Research Byte: Lets hear it (again) for #visual-spatial (#Gv) #workingmemory (#Gwm) and math #reasoning (#Gf-RQ) — #CHC #SPED #EDPSY #schoolpsychology #schoolpsychologist #WJV

From Spatial Construction to Mathematics: Exploring the Mediating Role of Visuospatial Working Memory.  Developmental Psychology.  An open access article that can be downloaded—Click here.

Yuxin Zhang, Rebecca Bull, and Emma C. Burns.

Abstract

This study examined the longitudinal pathways from early spatial skills at 5 and 7 years to their mathematics reasoning abilities at 17 years in a large cohort sample (N = 16,338) from the Millennium Cohort Study. Children were assessed at four time points: Sweep 3 (Mage = 5.29), Sweep 4 (Mage = 7.23), Sweep 5 (Mage = 11.17), and Sweep 7 (Mage = 17.18), with measures including spatial construction skills, visuospatial working memory, mathematics achievement, and mathematics reasoning skills. Path analyses revealed that spatial construction at age 5 directly predicted mathematics achievement at age 7 after accounting for sex, age, socioeconomic status, vocabulary, and nonverbal reasoning ability. Furthermore, spatial construction at 5 and 7 years was directly associated with mathematics reasoning skills at 17, and spatial working memory at age 11 partially mediated this relationship. Notably, the direct effects of spatial construction on mathematics reasoning at age 17 remained significant and robust after accounting for the mediator and covariates. These findings highlight the potential value of early spatial construction skills as predictors of subsequent mathematical development over the long term.

Public Significance Statement.Children with stronger spatial skills at age 5 are more likely to achieve higher scores in mathematics at ages 7 and 17. Visuospatial working memory partly explained this link, and early spatial skills showed a direct and robust association with later mathematics. This study identified early spatial skills as an important long-term predictor of mathematics from preschool through adolescence. The findings highlight the potential of infusing spatial thinking and using spatial strategies to better understand and solve mathematics problems.

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Comment:  I recently made a post regarding research that demonstrated the importance of visual-spatial working memory abilities for spatial navigation where I also mentioned the new (not yet online as far as I know) WJ V Visual Working Memory test, which was decades in development—an interesting test development “back story”.  

Research Byte: General Ability (#g) Level Moderates Cognitive–#Achievement Relations for #Mathematics (#WJIV)—#WJIV #WJV #schoolpsychology #mathematics #SPED #EDPSYCH

[Blogmaster comment:   First…COI info…I’m a coauthor of the WJ IV and WJ V.  Second, regular readers may have noticed that I’ve been MIA on my various social media outlets the past 2-3 months.  I needed a break after spending the last five years working on the WJ V.  I also needed to attend to some family issues.  I plan to restart my sharing of interesting new research and FYI opinion posts].

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New pub in Journal of Intelligence.  Click here to view and download (open access).

General Ability Level Moderates Cognitive–Achievement Relations for Mathematics 

by 

Christopher R. Niileksela

  

Jacob Robbins

 

Daniel B. Hajovsky

 

Abstract

Spearman’s Law of Diminishing Returns (SLODR) suggests general intelligence would be a stronger predictor of academic skills at lower general ability levels, and broad cognitive abilities would be stronger predictors of academic skills at higher general ability levels. Few studies have examined how cognitive–mathematics relations may vary for people with different levels of general cognitive ability. Multi-group structural equation modeling tested whether cognitive–mathematics relations differed by general ability levels for school-aged children (grades 1–5 and grades 6–12) using the Woodcock-Johnson Third Edition (n = 4470) and Fourth Edition (n = 3891) standardization samples. Results suggested that relationships between cognitive abilities and mathematics varied across general ability groups. General intelligence showed a stronger relative effect on mathematics for those with lower general ability compared to those with average or high general ability, and broad cognitive abilities showed a stronger relative effect on mathematics for those with average or high general ability compared to those with lower general ability. These findings provide a more nuanced understanding of cognitive–mathematics relations.

Keywords: 

cognitive ability; academic skills; cognitive–achievement relations; Spearman’s Law of Diminishing Returns

Research Byte: Development of #Arithmetic Across the #Lifespan: A Registered Report. - #Gq #CHC #Gwm #EF #Gs #schoolpsychology #SPED #SLD

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Development of Arithmetic Across the Lifespan: A Registered Report.  

