Number Sense

Learner Variable · All learner variables
Evidence · 98 claims (70 show a difference, 18 mixed, 10 no difference) · 40 studies (23 associational, 9 causal, 2 review, 2 qualitative, 2 design, 2 theoretical), q1–q3 · 15 of 40 report an effect size · 96 claims rest on one study

Description

Number sense is a learner's grasp of how large numbers are and how they relate to one another. It is measured with magnitude comparison (which of two numbers or dot arrays is larger), number line estimation (placing a number on a line with labelled ends) and similar tasks. These measures correlate with mathematics achievement and predict later mathematics learning, and they can be improved by instruction such as number board games and number line activities. It is a domain-specific part of prior knowledge in mathematics.

How strongly it relates to achievement

Mathematics. These are correlations across meta-analyses (Breit et al. 2025, a systematic review of 30 meta-analyses; overview [+W]): how strongly learners who differ on this characteristic differ in mathematics achievement, not how much changing it would change achievement. Many of these characteristics are correlated with one another, and the review is about mathematics only.

• Number line estimation r = .44, larger after age 9 (.49) than before 6 (.30); symbolic magnitude comparison .30, nonsymbolic .24, smaller in older samples. Claim [+W]

Implications

Context

• Early-years and primary mathematics, and diagnosing mathematics difficulties.

Target Learners

• Young children starting mathematics; learners at risk of mathematics difficulties.

Target Learning Objectives

• Arithmetic and later mathematics achievement, including fractions.

