Highly recommended AI paper regarding human & AI capabilities. HCQM: A dual-use human capability assessment and prescriptive target for engineering synthetic cognitive architectures (AI)

I recently exchanged emails and zoomed with Kameron Green who works in the AI space regarding his proposed Human Capability Quotient Map (HCQM).  I was thoroughly impressed with his proposed dual-use meta-taxonomy of human competence taxonomies (e.g., CHC; executive function; self-regulation; motivation; etc) into a grand overarching ability and capacity taxonomy.  As stated in the paper “HCQM is positioned to support broad human capability assessment while also providing a partial prescriptive target, at the capacity layer, for engineering synthetic cognitive architectures.”  

IMHO his grand model is one of the most comprehensive proposed high-level integrations of human individual difference constructs and emerging AI competencies I have read.  Although long, I urge those interested in human individual difference domains and AI evaluation frameworks to read his working paper. The paper is relevant to those studying individual differences in humans and those working on models by which to evaluate AI.  

The paper can be found (and downloaded) at the link provided by Kameron (click here).  He has also shared access to his paper at his LinkedIN profile (which is the URL associated with the hyper-link with his name in the first sentence of this post).

I’m sharing this link/paper with his permission.

 

Abstract

The field of intelligence research has long been characterized by fragmentation, with distinct traditions examining general cognitive abilities (Carroll, 1993; McGrew, 2009), emotional and social competencies (Salovey & Mayer, 1990; Goleman, 1995), creativity (Guilford, 1950), metacognition (Flavell, 1979), grit and adaptability (Duckworth et al., 2007), and more recent constructs such as digital intelligence (Park, 2019) and systems thinking (Senge, 1990; Meadows, 2008). While each line of inquiry has yielded valuable insights and measurement tools, the absence of an integrated taxonomy limits holistic assessment of human potential and the principled design of synthetic cognitive architectures. This paper proposes the Human Capability Quotient Map (HCQM) as a hierarchical synthesis that organizes eight top-level domains (General Cognitive Intelligence, Executive/Self-Regulatory Intelligence, Emotional & Social Intelligence, Creative & Innovation Intelligence, Motivational & Adaptive Intelligence, Learning & Knowledge Intelligence, Digital & Technological Intelligence, and Systems & Strategic Intelligence) into a coherent framework. Each domain includes subcomponents and observable indicators drawn from established psychometric, psychological, and cognitive-science literature.

HCQM makes three contributions: the integration itself, a coverage-asymmetry observation, and an explicitly dual-use framing; the two durable differentiators are the integration and the dual-use framing. HCQM is positioned to support broad human capability assessment while also providing a partial prescriptive target, at the capacity layer, for engineering synthetic cognitive architectures, with the explicit limitation that full architectural prescriptiveness requires a companion specification document (§6.6). These are applied to a coverage asymmetry: the human-capability tradition treats motivational, affective, cultural, and adversity capability as first-class (contemporary CHC, for example, now includes emotional intelligence as a broad ability), whereas contemporary AI architecture and evaluation frameworks largely do not. Unlike purely evaluative taxonomies such as DeepMind's 2026 Measuring Progress Toward AGI: A Cognitive Framework (Burnell et al., 2026), which identifies 10 cognitive faculties for benchmarking AGI progress, HCQM brings these dimensions to bear as a specification target. Unlike engineering-oriented architectural frameworks such as CoALA (Sumers et al., 2024), which specifies memory modules, action spaces, and decision loops for language agents, HCQM specifies the capacity surface those structural slots are expected to implement. The dimensions the AI frameworks omit are not a miscellaneous remainder: they concentrate in the motivational, adaptive, and metacognitive capacities (persistence under failure, strategy revision, self-monitoring, calibration) that govern whether a long-horizon autonomous agent is reliable, as distinct from whether it is capable. HCQM's distinctive AI-facing contribution is to organize these as a first-class reliability-and-autonomy layer and specify it at the capacity level (§5.2); a worked example maps a documented long-horizon agent failure pattern to the layer it omits. HCQM consolidates and ports existing constructs rather than claiming to discover them.