Open access paper available at Developmental Psychology journal.  Click here to access

Abstract

 

Arithmetic skills are needed at any age. In everyday life, children to older adults calculate and deal with numbers. The processes underlying arithmetic seem to change with age. From childhood to younger adulthood, children get better in domain-specific numerical skills such as place-value processing. From younger to older adulthood, domain-general cognitive skills such as working memory decline. These skills are needed for complex arithmetic such as addition with carrying and subtraction with borrowing. This study investigates how the domain-specific (number magnitude, place-value processing) and domain-general (working memory, processing speed, inhibition) processes of arithmetic change across the lifespan. Thereby, arithmetic effects (carry and borrow effects), numerical effects (distance and compatibility effects), and cognitive skills were assessed in children, younger and older adolescents, and younger, middle-aged and older adults. The results showed that numerical and arithmetic skills improve from childhood to young adulthood and remain relatively stable throughout adulthood, even though domain-general pro-cesses, particularly working memory and processing speed, decline with age. While number magnitude and place-value processing both develop until adulthood, number magnitude processing shows deficits during aging, whereas place-value processing remains intact even in old age. The carry effect shifts from a categorical all-or-none decision (whether or not a carry operation is needed) to a more continuous magnitude process in adulthood, reflecting increasing reliance on domain-specific skills. In contrast, the borrow effect remains largely categorical across all age groups, depending on general cognitive processes. These results provide critical insights into how arithmetic skills change over the lifespan, relying on both domain-specific and domain-general processes.

Public Significance Statement 

Numerical and arithmetic skills improve significantly during school and are mostly preserved throughout adulthood—despite a decline in cognitive skills such as working memory and processing speed during aging. When facing complex arithmetic, all—from children up to older adults—need longer to calculate, but lifelong experience helps in dealing with arithmetic complexity. Throughout the lifespan, arithmetic requires both cognitive skills as well as numeric skills.

Research byte: Variability in #math (#Gq) achievement growth among students with early math learning difficulties and the role of school supports.—attention #schoolpsychology #SPED

Yet another new math achievement related research report.  I’ve detected a trend towards more high quality published research re the predictors of math achievement and longitudinal growth…which is reflected in more frequent math-related “research bytes” here at IQs corner.

Variability in math achievement growth among students with early math learning difficulties and the role of school supports.

Gesuelli, K.-A., Miller-Cotto, D., & Barbieri, C. A. (2025). Variability in math achievement growth among students with early math learning difficulties and the role of school supports. Journal of Educational Psychology. Advance online publication. https://doi.org/10.1037/edu0000928

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Research Byte: #Cognitive Factors Underlying #Mathematical Skills: A Systematic Review and #MetaAnalysis - relevant for #schoolpsychology

Cognitive Factors Underlying Mathematical Skills: A Systematic Review and Meta-Analysis.  

Amland, T., Grande, G., Scherer, R., Lervåg, A., & Melby-Lervåg, M. (2024). Cognitive factors underlying mathematical skills: A systematic review and meta-analysis.Psychological Bulletin.Advance online publication. 

(click to download and read—open access)

Abstract

In understanding the nature of mathematical skills, the most influential theories suggest that mathematical cognition draws on different systems: numerical, linguistic, spatial, and general cognitive skills. Studies show that skills in these areas are highly predictive of outcomes in mathematics. Nonetheless, the strength of these relations with mathematical achievement varies, and little is known about the moderators or relative importance of each predictor. Based on 269 concurrent and 174 longitudinal studies comprising 2,696 correlations, this meta-analysis summarizes the evidence on cognitive predictors of mathematical skills in children and adolescents. The results showed that nonsymbolic number skills (often labeled approximate number sense) correlate significantly less with mathematical achievement than symbolic number skills and that various aspects of language relate differently to mathematical outcomes. We observed differential predictive patterns for arithmetic and word problems, and these patterns only partly supported the theory of three pathways—quantitative, linguistic, and spatial—for mathematical skills. Concurrently, nonsymbolic number and phonological skills were weak but exclusive predictors of arithmetic skills, whereas nonverbal intelligence quotient (IQ) predicted word problems only. Only symbolic number skills predicted both arithmetic and word problems concurrently. Longitudinally, symbolic number skills, spatial ability, and nonverbal IQ predicted both arithmetic and word problems, whereas language comprehension was important for word problem solving only. As in the concurrent data, nonsymbolic number skill was a weak longitudinal predictor of arithmetic skills. We conclude that the candidates to target in intervention studies are symbolic number skills and language comprehension. It is uncertain whether the two other important predictors, nonverbal IQ and spatial skills, are actually malleable.

