Research Byte: Stability of early #numbersense competencies for predicting #math difficulties —#CHC #coreknowledgesystems #schoolpsychology #schoolpsychologists #cognitive #Gq #math #SLD

Stability of early number sense competencies for predicting mathematics difficulties

Learning and Individual Differences (2025).  Click here to go to journal page with author, etc. info.

It is my current working hypothesis that measures of number sense (and other Gq abilities such as magnitude recognition) may measure what developmental cognitive psychologists consider part of a quantitative “core knowledge system”.  Click here for access to an excellent article that discusses all core knowledge systems.  Perhaps these are fundamental cognitive mechanisms that lie beneath the narrow ability stratum in the CHC model of human cognitive abilities.

Abstract

Significant individual differences in children's number competencies exist in early childhood, and these competencies can have long-term implications for academic and economic success (National Research Council, 2009). The present study assessed the classification accuracy of the Screener for Early Number Sense (SENS), a screening tool grounded in an evidence-informed conceptual model of number sense that is designed for children in pre-kindergarten (pre-K), kindergarten, and first grade. A cohort of 450 children was assessed on the SENS, followed by a standardized mathematics achievement measure one year later. Receiver operating characteristic (ROC) curve analyses indicated that the SENS effectively differentiated children who went on to show math difficulties (MD) from those without MD. Accuracy rate was acceptable for pre-K, kindergarten, and first grade. An analysis of SENS performance over time categorized by MD risk status revealed differing patterns of growth across the pre-K vs. kindergarten year. These collective findings underscore the importance of math screening as early as pre-K.

Educational relevance

Educators need reliable and valid tools to identify young children who may be at risk for mathematics learning difficulties. The present study presents a number sense screener that accurately predicts pre-kindergarten, kindergarten, and first grade students' later mathematical difficulties. The study demonstrates how screener results and prevalence rates can be used to identify individual-level student risk and to make subsequent instructional decisions across varying schools or districts.

Research byte: Early #numeracy and #mathematics development: A longitudinal #metaanalysis on the predictive nature of early numeracy—attention #schoolpsychology #SPED #WJV

Early numeracy and mathematics development: A longitudinal meta-analysis on the predictive nature of early numeracy.

Liu, Y., Peng, P., & Yan, X. (2025). Early numeracy and mathematics development: A longitudinal meta-analysis on the predictive nature of early numeracy. Journal of Educational Psychology. Advance online publication. https://doi.org/10.1037/edu0000925

As an FYI, the forthcoming WJ V now includes, in the achievement battery, a measure of numeracy (Number Sense).  An age truncated version of this test was in the WJ IV ECAD.  In the WJ V this test covers the entire age span from young to old age.  

COI - although I am a coauthor of the WJ V, my WJ V contract is no longer a royalty-earning contract. I was paid for my work as an independent contractor—thus I have ZERO financial interests based on sales).  Complete COI available here.

Click on image to enlarge for easy reading

The relations between executive functions, numerosity and later math achievement

Numerosity (aka number sense) has been a very hot and intriguing area of research this past decade. Yet another interesting study, this time demonstrating the role of executive functions...which are repeatedly found to be important for math cognition and achievement.

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Number sense: Two dimensional construct that may either be Gf, Gq or mixed Gf/Gq in CHC taxonomy

 

Very interesting article on the structure of number sense (numerosity) and correlates of the dimensions of number sense. Joel Schneider and I, in our 2012 CHC book chapter, suggest that number sense is likely a new ability that needs to be included in the CHC taxonomy. At this time there is no research I am aware of that helps determine where number sense fits in the CHC taxonomy. As Joel and I have written, we believe it likely would fall under Gq or Gf. It is my current thinking, based on the study featured here and other research I have read, that number sense most likely is a factorially complex ability that will fall under Gq and Gf (RQ). There is likely going to be an increase in standardized measures of number sense (or numerosity) in future individually administered test batteries.

Click on images below to enlarge

"NS at an early age has been denoted as the most important predictor of later mathematics performance: more important than general intelligence, and still present when controlling for other measures such as working memory (e.g., Geary, Hoard, Nugent, & Bailey, 2013; Mazzocco, Feigenson, & Halberda, 2011). Similarly, problems in early NS may precede long-lasting problems in mathematics performance throughout the academic career of a child (Ansari & Karmiloff-Smith, 2002; Butterworth, 2005). In the past decades, research concerning the components of NS, its predictive role for later performance, and the possibilities to remediate delays in NS has been expanded (e.g., Dyson, Jordan, & Glutting, 2013; Toll & Van Luit, 2013a). The present study builds on current understandings of NS and aims to inves-tigate the factor structure of NS and the predictive role of working memory (WM)."