Drawing on CHC theory (Carroll, 1993; Schneider & McGrew, 2018), multiple-intelligences and triarchic models (Gardner, 1983; Sternberg, 1985), cultural intelligence (Earley & Ang, 2003), computational thinking (Wing, 2006), and modern cognitive architectures for language agents (Sumers et al., 2024), HCQM offers a synthesis rather than a novel discovery. We outline design principles, detail the hierarchical structure, discuss applications in human development and AI engineering, and acknowledge limitations, including the need for empirical validation, operationalized assessment instruments, and an explicit evaluation protocol. This paper aims to stimulate cross-disciplinary dialogue and guide future instrument development and architectural design.

Keywords: human capabilities, intelligence taxonomy, cognitive architecture, AGI evaluation, capability-grounded architectures, autonomous agents, agent reliability, long-horizon agents, metacognition, grit, cultural intelligence, systems thinking, CHC theory, CoALA.

Click on image to enlarge for easy viewing

AI Brief: The trilogy-of-the-mind individual difference construct (cognitive, conative, affective) “band is getting back together” as CAMML

I am currently working to expand my skill set by incorporating AI tools. Although adapting to new technologies can be challenging, leveraging these resources offers significant benefits for professional growth.

This AI Brief was produced by requesting Google NotebookLM—recommended by Dr. Adam Lockwood—to generate a narrative summary of my 2022 PDF article describing the Cognitive-Affective-Motivation-Model of Learning (CAMML). While I found the first results promising, I made more edits to enhance its accuracy and informativeness. My next goal is to use AI to summarize multiple articles, find similarities and differences, and potentially create comparative tables (again following guidance graciously provided by Dr. Lockwood).

These incremental steps mark my transition toward utilizing AI to support one of my primary professional interests: producing informative blog and social media posts aimed at professionals such as school psychologists and special education teachers working with students who often are marginalized in educational contexts. The goal is to help bridge the gap between theory, technology, research, and practical application.

 

Feedback is encouraged and may be directed to iqmcgrew@gmail.com or via the social media platform (LinkedIn, Twitter/X, BlueSky) comment feature where this blog post was discovered. I’m hoping to add AI Briefs as a regular feature of IQs Corner Blog and associated social media platforms.

 

 

AI Brief: The trilogy-of-the-mind individual difference construct (cognitive, conative, affective) “band is getting back together” as CAMML

 

Dr. Kevin McGrew with assist from Google NotebookLM

 

The Cognitive-Affective-Motivation Model of Learning (CAMML; McGrew, 2002)[1] is a proposed theoretical framework designed to integrate contemporary motivational, affective, and cognitive constructs into a unified model for the practice of school psychology. The central thesis of the framework is that school psychologists must move beyond a narrow focus on intelligence (general intelligence or psychometric g in particular) to embrace an updated "trilogy-of-the-mind" model, which views intellectual functioning as the inseparable interaction of cognition, conation (motivation/volition), and affect.

Theoretical Foundations and the Rebirth of Conation

 

The CAMML framework is heavily rooted in the seminal work of Richard Snow, specifically his research on aptitude trait complexes. McGrew argues that the field of school psychology has historically neglected Snow’s broader definition of aptitude—which includes personality and motivational differences alongside cognitive abilities—and instead, has favored a restricted view of aptitude as synonymous with IQ or psychometric g.

 

CAMML seeks to resurrect conation (the proactive part of motivation connecting cognition and affect to behavior) as a core pillar of intellectual functioning. By "standing on the shoulders of giants" like Snow, Spearman, and Wechsler, the model asserts that cognitive processes cannot be understood in isolation from the "nonintellectual" (conative) factors that drive and direct them. For example, David Wechsler defined intelligence as "the aggregate or global capacity of the individual to act purposefully, to think rationally, and to deal effectively with his environment." While this is the core of Wechsler’s definition, he also strongly emphasized this capacity is influenced by non-intellective (conative) variables such as drive, persistence, interest, emotional states, and personality traits.