Public Significance Statement 

This systematic review and meta-analysis found that symbolic number skills, language comprehension, and nonverbal reasoning skills are the most important foundational skills of achievement in mathematics in childhood and early adolescence. Children's understanding of digits and number words seems to be the most promising target to design content that can be tested in future intervention studies. Moreover, whether interventions targeting language comprehension could benefit children struggling with mathematical word problems should be further examined. Mathematical skills is a fundamental factor both for a productive society and for individual development and employment and finding ways that might increase mathematical abilities can potentially have great consequences.

Keywords: mathematics achievement, language, spatial ability, number sense, meta-analytic structural equation modeling

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Research Byte: Domain-specific and domain-general skills as predictors of #arithmetic #fluency development—New #WJV will have similar measure—#MagnitudeComparison test

 Domain-specific and domain-general skills as predictors of arithmetic fluency development

Author links open overlay panel, , , , , 

Link to PDF appears available at journal page (click here to go directly to PDF)

Abstract

We investigated Norwegian children's (n = 262) development in arithmetic fluency from first to third grade. Children's arithmetic fluency was measured at four time points, domain-specific (i.e., symbolic magnitude processing and number sequences) and domain-general skills (i.e., working memory, rapid naming, non-verbal reasoning, and sustained attention) once in the first grade. Based on a series of growth mixture models, one developmental trajectory best described the data. Multigroup latent growth curve models showed that girls and boys developed similarly in their arithmetic fluency over time. Symbolic magnitude processing and number sequence skills predicted both initial level and growth in arithmetic fluency, and working memory predicted only initial level, similarly for boys and girls. Mother's education level predicted the initial level of arithmetic fluency for boys, and rapid naming predicted growth for girls. Our findings highlight the role of domain-specific skills in the development of arithmetic fluency.

As an FYI, the forthcoming WJ V (Q1, 2025) has a new test (Magnitude Comparison) that measures abilities similar to the symbolic magnitude processing ability measure used in this study (COI - I’m a coauthor of the WJ V)

https://www.sciencedirect.com/science/article/pii/S104160802400178X

Research Byte: Evaluating the treatment utility of the Cognitive Assessment System (#CAS): A #metaanalysis of #reading and #mathematics outcomes

 

Richard J. McNulty a 1 2 Randy G. Floyd a 2

, , , , 

https://doi.org/10.1016/j.jsp.2024.101384

Abstract

There has been a long search for cognitive assessments that reveal aptitudes thought to be useful for treatment planning. In this regard, since the 1990s, there has been some enthusiasm for the Cognitive Assessment System (CAS) and its potential promise for informing treatment due to its alignment of theory, assessment instrument, and suite of interventions. The purpose of this meta-analytic review was to synthesize research pertinent to the treatment utility of the CAS according to a taxonomy of treatment utility. A total of 252 articles were produced by an electronic search and eligibility screening yielded 16 articles meeting criteria for consideration. Most studies described in these articles utilized obtained difference designs, focused on the Planning composite scores from the CAS, and addressed math interventions. Only seven studies with publication dates from 1995 to 2010 yielded sufficient information to be included in the meta-analysis. A random effects model was employed to determine the overall treatment utility effect across 114 participants apportioned to 14 groups and comprising eight comparisons. Results yielded an overall moderate effect size (0.64, 95% CI [0.24, 1.03], p = .002), but it was associated with significant imprecision (due to a low number of viable studies and small sample sizes across most studies) that prohibits reliable conclusions from being drawn. Assessment of between-study heterogeneity and moderator analysis was not possible. Considering these findings, additional research is needed to support the treatment utility of the CAS—even after more than 27 years of study. Furthermore, there are no published studies regarding the treatment utility of the second edition of the CAS, which was published in 2014. These results suggest that there is insufficient empirical grounding to enable practitioners to use this instrument to develop effective treatments for reading, mathematics, or writing. More direct interventions designed to enhance academic skill development should be employed.

