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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Notable open access Journal of #Intelligence articles by topics: #Gf #Gwm #criticalthinking #creativity etc

The Journal of Intelligence has organized “notable” papers as per certain topics (fluid intelligence, creativity, working memory, etc). Below are the different notable paper topics with links to pages where they are listed. JOI is an open access journal so all articles are free to download. You may need to cut-and-past the URL’s into your browser to access. Time to stock up on journal articles to read during the holidays.😄

Notable Papers in the Field of /Fluid Intelligence/
https://www.mdpi.com/journal/jintelligence/announcements/9960

Notable Papers in the Field of /Creativity/
https://www.mdpi.com/journal/jintelligence/announcements/9340

Notable Papers in the Field of /Working Memory/
https://www.mdpi.com/journal/jintelligence/announcements/8927

Notable Papers in the Field of /Critical Thinking/
https://www.mdpi.com/journal/jintelligence/announcements/8240

Notable Papers in the Field of /Emotional Intelligence/
https://www.mdpi.com/journal/jintelligence/announcements/7166

Notable Papers in the Field of /Metacognition/
https://www.mdpi.com/journal/jintelligence/announcements/6450

Notable Papers in the Field of /Personality/
https://www.mdpi.com/journal/jintelligence/announcements/6202

Editor's Choice Papers
https://www.mdpi.com/journal/jintelligence/editors_choice

We will be honored if you could keep an eye on the publications in our
journal. All papers can be downloaded freely.

FYI: A guide to the #WAISV ancillary index scores for #schoolpsychology and other #intelligence assessment professionals

Most assessment professionals have probably already received an email with this info.  The WAIS-V has many new ancillary index scores.  Click here for link to info.

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“Be and see” the #WISC-V correlation matrix: Unpublished analyses of the WISC-V #intelligence test

 I often “play around” with data sets until I satisfy my curiosity…and never submit the results for publication.  These WISC-V analyses were completed 3+ years ago.  I stumbled upon the folder today and decided to simply post the information for assessment professionals interested in the WISC-V.  These results have not been peer-reviewed.  One must know the WISC-V subtest names to decipher the test abbreviations in some of the figures.  

This is a Gv (visual; 8 slides) summary a set of exploratory structural analyses I completed with the WISC-V summary correlation matrix (Table 5.1 in WISC-V manual). View and enjoy. 

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Research byte: Good article with summary of the major #cognitive #neuroscience models of human #intelligence

OPINIONVolume 22, Issue 1P8-20January 2018

Network Neuroscience Theory of Human Intelligence
Aron K. Barbey.  Open access available for download

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Quote2note: Niels Bohr on experts and mistakes

An expert is a man who has made all the mistakes, which can be made, in a very narrow field.

Niels Bohr, recalled on his death, November 18, 1962

The #Cattell-Horn-Carroll (#CHC) periodic table of #cognitive elements: Just in time for the holidays and your favorite #schoolpsychology #intelligence testing friend

Print and build your own CHC periodic table of elements laminated reference card, t-shirt, etc.  See prior 2018 post for details and links to free high resolution images to download to use as you see fit.  Enjoy.

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Research byte: Prediction of human #intelligence (#g #Gf #Gc) from #brain (#network) #connectivity - #CHC

Choosing explanation over performance: Insights from machine learning-based prediction of human intelligence from brain connectivity 

,  ,  ,   

PNAS Nexus, Volume 3, Issue 12, December 2024, pgae519,

Online and PDF download available at this link:  https://doi.org/10.1093/pnasnexus/pgae519

Abstract

A growing body of research predicts individual cognitive ability levels from brain characteristics including functional brain connectivity. The majority of this research achieves statistically significant prediction performance but provides limited insight into neurobiological processes underlying the predicted concepts. The insufficient identification of predictive brain characteristics may present an important factor critically contributing to this constraint. Here, we encourage to design predictive modeling studies with an emphasis on interpretability to enhance our conceptual understanding of human cognition. As an example, we investigated in a preregistered study which functional brain connections successfully predict general, crystallized, and fluid intelligence in a sample of 806 healthy adults (replication: N = 322). The choice of the predicted intelligence component as well as the task during which connectivity was measured proved crucial for better understanding intelligence at the neural level. Further, intelligence could be predicted not solely from one specific set of brain connections, but from various combinations of connections with system-wide locations. Such partially redundant, brain-wide functional connectivity characteristics complement intelligence-relevant connectivity of brain regions proposed by established intelligence theories. In sum, our study showcases how future prediction studies on human cognition can enhance explanatory value by prioritizing a systematic evaluation of predictive brain characteristics over maximizing prediction performance (emphasis added).