 

Structural Components of the CAMML Framework

 

The model organizes individual differences characteristics into three functional categories, which could be called the 3-D model.

 

●      Affective “Dispositions”: These are distal-to-learning traits, primarily represented by the Big 5 personality traits (specifically Openness and Conscientiousness) and their associated social-emotional facets (e.g, curiosity, creativity, persistence, focus, determination). These personality traits act as dispositions that indirectly influence learning through more proximal mechanisms.

 

●      Motivational "Drivers": Motivation is conceptualized as the initiation of behavior, formed by achievement orientations (e.g., goals, interests) and self-beliefs (e.g., self-efficacy, self-concept). These constructs are typically domain-specific (e.g., math) and work in synergistic "complexes" to energize a student's readiness to act.[2]

 

●      Volitional "Directors": Volition, or self-regulated learning (SRL), represents the post-decisional phase of action. These are the mechanisms that direct, control, and regulate behavior toward goals once a commitment to learn has been made.

 

A more detailed list of the 3-D CAMML domain constructs and definitions is available here. See figure below for a visual representation of the major affective and conative MACM constructs (click on image to enlarge for easy viewing and reading).

 

The "Crossing the Rubicon" Investment Model

 

The functional heart of CAMML is the "Crossing the Rubicon" model, which illustrates the pathway from initial desire to engaged motivated learning. In this model:

 

1. Pre-decisional Phase: Achievement orientations and self-beliefs drive or prepare the learner to start a wish—>want—> intention sequence, that eventually eventuates in motivated action.

2. Commitment: When the learner "crosses the Rubicon," they are making a firm commitment to motivated action through cognitive engagement.

3. Action Phase: Volitional (SRL) strategies steer the cyclical process via action results feedback while the learner invests cognitive abilities (such as those defined by CHC theory) to acquire knowledge.

4. Outcomes: This personal investment of fluid cognitive processes (Cattell's general gf that subsumes broad Gf, Gv, Ga, Gwm, Gl, Gr, and Gs abilities) during learning results in the development of crystallized knowledge systems (Cattell’s general gc that subsumes broad Gc, Grw, Gq, and Gkn abilities).

 

See figure below for visual representation of “the CAMML crossing the Rubicon model of motivated learning” (click on image to enlarge for easy viewing and reading).

 

Implications for School Psychology Practice

 

CAMML advocates for a paradigm shift in assessment and intervention. It suggests that school psychologists should transition from routine, comprehensive cognitive testing toward more time-efficient selective, referral-focused cognitive assessments combined with the assessment of key conative (non-cognitive) characteristics that contribute to learning aptitude complexes. This approach prioritizes identifying manipulable instructional levers, such as a student's motivational orientation (e.g., intrinsic motivation, interests, goal orientation), self-beliefs (e.g., locus of control, self-efficacy, growth or competence mindset), rather than relying exclusively on cognitive ability scores (especially full-scale IQ or g) that have proven hard to modify.

 

The framework provides a "whole-child" perspective to better address the nuances of individual differences, particularly as students move from the traditional “industrial” model of education (i.e., regularly scheduled, structured, in-class teacher-directed learning) to more of an “information-age” paradigm of education—a paradigm that requires a fuller expression of independent motivated self-regulated learning (SRL).

PS - other CAMML related posts on this blog can be found by clicking here.

[1] All relevant references can be found in McGrew (2022).

[2] The motivation constructs included in the CAMML framework are drawn from earlier efforts to develop the McGrew Model of Achievement Competence Motivation (MACM). A detailed explanation of the evolution and development of the MACM model is available elsewhere (McGrew et al., 2004). A series of recent MACM PowerPoint® modules is available here.