"Although research concerning NS has recently increased, there is limited consensus with regard to its definition. Dehaene (1992, 2001) stressed the intuitive capacity to mentally represent quantities, but other definitions focus on declarative knowledge of numbers, and the ability to compare between and manipulate them, as evidenced by di-verse batteries of quantity-related tests (Jordan, Glutting, Ramineni, & Watkins, 2010; Malofeeva et al., 2004). Also, a limited number of studies have targeted the factors underlying the construct."

"The factor analysis yielded a factor structure of two distinct components. The first component can be characterised as symbolic processing and is primarily based on culture-based taught skills: number recognition, counting, and using number words in a meaningful context. This factor could predict performance on digit knowledge and counting, but also on the symbolic versions of the number comparison and number line test, as formal knowledge of number symbols and words was needed for successful completion of these tasks. The second factor could be characterised as nonsymbolic processing, and primarily indicated the intuitive processing of number and magnitude, quite similar to the influential definition of NS given by Dehaene (2001), who postu-lated that NS is quick and intuitive. This factor could predict performance on both the symbolic and the nonsymbolic comparison and number line tests."

"We found that both symbolic and nonsymbolic processing could be predicted by WM components. However, whereas both the central executive and visuospatial sketchpad could significantly predict symbolic number processing, variance in nonsymbolic processing was only predicted by the central exec-utive, whilst measures of the slave systems added no additional explained variance. Yet, each individual measure of WM did correlate with measures loading onto nonsymbolic NS, highlighting the importance of analysing these associations in integrated models in order to control for shared variance between tasks. The significant associations between symbolic processing and both the central executive and visuospatial sketchpad suggested that to successfully count and use number words and symbols, both visuospatial storage and processing is needed

 

 

 

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Research bytes: MS & Gs, numerical development, working memory & bilinguals, Ga-pseudo word repetition tasks, etc

Denney, D. R., Gallagher, K. S., & Lynch, S. G. (2011). Deficits in Processing Speed in Patients with Multiple Sclerosis: Evidence from Explicit and Covert Measures. Archives of Clinical Neuropsychology, 26(2), 110-119

Cognitive slowing in individuals with multiple sclerosis (MS) has been documented by numerous studies employing explicitly timed measures in which speed of responding is an obvious focus of task performance. The present study examined information processing speed in MS patients and controls with a computerized battery of covertly timed as well as explicitly timed measures. The explicit measures were derived from two tests requiring rapid serial processing of visual stimuli, the Stroop Test and a Picture Naming Test. Covert measures were derived from the Rotated Figures Test, Remote Associates Test, and Tower of London, all tasks in which participants’ attention was drawn toward arriving at an accurate solution, and the latency with which they arrived at these solutions was timed by the computer “behind the scenes.” Significant differences in processing speed for patients and controls occurred on both types of measures, although the effect sizes were notably larger on the explicit measures.



Jones, G. (2011). A computational simulation of children's performance across three nonword repetition tests. Cognitive Systems Research, 12(2), 113-121

The nonword repetition test has been regularly used to examine children’s vocabulary acquisition, and yet there is no clear explanation of all of the effects seen in nonword repetition. This paper presents a study of 5–6year-old children’s repetition performance on three nonword repetition tests that vary in the degree of their lexicality. A model of children’s vocabulary acquisition is then presented that captures the children’s performance in all three repetition tests. The model represents a clear explanation of how working memory and long-term lexical and sub-lexical knowledge interact in a way that is able to simulate repetition performance across three nonword tests within the same model and without requiring test specific parameter settings



Bonifacci, P., Giombini, L., Bellocchi, S., & Contento, S. (2011). Speed of processing, anticipation, inhibition and working memory in bilinguals. Developmental Science, 14(2), 256-269.

Literature on the so-called bilingual advantage is directed towards the investigation of whether the mastering of two languages fosters cognitive skills in the non-verbal domain. The present study aimed to evaluate whether the bilingual advantage in non-verbal skills could be best defined as domain-general or domain-specific, and, in the latter case, at identifying the basic cognitive skills involved. Bilingual and monolingual participants were divided into two different age groups (children, youths) and were tested on a battery of elementary cognitive tasks which included a choice reaction time task, a go/no-go task, two working memory tasks (numbers and symbols) and an anticipation task. Bilingual and monolingual children did not differ from each other except for the anticipation task, where bilinguals were found to be faster and more accurate than monolinguals. These findings suggest that anticipation, which has received little attention to date, is an important cognitive domain which needs to be evaluated to a greater extent both in bilingual and monolingual participants