machine learning, intelligence, cognitive ability, functional brain connectivity, predictive modeling

#Intelligence (#IQ) #cognitive testing in perspective: An #ecological systems brief video explanation—useful for #schoolpsychology

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An oldie but goodie!  This is a 19+ minute narrated video (sit down with your favorite beverage and enjoy) where I explain how intelligence (IQ) or cognitive ability testing should be better understood in the context of a larger ecological systems model perspective (Bronfenbrenner).  

I first posted the video in 2015—-9 years ago! So be gentle…I’m much better with these videos now :) Thus, some of my COI statements/disclaimers/affiliations are no longer accurte (and updated version can be found a theMindHub.com—Under About IAP: The Director: Disclosures & Bio).

If all works well, just click the start arrow on the video screen…and tap the enlarge icon in the lower right corner.  This video is now hosted on YouTube, so it may be possible that you may first encounter 1-2 very brief adds that you can skip within the first 15-10 seconds.  It is possible (it seems to vary everytime) that you might be asked to “sign in” to show you are not a bot.  All you need to do is press the message, or if images of muliptle videos appear, press the first one…if you only get the message you may need to back up and try link again (no signing in….I hate having lost control of how these work by using YouTube 9 years ago…as now the starting has these mild annoyances..but it is the price for a free service).  Be aware that some of the first 4-5 slides may have minimal or no narration and you can skip ahead to the beginning…it is the first slide shown immediately below before the video. Given the caveats above, it is possible the video might not deploy exactly how I describe…the platform seems to be a bit tempormental, at least for me.  Enjoy.

#quote2note: #Galton on #measurement

Whenever you can, count.     

              — Sir Francis Galton

Applied #psychometrics 101: Strong programs of #constructvalidity—the #theory - #measurement framework with emphasis on #substantive & #structural validity - #WJIV #WJV #shoolpsychology #psychology

The validity of psychological tests “is an overall judgment of the degree to which empirical evidence and theoretical rationales support the adequacy and appropriateness of inferences and actions based on test scores or other modes of assessment” (Messick, 1995, p. 741).

The ability to draw valid inferences regarding theoretical constructs from observable or manifest measures (e.g., test or composite scores) is a function of the extent to which the underlying program of validity research attends to both the theoretical and measurement domains of the focal constructs (Bensen, 1998; Bensen & Hagtvet, 1996; Cronbach, 1971; Cronbach & Meehl, 1955; Loevinger, 1957; Messick, 1995; Nunnally, 1978). 

The theoretical—measurement domain framework that has driven the revisions of the WJ test batteries, particularly from the WJ-R to the forthcoming WJ V cognitive and achievement test batteries (Q1, 2025; COI disclosure: I am a coauthor of the current WJ IV and forthcoming WJ V), is represented in the figures below.  

The goal of this post is to provide visual-graphic (Gv) images that hopefully, if properly studied by the reader (and if I did a decent job), provide the basic concepts of what constitutes the substantive component (and to a more limited extent the structural component) of a strong program of construct validity—in particular, the theoretical-measurement domain mapping framework used in the WJ-R to the forthcoming WJ V. The external stage of construct validity is not highlighted in this current post.  The goal is for conceptual understanding…thus the absence of empirical data, etc.

For those who want written background information, the most succinct conceptual overview of a “strong program of construct validation” is Bensen (1998; click to download and read).  

Otherwise…sit back and enjoy the Gv presenation…where five images equal at least one or more chapter in a technical manual :). 

Be sure to click on each image to enlarge (and make readable)

This figure below was first published in a book on CHC theoretical (then known as Gf-Gc) interpretation of the Wechsler intelligence test batteries (Flanagan, McGrew, & Ortiz, 2000).