A #metaanalysis of #assessment of self-regulated learning (#SRL) - #selfregulatedlearning #learning #motivation #CAMML #EDPSY #schoolpsychologists #schoolpsychology #conative

Self-regulated learning (SRL) strategies are an important component of models of school learning.  Below is a new meta-analysis of SRL assessment methods.  Overall effect sizes are not large.  More R&D is needed to develop applied practical SRL measurement tools.  SRL is a one of the major components of the 2022 Cognitive-Affective-Motivation Model of Learning; CAMML; click here to access article),

Multimethod assessment of self-regulated learning in primary, secondary, and tertiary education – A meta-analysis.  Learning and Individual Differences (open access—click here to access).

Author links open overlay panel

Julia Ruhl, Franziska Perels , Laura Dorrenbacher-Ulrich

Abstract

Self-regulated learning (SRL) can be measured in several ways, which can be broadly classified into online and offline instruments. Although both online and offline measurements have advantages and disadvantages, the over-dependence of SRL research on offline measurements has been criticised considerably. Currently, efforts are being made to use multimethod SRL assessments. We examined 20 articles with 351 effect sizes that assessed SRL with at least two instruments on at least two SRL components. Most effect sizes were not statistically significant but descriptively higher than others. Combinations of two online instruments showed the highest effect size (r = 0.24). Overall correlations between instruments were highest for university students (r = 0.21). Additionally, results for cognition showed the highest effect size measured with behavioural traces (r = 0.28), and for metacognition measured with microanalysis (r = 0.35). The component of motivation was best measured using self-report questionnaires (r = 0.29).

Educational relevance statement

Self-regulated learning is an important predictor of academical success. It is therefore necessary to measure it as precise and comprehensive as possible. Knowing which instruments are best suited for each age group, SRL component, or reliably predict a specific achievement variable can help educators pick the best instrument for their needs.

Research Byte: Is trying hard enough? Causal analysis of the effort-IQ relationship suggests not - #intelligence #IQ #motivation #volition #CAMML #conative #noncognitive

Is Trying Harder Enough? Causal Analysis of the Effort-IQ Relationship Suggests Not.  Timothy Bates. Intelligence and Cognitive Abilities (open access—click here to locate article to read or download)

Abstract

Claims that effort increases cognitive scores are now under great doubt. What is needed is randomized controlled trials optimized for testing causal influence and avoiding confounding of self-evaluation of performance with feelings of good effort. Here we report three large studies using unconfounded measures of effort and instrumental analysis to isolate any causal effect of effort on cognitive score. An initial study (N = 393) validated an appropriate effort measure, demonstrating excellent external and convergent validity (β = .61). Study 2 (N = 500, preregistered) randomly allocated subjects to a performance incentive, using an instrumental variable analysis to detect causal effects of effort. The incentive successfully manipulated effort (𝛽 = .18, p = .001). However, the causal effect of effort on scores was near-zero and non-significant (𝛽 = .04, p = .886). Study 3 (N=1,237) replicated this null result with preregistered analysis and an externally developed measure of effort: incentive again raised reported effort (𝛽 = .17, p <.001), but effort had no significant causal effect on cognitive score (β2 = .27 [-0.07, 0.62]), p = .15). Alongside evidence of research fraud and confounding in earlier studies, the present evidence for the absence of any causal effects of effort on cognitive scores, effort research should shift its focus to goal setting – where effort is useful – rather than raising basic ability, which it appears unable to do.

Select quote from discussion: “The present results suggest a potential ‘central dogma of cognition’: that volitional effort can direct cognitive resources but cannot fundamentally alter or bypass the efficacy of the underlying cognitive systems themselves”

These findings are consistent with my proposed cognitive-affective-motivation-model-of-learning (CAMML), grounded extensively on Richard Snows concept of aptitude trait complexes, where motivational constructs are seen as driving and directing the use of cognitive abilities (via personal investment mechanisms), but not directly having a causal effect on cognitive abilities.  See first of two figures below.  Note lack of causal arrows from conative and affective domain constructs to CHC cognitive abilities.  Paper can be accessed by clicking here.