Claims

• Contrary to the science comprehension thesis, political polarization of data interpretation did not abate among the most numerate subjects but increased [+M] — learners who differ on it differ in outcomes
• DreamBox effects on the Problem Solving, Number Sense, and Statistics and Probability subtests were not statistically significant [-M] — instruction changes it
• Early numeracy mastery at 54 months predicts college attendance [+W] — learners who differ on it differ in outcomes
• Early numeracy mastery at 54 months predicts high school math course-taking [+W] — learners who differ on it differ in outcomes
• Number Board Games Improve Numerical Knowledge [+M] — instruction changes it
• Numerical routines individualize through a three-stage sequence of vertical and horizontal bonding [+W] — instruction changes it
• Students in the TEC Summer Learning Program showed a 20% pre-to-post gain in numeracy skills [+W] — instruction changes it
• Vision is not required for developing number sense and math skills in BVI learners [+W] — instruction changes it
• ANS acuity correlates with later number sets fluency but does not emerge as a unique predictor once symbolic knowledge is controlled [~M] — learners who differ on it differ in outcomes
• ANS acuity is not related to algebra achievement once covariates are controlled, whereas retrieval errors remain predictive [-M] — learners who differ on it differ in outcomes
• ANS acuity predicts accuracy of coordinate plane placements and expression evaluation accuracy, but not equation memory, in 9th graders [+M] — learners who differ on it differ in outcomes
• Base-10 blocks training was followed by a significant drop in kindergarteners' numerals-condition scores [-M] — instruction changes it
• Both numerical magnitude processing tasks correlate positively with arithmetic fact retrieval, more strongly for symbolic [+M] — learners who differ on it differ in outcomes
• Both symbolic and nonsymbolic magnitude processing correlate with subtraction accuracy, but subtraction speed is associated only with symbolic tasks [~M] — learners who differ on it differ in outcomes
• Characteristic distance effects occur in both nonsymbolic and symbolic single-digit approximate addition [+M] — learners who differ on it differ in outcomes
• Inhibition does not uniquely predict arithmetic fact retrieval above numerical magnitude processing [+M] — learners who differ on it differ in outcomes
• More accurate symbolic number line representations relate to better performance in exact, but not approximate, addition formats [~M] — learners who differ on it differ in outcomes
• Neither first-grade whole number magnitude nor arithmetic knowledge uniquely predicted eighth-grade reading achievement [-M] — learners who differ on it differ in outcomes
• Non-symbolic magnitude processing shows mixed associations with inhibition measures [~M] — learners who differ on it differ in outcomes
• Nonsymbolic exact addition is predicted by the VSSP plus the CE and symbolic number line estimation, suggesting an alternate transcoding to the symbolic code [+M] — learners who differ on it differ in outcomes
• Number sense measures are non-significant predictors of math once more robust predictors are included [-M] — learners who differ on it differ in outcomes
• Numerical magnitude processing is significantly associated with children's mental multi-digit subtraction performance, controlling for intellectual ability and motor speed [+M] — learners who differ on it differ in outcomes
• Point-to-x is the most consistent end-of-preschool predictor of kindergarten number sets performance across item types [+M] — learners who differ on it differ in outcomes
• Preschool one- and two-knowers perform at least 0.5 SDs lower on the kindergarten number sets test than early cardinal-principle knowers [+M] — learners who differ on it differ in outcomes
• Preschoolers' cardinal knowledge predicts fluent processing of symbolic and nonsymbolic magnitudes on the kindergarten number sets test two years later [+M] — learners who differ on it differ in outcomes
• Preschoolers' implicit understanding of arithmetic (nonverbal calculation) predicts later number sets fluency above and beyond cardinal knowledge [+M] — learners who differ on it differ in outcomes
• Symbolic approximate addition is predicted by nonsymbolic number line estimation, the VSSP and the CE, consistent with transcoding to the nonsymbolic code [+M] — learners who differ on it differ in outcomes
• Symbolic exact addition is predicted by symbolic number line representation and the phonological loop, reflecting phonological storage of numerical information [+M] — learners who differ on it differ in outcomes
• Symbolic number comparison accuracy is the only number sense measure with a significant partial correlation with math [+M] — learners who differ on it differ in outcomes
• Symbolic numerical magnitude comparison has a more unique association than number line estimation with children's speed on indirect-addition subtraction items [+M] — learners who differ on it differ in outcomes
• Symbolic numerical magnitude processing is a powerful unique predictor of arithmetic fact retrieval [+M] — learners who differ on it differ in outcomes
• Symbols-only training improved kindergarteners' performance on difficult place value items, but base-10 blocks training did not [~M] — instruction changes it
• The association between numerical magnitude processing and subtraction is more prominent for items eliciting indirect addition than for direct subtraction items [~M] — learners who differ on it differ in outcomes
• The relation between early whole number magnitude knowledge and later fraction magnitude knowledge is not attributable to number line tasks being used at both measurement times [+M] — learners who differ on it differ in outcomes
• The visuospatial sketchpad is the best and only unique predictor of kindergarteners' nonsymbolic approximate addition [+M] — learners who differ on it differ in outcomes
• Visual fraction models yield more accurate magnitude comparisons than Arabic numeral fractions for all ability groups, but the visual model advantage persists through Grade 8 only for children with MLD [+M] — instruction changes it