Hyde, D. C., & Spelke, E. S. (2011). Neural signatures of number processing in human infants: evidence for two core systems underlying numerical cognition. Developmental Science, 14(2), 360-371

Behavioral research suggests that two cognitive systems are at the foundations of numerical thinking: one for representing 1–3 objects in parallel and one for representing and comparing large, approximate numerical magnitudes. We tested for dissociable neural signatures of these systems in preverbal infants by recording event-related potentials (ERPs) as 6–7.5-month-old infants (n = 32) viewed dot arrays containing either small (1–3) or large (8–32) sets of objects in a number alternation paradigm. If small and large numbers are represented by the same neural system, then the brain response to the arrays should scale with ratio for both number ranges, a behavioral and brain signature of the approximate numerical magnitude system obtained in animals and in human adults. Contrary to this prediction, a mid-latency positivity (P500) over parietal scalp sites was modulated by the ratio between successive large, but not small, numbers. Conversely, an earlier peaking positivity (P400) over occipital-temporal sites was modulated by the absolute cardinal value of small, but not large, numbers. These results provide evidence for two early developing systems of non-verbal numerical cognition: one that responds to small quantities as individual objects and a second that responds to large quantities as approximate numerical values. These brain signatures are functionally similar to those observed in previous studies of non-symbolic number with adults, suggesting that this dissociation may persist over vast differences in experience and formal training in mathematics


Schleifer, P., & Landerl, K. (2011). Subitizing and counting in typical and atypical development. Developmental Science, 14(2), 280-291.

Enumeration performance in standard dot counting paradigms was investigated for different age groups with typical and atypically poor development of arithmetic skills. Experiment 1 showed a high correspondence between response times and saccadic frequencies for four age groups with typical development. Age differences were more marked for the counting than the subitizing range. In Experiment 2 we found a discontinuity between subitizing and counting for dyscalculic children; however, their subitizing slopes were steeper than those of typically developing control groups, indicating a dysfunctional subitizing mechanism. Across both experiments a number of factors could be identified that affect enumeration in the subitizing and the counting range differentially. These differential patterns further support the assumption of two qualitatively different enumeration processes.

















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Research bytes 10-7-2010: Parents--early "number talk" important for later math achievement

Levine, S. C., Suriyakham, L. W., Rowe, M. L., Huttenlocher, J., & Gunderson, E. A. (2010). What Counts in the Development of Young Children's Number Knowledge? Developmental Psychology, 46(5), 1309-1319.

Prior studies indicate that children vary widely in their mathematical knowledge by the time they enter preschool and that this variation predicts levels of achievement in elementary school. In a longitudinal study of a diverse sample of 44 preschool children, we examined the extent to which their understanding of the cardinal meanings of the number words (e.g., knowing that the word “four” refers to sets with 4 items) is predicted by the “number talk” they hear from their primary caregiver in the early home environment. Results from 5 visits showed substantial variation in parents' number talk to children between the ages of 14 and 30 months. Moreover, this variation predicted children's knowledge of the cardinal meanings of number words at 46 months, even when socioeconomic status and other measures of parent and child talk were controlled. These findings suggest that encouraging parents to talk about number with their toddlers, and providing them with effective ways to do so, may positively impact children's school achievement.

Technorati Tags: Psychology, school psychology, developmental psychology, educational psychology, forensic psychology, neuropsychology, special education, intelligence, cognitive abilities, cognition, intelligence theories, CHC theory, CHC, Cattell-Horn-Carroll, intelligence, cognition, IQ, IQ tests, Gq, math, math LD, dyscalculia, number sense, number talk

Nmber sense (Gq/Gf-RQ): Special issue of BBS

The recent issue of Behavioral and Brain Sciences was devoted to the development of number concepts and number sense in children.  If you are not familiar with this journal, its format is to have one main article that is then followed by dozens of "open commentaries" by other scholars.  The TOC for this issue can be viewed by clicking here.

The main article is listed below (along with abstract).  If any IQs Corner reader would like to read the issue and provide a guest blog post, email me and I'll provide a copy.

From numerical concepts to concepts of number

Lance J. Rips, Amber Bloomfield and Jennifer Asmuth

Behavioral and Brain Sciences , Volume 31, Issue 06, December 2008, pp 623-642

• Abstract: Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children’s understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a þ b ¼ b þ a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas.