Click on images to enlarge for easier viewing

Journal of #Intelligence special issue: Interplay of intelligence and non #cognitive (#conative) constructs in predicting #achievement - #schoolpsychology #cognitive #EDPSY #education

More info availble re JOI special issue here. Click on image to enlarge for easier reading.

If interested, you might want to check out my pub describing the Cognitive-Affective-Motivation Model of Learning #CAMML)

The McGrew Model of Achievement Competence Model (MACM)--Standing on the shoulders of giants: CJSP article supplementary materials

The Model of Achievement Competence Motivation (MACM) has been  under development since the early 2000's by Dr. Kevin S. McGrew.   The work is (has) been formally presented in an invited article--"The Model of Achievement Competence Motivation (MACM)--Standing on the shoulders of giants" (McGrew, in press, 2021), for a forthcoming special issue on motivation in the Canadian Journal of School Psychology). 

Due to the page length constraints of the journal, significant background and explanatory information could not be presented in the article.  Thus, I have "off-loaded" this material for supplementary viewing via on-line PPT slide shows and downloadable PDF files.

Five MACM PPT modules have been posted at SlideShare and can be viewed and downloaded from that site.  For those who would prefer to directly download PDF versions of the PPT modules from one page...here it is.  Below are the titles of the five modules and associated download links.  In addition, the paper includes, in a table footnote, definitions for 16 self-regulatory constructs from a recent article by Sitzman and Ely (2011).  That PDF file is also available from download below.

Enjoy.

The Model of Achievement Competence Motivation (MACM)

• Introduction and overview (A)
  
• Overview of the model (B)
• The motivation domains defined (C)
• The volition and self-regulation domain (D)
• Crossing the Rubicon Commitment Pathway Model to Learning (E)
  
• 16 self-regulatory constructs (from article definition table)
  

The Model of Achievement Competence Motivation (MACM) Part E: Crossing the Rubicon Commitment Pathway Model to Learning

 

The Model of Achievement Competence Motivation (MACM) is a series of slide modules.  By clicking on the link you can view the slides at SlideShare.  This is the fifth and final (Part E) in the series.  This one is brief...only 11 slides.  Crossing the Rubicon Commitment Pathway Model to Learning.  There will be a total of five modules.  The modules will serve as supplemental materials to "The Model of Achievement Competence Motivation (MACM)--Standing on the shoulders of giants" (McGrew, in press, 2021 - in a forthcoming special issue on motivation in the Canadian Journal of School Psychology)

You should be able to access the prior modules (A-C) from the link above.

Click here for prior "beyond IQ" labeled posts at this blog.

The Model of Achievement Competence Motivation (MACM): Part D-Volition and Self-Regulated Learning Domains

 The Model of Achievement Competence Motivation (MACM) is a series of slide modules.  By clicking on the link you can view the slides at SlideShare.  This is the fourth (Part D) in the series--Volition and Self-regulated Learning Domains described..  There will be a total of five modules.  The modules will serve as supplemental materials to "The Model of Achievement Competence Motivation (MACM)--Standing on the shoulders of giants" (McGrew, in press, 2021 - in a forthcoming special issue on motivation in the Canadian Journal of School Psychology)

You should be able to access the prior modules (A-C) from the link above.

Click here for prior "beyond IQ" labeled posts at this blog.

The Model of Achievement Competence Motivation (MACM) Part B: An overview of the MACM model

The Model of Achievement Competence Motivation (MACM) is a series of slide modules.  By clicking on the link you can view the slides at SlideShare.  This is the second (Part B) in the series--An overview of the model.  There will be a total of five modules.  The modules will serve as supplemental materials to "The Model of Achievement Competence Motivation (MACM)--Standing on the shoulders of giants" (McGrew, in press, 2021 - in a forthcoming special issue on motivation in the Canadian Journal of School Psychology)

Click here for first of the series (Part A:  Introduction and Background)

Click here for prior "beyond IQ" labeled posts at this blog.