Research Byte: On the Relationship Between #Bilingualism and #Mathematical Performance: A Systematic #Review

 Abstract

As part of the demands of a globalized and interconnected world, studying second languages has become a major priority. Bilingual programs implemented in recent decades have motivated an educational strategy in which content area courses are taught through L2. The potential costs of this strategy in academic performance are debated, especially in challenging areas such as mathematics. The present work systematically reviewed 71 papers based on experiments measuring mathematics performance in bilinguals in order to establish if bilinguals show a (dis)advantage in mathematics compared to monolinguals. The results of a total of 305,136 participants (57,703 bilinguals and 247,503 monolinguals) show that bilingualism does not seem to affect mathematical performance, but this is dependent on whether subjects are highly proficient bilinguals. This type of bilingual may only be affected by lower reaction times depending on the testing language. On the other hand, low language proficiency negatively impacts mathematical performance. Lastly, bilingualism enhances mathematical encoding and processes in non-language-related tasks.

Keywords: 

bilingualism; monolingualism; mathematics; arithmetic; language proficiency; cognitive abilities

Journal of Intelligence Open Access article can be downloaded or read on line by clicking here.

Longitudinal Analysis of Associations between 3-D Mental Rotation and Mathematics Reasoning Skills during Middle School: Across and within Genders

File under Gv and Gq/Gf as per CHC model of intelligence

Longitudinal Analysis of Associations between 3-D Mental Rotation and Mathematics Reasoning Skills during Middle School: Across and within Genders

Caitlin McPherran Lombardia, Beth M. Caseyb, Elizabeth Pezarisb, Maryam Shadmehrb, and Margeau Jong

JOURNAL OF COGNITION AND DEVELOPMENT 2019, VOL. 20, NO. 4, 487–509 

https://doi.org/10.1080/15248372.2019.1614592

ABSTRACT

The development of math reasoning and 3-d mental rotation skills are intertwined. However, it is currently not understood how these cognitive processes develop and interact longitudinally at the within-person level – either within or across genders. In this study, 553 students (52% girls) were assessed from fifth to seventh grades on 3-d mental rotation spatial skills (assessed each fall) and numerical and algebraic math reasoning skills (assessed each spring). Boys outperformed girls on mental rotation tests across all three grades, and on fifth and seventh grade math reasoning tests. Consistent with the literature on between-person comparisons, there was a positive correlation between mental rotation and math reasoning skills in the full sample and for both genders. A random inter-cept cross-lagged panel model was used to control for these confounding group-level differences in order to isolate within-person associations between earlier and later performance. Initially in fifth grade, math reasoning predicted subsequent sixth grade mental rotation skills. By seventh grade, more advanced mental rotation skills were associated with subsequent math reasoning skills while math reasoning skills were no longer predictive of mental rotation skills. An examination of gender differences revealed that this pattern was driven by boys while girls experienced less within-person change. These findings suggest that boys may initially rely in part on their math reasoning skills to solve 3-d mental rotation tasks. However, as their 3-d mental rotation skills mature, they begin to primarily depend upon these developing spatial skills to solve math reasoning problems rather than the reverse

Research Byte: Spatial (Gv) training improves math ach (Gq) positive study

Spatial Training Improves Children's Mathematics Ability

Yi-Ling Cheng and Kelly S. Mix

Michigan State University

We tested whether mental rotation training improved math performance in 6- to 8-year-olds. Children were pretested on a range of number and math skills. Then one group received a single session of mental rotation training using an object completion task that had previously improved spatial ability in children this age (Ehrlich, Levine, & Goldin-Meadow, 2006). The remaining children completed crossword puzzles instead. Children's posttest scores revealed that those in the spatial training group improved significantly on calculation problems. In contrast, children in the control group did not improve on any math tasks. Further analyses revealed that the spatial training group's improvement was largely due to better performance on missing term problems (e.g., 4+_____=11)

Article link.

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Research Byte: Executive functioning and working memory deficits in kingergarten are predictive of reading and math deficits in first grade

 

Nice study.  For WJ III/WJ IV users, the measure of working memory (Gwm), which was the most predictive variable of first grade reading and math, was Numbers Reversed.

