Table 4 Reliability and Criterion Validity for Identified Mathematical Assessments and Screeners
Name of Measurement Tool (Related Papers) | Reliability | Criterion Validity | ||||
|---|---|---|---|---|---|---|
Method(s) | Results | Rating | Method(s) | Results | Rating | |
Mathematical assessments | ||||||
Academic Rating Scale (ARS)-adapted (Kilday et al., 2012) | NR | NR | NA | Concurrent (TEMA-3; M-TEAM) | β = .44–.52 | Low |
Ani Banani Test (ten Braak & Størksen, 2021) | NR | NR | NA | Concurrent (PENS-B) Predictive (PENS-B; NSMA; end of year) | r = .53 r = .59–.65 | Low Mixed |
Arithmetic Calculation Efficiency Test (TECA) (Singer & Cuadro, 2014) | Test–retest (interval NR) | r = .85–.94 | Acceptable | NR | NR | NA |
Assessment of Algebraic Thinking (AAT) (Ralston et al., 2018) | Inter-rater | 94% | Acceptable | NR | NR | NA |
Birthday Party- Long Version (English) (Lee, 2016) | Test–retest (2 weeks) Inter-rater | r = .24–.82 k = .71–1.00 | Mixed Acceptable | Concurrent (YCAT) Predictive (YCAT; 1–2 years) | r = .32–.75 r = .28–.66 | Mixed Mixed |
Birthday Party- Long Version (Spanish) (Lee, 2016) | NR | NR | NA | Concurrent (YCAT) | r = .19–.69 | Mixed |
CIRCLE Progress Monitoring (CPM) Math Subtest (Assel et al., 2020) | Test–retest (beginning to middle of school year) | r = .78 | Acceptable | Concurrent (WJ-III-AP; TEMA-3) Predictive (WJ-III-AP; TEMA-3; 1–2 years) Divergent (EOWPVT; WJ-III-LW; WJ-III-PC) | r = .65 r = .55 r = .42–.61 | Acceptable Low Mixed |
Cognitive Diagnostic Test (Li et al., 2020) | NR | NR | NA | Concurrent (WJ-IV-AP; WJ-IV-C) | r = .62–.77 | Acceptable |
Comprehensive Learning Test-Mathematics (CLT-M) (Lee et al., 2017) | Test–retest (2 weeks) | r = .87 | Acceptable | NR | NR | NA |
Comprehensive Research-Based Early Math Ability Test (CREMAT) (Clements et al., 2022) | NR | NR | NA | NR | NR | NA |
Curriculum Based Measures for Kindergarten- Grade 3 (Lee & Lembke, 2016) | Test–retest (2 weeks) | r = .36–.86 | Mixed | Concurrent (WJ-III-Math) | r = .14- .58 | Low |
DIFER School Readiness Test Battery Counting and Basic Numeracy (Csapó et al., 2014; Józsa et al., 2023) | NR | NR | NA | Divergent (other DIFER domains) | r = .69–.77 | Acceptable |
Early Arithmetic, Reading and Learning Indicators (EARLI) – Numeracy measures (Cheng et al., 2017; Lei et al., 2009) | NR | NR | NA | Concurrent (WJ-III-AP; WJ-III-QC) | r = .32–.83 | Mixed |
Early Grade Mathematics Assessment (EGMA) (Ketterlin-Geller et al., 2018; Perry, 2020) | NR | NR | NA | NR | NR | NA |
Early Learning Outcomes Measure (ELOM) (Anderson et al., 2021; Snelling et al., 2019) | Test–retest (1 week) Inter-rater | r = .90 k = .68–.92 | Acceptable Mixed | Concurrent (WPPSI-IV) | r = .64 | Acceptable |
Early Measurement Assessment Tool (EMAT) (Ceylan & Aslan, 2023) | Test–retest (6 weeks) | r = .91 | Acceptable | Concurrent (TEMA-3) | r = .76–.84 | Acceptable |
Early Years Toolbox-Early Numeracy (Howard et al., 2022) | Test–retest (1 week) | r = .89 | Acceptable | Concurrent (DAS; PENS) | r = .74–.80 | Acceptable |
Evaluación Neuropsicológica Infantil-Preescolar (ENI-P)- Numerical Abilities Test (Beltrán-Navarro et al., 2018) | Test–retest (15 days) | r = .30–.84 | Mixed | NR | NR | NA |
Galileo Early Maths-Revised (Kowalski et al., 2018) | NR | NR | NA | Concurrent (Child-direct tasks) | r = .47 | Low |