• Here is a description of the journal as lifted from its official site.  BBS is the internationally renowned journal with the innovative format known as Open Peer Commentary. Particularly significant and controversial pieces of work are published from researchers in any area of psychology, neuroscience, behavioural biology or cognitive science, together with 10-25 commentaries on each article from specialists within and across these disciplines, plus the author's response to them. The result is a fascinating and unique forum for the communication, criticism, stimulation, and particularly the unification of research in behavioural and brain sciences from molecular neurobiology to artificial intelligence and the philosophy of the mind. As Cambridge continues its philosophy of moving towards fully online submission, refereeing and commentary, see preprints of articles currently undergoing commentary at http://www.bbsonline.org

Technorati Tags: psychology, school psychology, educational psychology, neuropsychology, cognition, intelligence, quantitative, quantitative reasoning, quantitative knowledge, number sense, number concepts

Number sense can be trained. Plus Gq factor structure info

Last October I made a brief post re: the ability of number sense, an preschool skill that appears important in the development of future mathematical skill and ability development (Gq-general quantitative knowledge as per CHC theory) At that time I wondered aloud if anyone was aware of any factor analysis research of good markers of number sense abilities. This past week my prayers were answered...at least partially. Ramani and Seigler (2008) published an article in Child Development that addressed the the ability to improve number sense abilities in low-income preschool children via the playing of linear board games.

The abstract is below. The introduction provides a nice overview of the number sense literature in preschool children. Also of significant interest (to those of us working in education) was the finding that playing number board games increased number sense competencies...and...more importantly, these gains were sustained after training was completed (up to nine weeks later).

Of interest to me was the inclusion of an exploratory factor analysis of the number sense measures used in the study. The authors reported three possible number sense dimensions -- numerical magnitude, numerical identification skill, and counting skill. Currently the Gq domain in the CHC taxonomy is not well understood. Most contemporary treatments of the broad stratum II ability only lists two narrow stratum I abilities (Mathematical Knowldge, KM; Mathematical Achievement, A3). The current study suggests the Gq domain may be much more differentiated than currently understood. The three number sense factors identified in this study might represent narrow stratum I abilities in their own right, or, might represent an even narrower stratum of Gq abilities below stratum I. Only future research with a broader array of Gq variables (and other CHC ability variables) will help answer this question.

I smell some possible good dissertations.

Abstract

• Theoretical analyses of the development of numerical representations suggest that playing linear number board games should enhance young children’s numerical knowledge. Consistent with this prediction, playing such a game for roughly 1 hr increased low-income preschoolers’ (mean age 5 5.4 years) proficiency on 4 diverse numerical tasks: numerical magnitude comparison, number line estimation, counting, and numeral identification. The gains remained 9 weeks later. Classmates who played an identical game, except for the squares varying in color rather than number, did not improve on any measure. Also as predicted, home experience playing number board games correlated positively with numerical knowledge. Thus, playing number board games with children from low-income backgrounds may increase their numerical knowledge at the outset of school.

Technorati Tags: psychology, educational psychology, school psychology, neuropsychology, math, mathematics, Gq, number sense, intervention, CHC theory

Born to count?

Interesting post at Deric Bownds Mindblog re: article suggesting we have an innate number sense.

Technorati Tags: psychology, educational psychology, school psychology, education, math, arithmetic, number sense, genetics, Gq, IQs Corner, Mindblog

Quantitive abilities - number sense

Someone recently sent me a nice article (click here to view) re: "number sense" that was previously published in the Journal of Learning Disabilities. According to the authors, a review of the diverse literature suggest that number sense "constitutes an awareness, intuition, recognition, knowledge, skill, ability, desire, feel, expectation, process, conceptual structure,or mental number line." I'd love to see some factor analysis research of comprehensive measures of number sense of good markers of Gf/Gq (RQ, KM, A3), to ascertain the narrow CHC domain(s) where these skills may lie. Does anyone have knowledge of any such research?

Technorati Tags: psychology, educational psychology, education, neuropsychology, CHC theory, quantiative, quantitative reasoning, Gf, Gq, number sense, learning disabilities
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More on math disabilities and early number sense

The BBC story on the possible localization of brain regions related to serious math disorders (dyscalculia) has been making the rounds in the blogsphere. I was first made aware of the news report from Al Fin. The Gene Expression blog has now picked up on the posting and has amplified the available information via links to two recommended books and one related journal article.

To continue the amplification of this thread, I'd like to alert readers to an interesting article (Jordan, 2006) I had skimmed just the other day that reported a longitudinal study of children (kindergarten) at risk for math difficulties. What I found of particular interest was the introduction and conceptual overview of the major components of early number sense....something I had not studied much before. CHC'rs...file under Gq and Gf-RQ.

Technorati Tags: psychology, educational psychology, school psychology, education, math, mathematics, kindergarten, math disabilities, learning disabilities, Gq, quantiative, dyscalculia, screening, number sense, CHC theory, CHC