The Model of Achievement Competence Motivation (MACM): Part A - Introduction to module series

The Model of Achievement Competence Motivation (MACM) is a series of slide modules.  By clicking on the link you can view the slides at SlideShare.  This is the first (Part A) in the series. The modules will serve as supplemental materials to "The Model of Achievement Competence Motivation (MACM)--Standing on the shoulders of giants" (McGrew, in press, 2021 - in a forthcoming special issue on motivation in the Canadian Journal of School Psychology)

Click here for prior "beyond IQ" labeled posts at this blog.

The big picture ecological systems perspective of intelligence (and IQ tests): Is COVID disrupting and rearranging the hierarchy of ecological system influences on children's learning?

Understanding intelligence testing in the context of Bronfrenbrenner's ecological systems model--is COVID seriously damaging, rearranging, decoupling, etc. the major proximal and distal sources of influence on a child's learning, resulting in a need to look closer at non-cognitive (conative) variables...beyond IQ?

This morning I revisited one of my favorite videos (of those I have posted), first posted in 2015, where I explained how intelligence testing needed to be understood in the context of distal and proximal influences in a child's environment.  I believe that a "big picture" understanding of the wide range of variables that influence school learning requires a "humbling" of the status of intelligence testing, a field where I have spent the majority of my professional career.  After one finishes the video, think about the "big picture" ecological systems model that is described. IMHO, COVID may be seriously impacting that the primary distal and proximal variables that influence (both positively and negatively) school learning (national educational policy; school systems and local community sources of formal and informal support; individual schools; the lack of in class learning; parents working from home or being unemployed), as well as peer interactions in a child's neighborhood (due to social distancing).  Stare at the final big picture figure and reflect on how COVID is disrupting all the primary sets of variables that influence school learning.  The range of disrupted causal influences is staggering. 

The end result, for many children, is learning via distance learning methods, often with the aid of parents who are not educators.  Although intelligence is very important, and may be more important as children must use their abilities to learn more independently, it strikes me that at this point in our countries (global) current crises, it may be the non-cognitive variables that might need better understanding and enhancement.  That is, the conative (aka., noncognitive) "beyond IQ" variables of motivation and self-regulated learning (aka., a part of volition) may be more important today than ever.  To engage in independent, loosely (dis)organized instruction, students who have strong motivation and independent self-regulation learning strategies may have a distinct advantage--those who do not, may be at a serious disadvantage.  Jack Carroll's seminal model of school learning, that spawned decades of research on models of school learning, reminds us, in elegant terms, that aside from key student individual difference variables, the quantity (opportunity for instruction) and quality of instruction are key variables in school learning.  Both of these are being seriously impacted due to COVID.

COVID appears to be a high level all encompassing distal variable (wielding impact at the global, national, community, and school system levels) that is rearranging the the relative importance of  variables in school learning.  Students now, and in the future, may need more assistance in acquiring critical non-cognitive motivational dispositions and independent self-regulated learning strategies in order to maximize what they can from their repertoire of cognitive abilities in order to continue and maintain academic growth.  If may be necessary to revise the degree of influence of distal and proximal school learning influence variables as per Bronfrenbreener's ecological systems model.

The importance of differential psychology for school learning: 90% of school achievement variance is due to student characteristics

This is why the study of individual differences/differential psychology is so important. If you don’t want to read the article you can watch a video of Dr. Detterman where he summarizes his thinking and this paper.

Education and Intelligence: Pity the Poor Teacher because Student Characteristics are more Significant than Teachers or Schools. Article link.