Yea…I know.  The following figure uses Gv as the sample cognitive ability construct domain and not Gf as in the prior figure.  I first crafted the figure below in 2005 and don’t have the time (nor attentional control focus bandwidth) to make a new version.  Consider the switch from the Gf domain (above) to Gv (below) as a test of your understanding of the material…and ability to generalize what you have learned.  And yes, I do see there is a spelling error (“on” for “one”)…but it is an old image file and I don’t have time to “clean it up” as noted above.  The primary new feature is the addition of the concept  of developing developmentally (difficulty) ordered sets of test items for the underling ability trait scales for manifest indicator tests C and D under the CHC theoretical narrow ability domain of spatial scanning, under the broad ability domain of Gv. This is where IRT (Rasch model) item scaling is involved.

The following figure is drawn from the WJ IV technical manual (McGrew, LaForte, Schrank, 2014) and illustrates the three-stage structural validity process used in the WJ IV.  The same process, with slightly different age groups and the addition of exploratory hierarchical psychometric network analysis (see exciting and ground-breaking work of Dr. Hudson Golino and colleagues) during stage 2A, will be presented in the WJ V technical manual (LaForte, Dailey & McGrew, Q1-2025).

#quote2note: Louis Agassiz on stages of #scientific truth

 

"Every great scientific truth goes through three stages. First, people say it conflicts with the Bible. Next they say it had been discovered before. Lastly they say they always believed it."

- Louis Agassiz

#quote2note: Voltaire on #individualdifferences

 

"Minds differ still more than faces"
-Voltaire

#quote2note: Marie Curie on getting s___t done :)

 “One never notices what has been done; one can only see what remains to be done"

- Marie Curie

Research Byte: The structure of adult thinking. A #network approach to #metacognitive processing —#cognition #executivefunction

Author links open overlay panel

Click here to access copy of article

Abstract

Complex cognitive processes have been broadly categorized into three general domains: first-order cognition (i.e., thinking directed to solve problems), metacognition (i.e., thinking about one's thinking during problem-solving), and epistemic cognition (i.e., thinking about the epistemic nature of problems and beliefs about criteria for knowledge justification). Few, if any studies, have empirically examined the conditional dependencies between a large inventory of components simultaneously. This paper aims to contribute the first set of preliminary explorations into the interrelationships between different thinking and reasoning components that represent key aspects of emerging adult cognitive processing using a psychological network approach. In two cross-sectional studies (combined N = 1496), data was collected from undergraduate students enrolled at a large public university. Scrutiny of the networks suggests that thinking dispositions and competency with probability are key bridges between metacognitive abilities and epistemic beliefs. Implications for instruction are discussed.

Educational relevance statement

It remains a perennial aim of all education systems to improve the thinking and reasoning of students. But which complex cognitive processes are worthwhile targets, and how do they fit among the plethora of metacognitive, self-regulatory, and epistemological belief aspects of students? The present set of studies is the first to apply a network approach to a broad array of cognitive components to uncover the central student-level variables that can be targeted with instruction. Based on the findings of the two studies presented, instruction aimed at epistemic dispositions could potentially assist in the development of complex cognition because of their centrality to networks of effective reasoning processes.

Click on images to enlarge for easier reading.

Research Byte: Past reflections, present insights: A systematic #review and new empirical research into the #workingmemory capacity (WMC)-#fluidintelligence (#Gf) relationship

Past reflections, present insights: A systematic review and new empirical research into the working memory capacity (WMC)-fluid intelligence (Gf) relationship

Ratko Đokić, Maida Koso-Drljević, Merim Bilalić 

Click here to go to journal

Abstract

According to the capacity account, working memory capacity (WMC) is a causal factor of fluid intelligence (Gf) in that it enables simultaneous activation of multiple relevant information in the aim of reasoning. Consequently, correlation between WMC and Gf should increase as a function of capacity demands of reasoning tasks. Here we systematically review the existing literature on the connection between WMC and Gf. The review reveals conceptual incongruities, a diverse range of analytical approaches, and mixed evidence. While some studies have found a link (e.g., Little et al., 2014), the majority of others did not observe a significant increase in correlation (e.g., Burgoyne et al., 2019; Salthouse, 1993; Unsworth, 2014; Unsworth & Engle, 2005; Wiley et al., 2011). We then test the capacity hypothesis on a much larger, non-Anglo-Saxon culture sample (N = 543). Our WMC measures encompassed Operation, Reading, and Symmetry Span task, whereas Gf was based on items from Raven's Advanced Progressive Matrices (Raven). We could not confirm the capacity hypothesis either when we employed the analytical approach based on the Raven's item difficulty or when the number of rule tokens required to solve a Raven's item was used. Finally, even the use of structural equation modeling (SEM) and its variant, latent growth curve modeling (LGCM), which provide more “process-pure” latent measures of constructs, as well as an opportunity to control for all relevant interrelations among variables, could not produce support for the capacity account. Consequently, we discuss the limitations of the capacity hypothesis in explaining the WMC-Gf relationship, highlighting both theoretical and methodological challenges, particularly the shortcomings of information processing models in accounting for human cognitive abilities.

