-classroom setting with systematic instruction emphasizing visualization.

Linguistic and spatial skills predict early arithmetic development via counting sequence knowledge.

Utilizing a longitudinal sample of Finnish children (ages 6-10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in kindergarten, predicted the level of arithmetic in first grade, and later growth through third grade. Study 2 (n = 378) further showed that these associations were mediated by counting sequence knowledge measured in first grade. These studies add to the literature by demonstrating the importance of written language for arithmetic development. The findings are consistent with the hypothesis that linguistic and spatial skills can improve arithmetic development by enhancing children's number-related knowledge.

Cognitive predictors of single-digit and procedural calculation skills and their covariation with reading skill.

This study examined the extent to which children's cognitive abilities in kindergarten and their mothers' education predict their single-digit and procedural calculation skills and the covariance of these with reading skill in Grade 4. In kindergarten, we assessed children's (N=178) basic number skills, linguistic skills, and visual attention. In Grade 4, we assessed their calculation and reading skills. Data on children's cognitive ability at 5 years of age and their mothers' level of education were also collected. The results showed that both of the core components of calculation, single-digit and procedural calculation, as well as their covariance with reading, were predicted by unique cognitive factors. Fluency in single-digit calculation and text reading shared an underlying cognitive process, that is, the ability to fluently retrieve verbal or visual-verbal associations from long-term memory. In contrast, procedural calculation was predicted not only by single-digit calculation but also by mother's education and conceptual knowledge of numbers. Overall, the results suggest that a multicomponential approach, including a hierarchical relation among various components, is fruitful when trying to understand the development of mathematical skill and its covariation with reading.

Basic numeracy in children with specific language impairment: heterogeneity and connections to language.

PURPOSE: This study examined basic numerical skills in children with specific language impairment (SLI) and how well linguistic factors explain the variance in these children's number skills. METHOD: The performance of children with SLI (n=29) was compared with that of typically developing children along a continuum ranging from preschool to 3rd grade (n=20, 47, 40, and 33). This facilitated both linguistic and educational age comparisons. To study number skills within the SLI group more closely, this group was divided into subgroups on the basis of their performance in verbal and nonverbal numerical skills. The performance of the different SLI subgroups on the linguistic and nonverbal reasoning task was analyzed. RESULTS: As a single group, the children with SLI lagged behind their educational age controls in both verbal and nonverbal numerical skills. Subgroup analyses revealed that the ability to retrieve arithmetic facts from the memory was connected to naming fluency, whereas the differences in nonverbal numerical skills were not explained by the cognitive skills measured (nonverbal reasoning skill, verbal short-term memory, vocabulary, comprehension, and naming fluency). CONCLUSIONS: This study demonstrates that children with SLI form a very heterogeneous group in their numerical skills, and thus specific hypotheses concerning the influence of linguistic deficits on developing numerical skills are required. The cognitive components of serial naming speed present a promising domain for further exploration.