• Accuracy on approximate addition decreases as ratio approaches 1, with a stronger ratio effect on the non-symbolic task [+M] — learners who differ on it differ in outcomes
• Adults with dyscalculia perform the number comparison task as accurately as controls but respond significantly more slowly [~M] — learners who differ on it differ in outcomes
• Adults with dyscalculia show less distinct non-symbolic number representations than matched controls in anterior parietal, frontal and temporal cortex [+M] — learners who differ on it differ in outcomes
• At all ages, children with developmental dyscalculia perform significantly lower than controls in magnitude comparison tasks using symbolic numbers [+W] — instruction changes it
• Both numerical training conditions improve magnitude processing more than a story-understanding control condition [+M] — instruction changes it
• Children succeed at non-symbolic approximate addition above chance with a ratio effect, without relying on non-numerical strategies [+M] — instruction changes it
• Children with MLD and LA are less accurate than TA children on symbolic but not non-symbolic approximate addition [+M] — learners who differ on it differ in outcomes
• Children's symbolic magnitude comparison performance improves significantly across all primary school grades [+M] — instruction changes it
• Cross-cultural evidence: adults without a counting system fail to develop exact representations of numbers beyond 3 or 4 despite a normal ANS [~W] — instruction changes it
• DD children's deficit in non-symbolic number magnitude processing appears only in studies of older children (10 years and above), not younger ones [~W] — instruction changes it
• First graders with MLD are slower than typically achieving peers on symbolic but not non-symbolic numerical magnitude comparison [~M] — learners who differ on it differ in outcomes
• Fourth graders' multiplication fact solving speed correlates significantly with both symbolic and nonsymbolic magnitude comparison speed [+M] — learners who differ on it differ in outcomes
• Group differences on symbolic tasks persist after controlling for number identification skill [+M] — learners who differ on it differ in outcomes
• Kindergarten children's non-symbolic addition performance correlates with end-of-year mathematics achievement, independent of literacy (Experiment 1) [+M] — learners who differ on it differ in outcomes
• Kindergarten predictors correlate robustly with grade 1 math outcomes, weakest for computation [~M] — learners who differ on it differ in outcomes
• Kindergarten symbolic number variables uniquely predict grade 1 math outcomes over and above counting and domain general predictors [+M] — learners who differ on it differ in outcomes
• Neither numerical training significantly improves Arabic number comparison performance [-M] — instruction changes it
• No group difference in the quality of symbolic number representations between adults with dyscalculia and controls [-M] — instruction changes it
• No univariate activation-level differences between adults with dyscalculia and controls during symbolic or non-symbolic number processing [-M] — learners who differ on it differ in outcomes
• Non-symbolic addition performance correlates with mathematics achievement in a new sample, surviving controls for verbal intelligence and literacy (Experiment 2) [+M] — learners who differ on it differ in outcomes
• Non-symbolic arithmetic performance correlates with children's mastery of number words and Arabic symbols (Experiment 2) [+M] — learners who differ on it differ in outcomes
• Number naming and number comparison are better predictors of kindergarten arithmetic than number line estimation [+W] — learners who differ on it differ in outcomes
• Numerical magnitude comparison explains significant unique variance in multiplication fact performance over and above phonological processing, intellectual ability, and general reaction time [+M] — learners who differ on it differ in outcomes
• Symbol mastery accounts for the association between non-symbolic arithmetic and school mathematics achievement in hierarchical regression [+M] — learners who differ on it differ in outcomes
• Symbolic magnitude comparison contributes more unique variance to fourth graders' multiplication fact performance than nonsymbolic magnitude comparison [+M] — learners who differ on it differ in outcomes
• Symbolic number predictors account for substantial additional variance in grade 1 math outcomes beyond counting and domain general predictors [+M] — learners who differ on it differ in outcomes
• Symbolic training transfers to the auditory modality, improving spoken number-word magnitude comparison [+M] — instruction changes it
• The association between nonsymbolic magnitude comparison and multiplication facts is similar across trial types (OTS/ANS range and congruency), and the symbolic comparison association is similar across numerical distances [+S] — learners who differ on it differ in outcomes
• The association between one-digit comparison and mathematics achievement decreases across grades, while the two-digit association remains stable [~M] — learners who differ on it differ in outcomes
• The authors hypothesize DD children's first deficit is dysfunction in building the exact representation of symbolic numbers, with reduced ANS acuity as a consequence rather than a cause [+W] — learners who differ on it differ in outcomes
• Training effects on the non-symbolic number line are size-specific: non-symbolic training improves large numerosities, symbolic training small numerosities [~M] — instruction changes it
• Typically achieving children outperform children with mathematical learning difficulties on the SYMP one-digit subtest in Grades 1–5 and the two-digit subtest in Grades 2–5, but not in Grade 6 [~M] — instruction changes it
• Arithmetic skill may predict algebra understanding better than fraction conceptual knowledge or magnitude understanding [-W] — learners who differ on it differ in outcomes