Douglas K. Detterman

Case Western Reserve University (USA)

Abstract

Education has not changed from the beginning of recorded history. The problem is that focus has been on schools and teachers and not students. Here is a simple thought experiment with two conditions: 1) 50 teachers are assigned by their teaching quality to randomly composed classes of 20 students, 2) 50 classes of 20 each are composed by selecting the most able students to fill each class in order and teachers are assigned randomly to classes. In condition 1, teaching ability of each teacher and in condition 2, mean ability level of students in each class is correlated with average gain over the course of instruction. Educational gain will be best predicted by student abilities (up to r = 0.95) and much less by teachers' skill (up to r = 0.32). I argue that seemingly immutable education will not change until we fully understand students and particularly human intelligence. Over the last 50 years in developed countries, evidence has accumulated that only about 10% of school achievement can be attributed to schools and teachers while the remaining 90% is due to characteristics associated with students. Teachers account for from 1% to 7% of total variance at every level of education. For students, intelligence accounts for much of the 90% of variance associated with learning gains. This evidence is reviewed


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Mathematical (Gq) giftedness: Review of cognitive, conative and neural variables

Click on image to enlarge.

Article link.




ABSTRACT

Most mathematical cognition research has focused on understanding normal adult function and child development as well as mildly and moderately impaired mathematical skill, often labeled developmental dyscalculia and/or mathematical learning disability. In contrast, much less research is available on cognitive and neural correlates of gifted/excellent mathematical knowledge in adults and children. In order to facilitate further inquiry into this area, here we review 40 available studies, which examine the cognitive and neural basis of gifted mathematics. Studies associated a large number of cognitive factors with gifted mathematics, with spatial processing and working memory being the most frequently identified contributors. However, the current literature suffers
from low statistical power, which most probably contributes to variability across findings. Other major shortcomings include failing to establish domain and stimulus specificity of findings, suggesting causation without sufficient evidence and the frequent use of invalid backward inference in neuro-imaging studies. Future studies must increase statistical power and neuro-imaging studies must rely on supporting behavioral data when interpreting findings. Studies should investigate the factors shown to correlate with math giftedness in a more specific manner and determine exactly how individual factors may contribute to gifted math ability.


SELECTIVE SUMMARY CONCLUSION STATEMENTS

In line with the heterogeneous nature of mathematical disabilities (e.g., Rubinsten and Henik, 2009; Fias et al., 2013), mathematical giftedness also seems to correlate with numerous factors—(see Appendix A for which factors were found in each study). These factors roughly fall into social, motivational, and cognitive domains. Specifically, in the social and motivational domains, motivation, high drive, and interest to learn mathematics, practice time, lack of involvement in social interpersonal, or religious issues, authoritarian attitudes, and high socio-economic status have all been related to high levels of mathematical achievement. Speculatively, it is interesting to ask whether some of these factors may be related to the so-called Spontaneous Focusing on Numerosity (SFON) concept which appears early in life and means that some children have a high tendency to pay attention to numerical information (Hannula and Lehtinen, 2005). To clarify this question, longitudinal studies could investigate whether high SFON at an early age is associated with high levels of mathematical expertise in later life. Better assessment of individual variability is also important, for example, Albert Einstein (who was a gifted even if sometimes “lazy” mathematician; see e.g., Isaacson, 2008) was famously anti-authoritarian.

In terms of cognitive variables, we found that spatial processing, working memory, motivation/practice time, reasoning, general IQ, speed of information processing, short-term memory, efficient switching from working memory to episodic memory, pattern recognition, inhibition, fluid intelligence, associative memory, and motor functions were all associated with mathematical giftedness. As a caveat it is important to point out that mere “significance counting” (i.e., just considering studies with statistical significant results regarding a concept) can be very misleading especially in the typically underpowered context of psychology and neuro-imaging research (see e.g., Szucs and Ioannidis, 2017). However, considering the patchy research, this is the best we can do at the moment. In addition, even if meta-analyses were possible, these also typically only take into account published research, so they usually (highly) overestimate effect sizes especially from small scale studies (see Szucs and Ioannidis, 2017).


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