 

Contemporary Educational Psychology

Available online 7 March 2016

In Press, Accepted Manuscript — Note to users

Executive functioning deficits increase kindergarten children's risk for reading and mathematics difficulties in first grade

• Paul L. Morgan, Ph.D.¹,
• Hui Li, Ph.D.¹,
• George Farkas, Ph.D.²,
• Michael Cook, M.S.¹,
• Wik Hung Pun, M.S.¹,
• Marianne M. Hillemeier, Ph.D., M.P.H.¹

• ¹ The Pennsylvania State University
• ² University of California, Irvine

Available online 7 March 2016

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doi:10.1016/j.cedpsych.2016.01.004

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Highlights

• Executive functioning deficits in kindergarten uniquely predict reading and mathematics difficulties in first grade

• Executive functioning deficits more strongly predict mathematics difficulties than reading difficulties, although these deficits predict both types of difficulties

• Working memory deficits more strongly predict mathematics and reading difficulties than cognitive flexibility deficits

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Abstract

Whether executive functioning deficits result in children experiencing learning difficulties is presently unclear. Yet evidence for these hypothesized causal relations has many implications for early intervention design and delivery. We used a multi-year panel design, multiple criterion and predictor variable measures, extensive statistical control for potential confounds including autoregressive prior histories of both reading and mathematics difficulties, and additional epidemiological methods to preliminarily examine these hypothesized relations. Results from multivariate logistic regression analyses of a nationally representative and longitudinal sample of 18,080 children (i.e., the Early Childhood Longitudinal Study-Kindergarten Cohort of 2011, or ECLS-K: 2011) indicated that working memory and, separately, cognitive flexibility deficits uniquely increased kindergarten children's risk of experiencing reading as well as mathematics difficulties in first grade. The risks associated with working memory deficits were particularly strong. Experimentally-evaluated, multi-component interventions designed to help young children with reading or mathematics difficulties may also need to remediate early deficits in executive function, particularly in working memory.

Keywords

• Executive functioning;
• working memory;
• cognitive flexibility;
• learning difficulties;
• longitudinal

Research byte: Simple addition problem solving may be autmoatic counting procedures and not quick retrieval from long-term memory

File under Gq, Glr, and Gr as per CHC model

 Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval? ^☆

• Kim Uittenhove,
• Catherine Thevenot,
• Pierre Barrouillet^,

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doi:10.1016/j.cognition.2015.10.008

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Highlights

•

It is universally assumed that the answer of small additions is retrieved from memory.

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Contrariwise, we replicate that they are solved by automated compacted procedures.

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Moreover, we show here that these procedures are limited to operands up to 4.

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Counterintuitively, RTs suggest that retrieval could be used for larger additions.

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Compacted procedures are faster than retrieval and consequently mistaken for it.

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Abstract

Contrary to a widespread assumption, a recent study suggested that adults do not solve very small additions by directly retrieving their answer from memory, but rely instead on highly automated and fast counting procedures (Barrouillet & Thevenot, 2013). The aim of the present study was to test the hypothesis that these automated compiled procedures are restricted to small quantities that do not exceed the size of the focus of attention (i.e., 4 elements). For this purpose, we analyzed the response times of ninety adult participants when solving the 81 additions with operands from 1 to 9. Even when focusing on small problems (i.e. with sums ⩽10) reported by participants as being solved by direct retrieval, chronometric analyses revealed a strong size effect. Response times increased linearly with the magnitude of the operands testifying for the involvement of a sequential multistep procedure. However, this size effect was restricted to the problems involving operands from 1 to 4, whereas the pattern of response times for other small problems was compatible with a retrieval hypothesis. These findings suggest that very fast responses routinely interpreted as reflecting direct retrieval of the answer from memory actually subsume compiled automated procedures that are faster than retrieval and deliver their answer while the subject remains unaware of their process, mistaking them for direct retrieval from long-term memory.

Working memory and math achievement: A new meta-analysis

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A quantitative research integration that continues to support the importance of working memory (Gwm) and school achievement—mathematics.  Caution……an average correlation of .35, although significant, still indicates that working memory and math achievement measures share only approximately 12 %  common variance.  The current findings probably have more relevance to the extant research that has suggested that the real impact of working memory is its indirect effect mediated through fluid reasoning/intelligence (Gf)