• First graders who missed kindergarten during COVID closures showed the greatest school-readiness loss in basic counting and numeracy skills against pre-pandemic cohorts: d = 0.16 after three months of closures and d = 0.23 for the cohort entering school a year later [+W] — instruction changes it
• Kindergarten closures hit children in low-SES schools hardest in basic counting and numeracy skills (d = 0.2 in 2020; d = 0.3 in 2021), widening inequalities [+W] — instruction changes it
• At-risk learners show lower initial levels and delayed growth in early numeracy components, especially counting skills, relative to typically developing peers [+M] — learners who differ on it differ in outcomes
• Children with higher initial levels in NRS or CS show slower subsequent linear growth in the same component [+W] — learners who differ on it differ in outcomes
• Correlations between NRS and CS decrease slightly over time, being stronger in kindergarten than in Grade 1 [+W] — learners who differ on it differ in outcomes
• Initial levels and growth in numerical relational skills contribute to counting skill development, suggesting NRS may precede CS [+W] — learners who differ on it differ in outcomes
• Numerical relational and counting skills both develop nonlinearly between mid-Kindergarten year 1 and the end of Grade 1, with NRS decelerating and CS accelerating [+W] — learners who differ on it differ in outcomes
• The interdependence between numerical relational and counting skills is weaker in at-risk learners [~M] — learners who differ on it differ in outcomes
• Both nonsymbolic and symbolic magnitude comparison skills longitudinally predict mathematical achievement above and beyond IQ and working memory [+M] — learners who differ on it differ in outcomes
• Fraction magnitude comparison correlated with general math achievement only in the U.S. samples, indicating number line estimation and magnitude comparison tap partly different aspects of fraction magnitude understanding [~M] — learners who differ on it differ in outcomes
• Fraction magnitude understanding, measured by number line estimation, predicts general mathematics achievement beyond fraction arithmetic skill in 5 of 6 Belgian, Chinese and U.S. grade samples, though not among Chinese 8th graders [+M] — learners who differ on it differ in outcomes
• Nonsymbolic magnitude comparison is only moderately predictive of future mathematical achievement, and only in kindergarten [~M] — learners who differ on it differ in outcomes
• Spatial language training improves children's numerical magnitude understanding (number words comparison) [+M] — instruction changes it
• Symbolic magnitude comparison is a robust and consistent longitudinal predictor of children's future mathematical achievement across kindergarten, grade 1 and grade 2 [+M] — learners who differ on it differ in outcomes
• Symbolic magnitude comparison is a stronger longitudinal predictor of mathematical achievement than nonsymbolic comparison [+M] — learners who differ on it differ in outcomes
• The relation between fraction magnitude understanding and mathematics achievement is a general cognitive characteristic, not attributable to specifics of the U.S. educational system, though instruction quality may strengthen or weaken it [+M] — learners who differ on it differ in outcomes
• The practiced group exceeded the control group on three of five tests (complex dotting, number code, letter code translation) by 5, 9, and 15 percent respectively, but did no better on digit-symbol substitution and slightly worse on digit-letter substitution. [~M] — instruction changes it
• Decimal magnitude comparison accuracy is unrelated to direction of effect judgment accuracy, indicating the errors do not stem from poor access to decimal magnitudes [-M] — learners who differ on it differ in outcomes
• Supported self-explaining improves accuracy of fraction magnitude comparisons more than a word-problem intervention component in at-risk fourth graders [+W] — instruction changes it
• Supported self-explaining produces higher-quality explanations of fraction magnitude differences than a word-problem component [+M] — instruction changes it
• The multi-component measurement-focused fraction intervention outperforms part-whole-focused control on NAEP items, number line estimation, and calculations [+M] — instruction changes it
• Number knowledge and numerosity discrimination are unique longitudinal predictors of arithmetic development over the first year of formal education [+M] — learners who differ on it differ in outcomes
• School-entry assessment of numerosity judgments and Arabic number knowledge may identify children at risk of arithmetic difficulties [+M] — learners who differ on it differ in outcomes
• Numerical abilities and serial retrieval fluency predict third-grade multiplication fluency, while working memory shows no significant association in the baseline model [+W] — learners who differ on it differ in outcomes
• Children can learn the meanings of novel number symbols through an artificial symbol learning paradigm, performing above chance on a subsequent symbolic comparison task [+W] — instruction changes it
• Learning number symbols from multiple concrete representations carries a cost compared with consistent single representations, whether concrete or abstract [+W] — instruction changes it
• Performance on the newly learned symbols shows canonical ratio effects, consistent with mapping novel symbols onto Approximate Magnitude System representations [+M] — instruction changes it

Related Learner Variables

Examples

Key Sources

• Breit, M., Schneider, M., & Preckel, F. (2025). Mathematics achievement and learner characteristics: A systematic review of meta-analyses. Learning and Individual Differences, 118, 102621. doi:10.1016/j.lindif.2024.102621

Page metadata

Field	Value
type	learner-variable
id	number-sense
title	Number Sense
description	A learner's understanding of numerical magnitudes and the relations among numbers, shown in tasks such as comparing two quantities or placing a number on a number line.
status	review
canonical	True
generated	by claude/unspecified on 2026-10-16
trust	unverified — no one has confirmed this page's content

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