Heidelberger Rechen Test (HRT) 1–4 (Hassler Hallstedt & Ghaderi, 2018) | Test–retest (3–7 days) | r = .29–.82 | Mixed | Concurrent (Math Battery) | r = .67–.82 | Acceptable |
KeyMath-Revised (Rhodes et al., 2015) | NR | NR | NA | NR | NR | NA |
Kieler Kindergartentest Mathematik (KiKi) (Van Hoogmoed et al., 2022) | NR | NR | NA | Concurrent (ENT-R) | r = .72 | Acceptable |
Mathematical and Arithmetic Competence Diagnostic (MARKO-D) (Bezuidenhout, 2018; Fritz et al., 2014; Henning et al., 2021) | NR | NR | NA | NR | NR | NA |
Mathematical Profile (MathPro) Test (Karagiannakis & Noël, 2020) | NR | NR | NA | Concurrent (Standardized maths test) | r = .47–.64 | Mixed |
Mathematical Reasoning Test (Nunes et al., 2015) | NR | NR | NA | NR | NR | NA |
mCLASS: Math (Ginsburg et al., 2016) | Inter-rater | k = .76- .95 | Acceptable | Concurrent (WJ-III-Math) | r = .50–.61 | Mixed |
Neuropsychological Test Battery for Number Processing and Calculation in Children – Revised (NUCALC- R) (Dos Santos et al., 2012; Koumoula et al., 2004) | NR | NR | NA | Concurrent (WISC-III-A) Divergent (ATHENA; WISC-III- DS) | r = .41–.64 r = .45–.52 | Mixed Low |
Number Sense Test (Malofeeva et al., 2004) | NR | NR | NA | Divergent (WPPSI-Vocabulary) | r = .33–.54 | Low |
Numeracy-Caregiver report questionnaire (Pushparatnam et al., 2021) | NR | NR | NA | NR | NR | NA |
Numeracy-Child direct assessment (Pushparatnam et al., 2021) | NR | NR | NA | NR | NR | NA |
Observing and Analysing Children’s Mathematical Development (OAMD) (Bunck et al., 2017) | Test–retest (2–6 months) | r = .47 | Low | Concurrent (CMT; CKT) | r = .39–.50 | Low |
Parent ratings of numeracy skills (Lin et al., 2021) | NR | NR | NA | Concurrent (Child direct tasks; PENS-B) | r = .31–.56 | Low |
Quantitative Reasoning Test (Nunes et al., 2015) | Test–retest (4.5 months) | r = .78 | Acceptable | Predictive (Math Reasoning Test; interval NR) | ΔR2 = .06–.24 | Low |
Research-Based Early Maths Assessment (REMA) (Clements et al., 2008; Dong et al., 2023) | Inter-rater | 98% | Acceptable | NR | NR | NA |
Research-Based Early Maths Assessment- Short Form (REMA-SF) (Dong et al., 2021; Weiland et al., 2012) | Test–retest (1 term) | r = .90 | Acceptable | Concurrent (REMA; WJ-III-AP) Divergent (PPVT-III; WJ-III-LW) | r = 71–.74 r = .64 | Acceptable Acceptable |
School Achievement Test-2nd Edition-Arithmetic Subtest (Viapiana et al., 2016) | NR | NR | NA | NR | NR | NA |
Teacher Rating Scale – Early Numeracy (TRS-EN) (Vessonen et al., 2023) | NR | NR | NA | Concurrent (ENT) Predictive (ENT; 1 year) | r = .60 r = .63–.69 | Acceptable Acceptable |
Teaching Strategies GOLD (Lambert et al., 2014, 2015; Russo et al., 2019; Vitiello & Williford, 2021) | Inter-rater | k = .92 | Acceptable | Concurrent (BBCS-R; WJ-III) Predictive (WJ-III; 1 term) Divergent (other TS Gold domains) | r = .27–.74 r = .39 r = .13–.44 | Mixed Low Low |
Test of Early Number and Arithmetic (TENA) (Bojorque et al., 2015) | Inter-rater | k = .92 | Acceptable | Concurrent (ENT) | r = .80–.89 | Acceptable |
The International Development and Early Learning Assessment (IDELA)- Emergent Numeracy (Pisani et al., 2018, 2022; Shavitt et al., 2022) | Inter-rater Test–retest (3 weeks) | k = .88–.99 ICC = .66 | AcceptableLow | Concurrent (EGMA) Predictive (EGMA; 2 years) | r = .63 R2 = .55 | AcceptableLow |