On making individual tests in #CHC #intelligence test batteries more #cogntivelycomplex: Two approaches

The following information is from a section of the WJ IV techncial manual (McGrew, LaForte & Schrank, 2014) and will again be included in the WJ V technical manual (LaForte, Dailey, McGrew, Q1, 2025).  It was first discussed in McGrew (2012)

On making individual tests in intelligence test batteries more cogntively complex

In the applied intelligence test literature, their are typically two different approaches typically used to increase the cognitive complexity of individual tests (McGrew et al., 2014). The first approach is to deliberately design factorially complex CHC tests, or tests that deliberately include the influence of two or more narrow CHC abilities. This approach is exemplified by Kaufman and Kaufman (2004a) in the development of the Kaufman Assessment Battery for Children–Second Edition (KABC-II), where:

the authors did not strive to develop “pure” tasks for measuring the five CHC broad abilities. In theory, Gv tasks should exclude Gf or Gs, for example, and tests of other broad abilities, like Gc or Glr, should only measure that ability and no other abilities. In practice, however, the goal of comprehensive tests of cognitive abilities like the KABC-II is to measure problem solving in different contexts and under different conditions, with complexity being necessary to assess high-level functioning. (p. 16)

In this approach to test development, construct-irrelevant variance (Benson, 1998; Messick, 1995) is not deliberately minimized or eliminated. Although tests that measure more than one narrow CHC ability typically have lower validity as indicators of CHC abilities, they tend to lend support to other types of validity evidence (e.g., higher predictive validity). The WJ V has several new cognitive tests that use this approach to cognitive complexity. 

The second approach to enhancing the cognitive complexity of tests is to maintain the CHC factor purity of tests or clusters (as much as possible) while concurrently and deliberately increasing the complexity of information processing demands of the tests within the specific broad or narrow CHC domain (McGrew, 2012). As described by Lohman and Lakin (2011), the cognitive complexity of the abilities measured by tests can be increased by (a) increasing the number of cognitive component processes, (b) including differences in speed of component processing, (c) increasing the number of more important component processes (e.g., inference), (d) increasing the demands of attentional control and working memory, or (e) increasing the demands on adaptive functions (assembly, control, and monitoring). This second form of cognitive complexity, not to be confused with factorial complexity, is the inclusion of test tasks that place greater demands on cognitive information processing (i.e., cognitive load), that require greater allocation of key cognitive resources (viz., working memory or attentional control), and that invoke the involvement of more cognitive control or executive functions. Per this second form of cognitive complexity, the objective is to design a test that is more cognitively complex within a CHC domain, not to deliberately make it a mixed measure of two or more CHC abilities.

A large number of prior IQs Corner’s posts regarding the topic of cognitive complexity in intelligence testing can be found here.

Benson, J. (1998). Developing a strong program of construct validation: A test anxiety example. Educational Measurement: Issues and Practice, 17(1), 10–22.

Lohman, D. F., & Lakin, J. (2011). Reasoning and intelligence. In R. J. Sternberg & S. B. Kaufman (Eds.), The Cambridge handbook of intelligence (2nd ed., pp. 419–441). New York, NY: Cambridge University Press.

McGrew, K. S. (2012, September). Implications of 20 years of CHC cognitive-achievement research: Back-to-the-future and beyond CHC. Paper presented at the Richard Woodcock Institute, Tufts University, Medford, MA. (click here to access)

Messick, S. (1995). Validity of psychological assessment: Validation of inferences from persons' responses in performances as scientific inquiry into score meaning. American Psychologist, 50, 741–749.