The Utrecht Test of Early Numeracy (ENT) Test (Aunio et al., 2006; David et al., 2015) | Test–retest (3 months) | r = .75 | Acceptable | Divergent (Raven’s progressive matrices) | r = .47 | Low |
Tools for Early Assessment in Math Danish Version (DK-TEAM) (Sjoe et al., 2019) | Test–retest (4.5 months) | r = .43–93 | Mixed | NR | NR | NA |
Screeners | ||||||
Arabic number-writing task (Moura et al., 2015) | NR | NR | NA | Diagnostic accuracy | Sensitivity = .58–.85 Specificity = .28–.88 | Low Mixed |
Assessing Student Proficiency of Early Number Sense (ASPENS) (Brafford et al., 2023; Sutherland et al., 2021) | Test–retest (interval NR) | r = .71–.87 | Acceptable | Diagnostic accuracy Concurrent (TerraNova) Predictive (TerraNova; end of year) | Sensitivity = .91 Specificity = .83 r = .56 r = .50–.53 | Acceptable Acceptable Low Low |
Basic Number Processing Test (BNPT) (Olkun et al., 2016) | NR | NR | NA | Concurrent (MAT; CPT) | r = − .64– − .20 | Mixed |
Birthday Party- Short Version (Lee, 2016) | NR | NR | NA | NR | NR | NA |
Dyscalculia screener (Butterworth, 2003) | NR | NR | NA | NR | NR | NA |
Dyscalculia Test (Eteng-Uket, 2023) | NR | NR | NA | NR | NR | NA |
Early Measurement Curriculum-Based Measures (EM-CBM) (Clarke et al., 2023) | Test–retest (10 weeks) | r = .33–.48 | Low | Concurrent (ASPENS) Predictive (EasyCBM; 10 weeks) | r = .25–.43 r = − .07–.44 | Low Low |
Early Numeracy (EN)- Test (Hellstrand et al., 2020) | NR | NR | NA | NR | NR | NA |
Early Numeracy Screener (Lopez-Pedersen et al., 2021) | NR | NR | NA | Predictive (Norwegian national test scores; 6 months) | r = .19–.25 | Low |
Early Numeracy Skill Indicators (Methe et al., 2008) | Test–retest (13 weeks) | r = .68–.98 | Mixed | Diagnostic accuracy Concurrent (TEMA-3) Predictive (TEMA-3; end of year) | 58–84% correct classification r = .20–.72 r = .41–.70 | Low Mixed Mixed |
House of Numbers (HoN) (Chatzaki et al., 2024) | NR | NR | NA | Diagnostic accuracy | Sensitivity = .91–1.00 Specificity = .85–.93 | Acceptable Acceptable |
Indicators of Basic Early Math Skills (IPAM) (de León et al., 2021; 2022) | Test–retest (3 months) | r = .43–.67 | Mixed | Concurrent (Sn-BADyG) Predictive (Sn-BADyG; end of year) | r = .48–.60 r = .36–.58 | Mixed Low |
Math Essential Skill Screener- Elementary Version (MESS-E) (Erford et al., 1998) | Test–retest (30 days) | r = .86 | Acceptable | Diagnostic accuracy Concurrent (WJ-R; WRAT-R; KeyMath-R) | Sensitivity = .98 Specificity = .88 r = .49–.80 | Acceptable Acceptable Mixed |
Mathematical School Readiness (MSR) (Mejias et al., 2019) | NR | NR | NA | Concurrent (TTR; KRT-R) | r = .56 | Low |
Number Line Assessment 0–20, 0–100 (Clarke et al., 2020) | Test–retest (interval NR) | r = .70–.72 | Acceptable | NR | NR | NA |
Number Line Assessment 0–100 (Sutherland et al., 2021) | Test–retest (8 months) | r = .58 | Low | Diagnostic accuracy | Sensitivity = .69–.91 Specificity = .39–.81 | Mixed Mixed |
Number Sense Screener (NSS) (English Version) (Jordan et al., 2010, 2012) | Test–retest (12 months) Test–retest (17 months) | r = .70–86 r = .61–.69 | Acceptable Low | Diagnostic accuracy Predictive (WJ-III-Math; 2 years) Divergent (DIBELS; WASI; Digit Span) | Sensitivity = .70–.86 Specificity = .35–.85 r = .70–.72 r = .12–.56 | Mixed Mixed Acceptable Low |
Number Sense Screener (NSS) (Turkish Version) (Aktulun, 2019; Kiziltepe, 2019) | NR | NR | NA | NR | NR | NA |
Number Sets Test (Geary et al., 2009) | NR | NR | NA | Diagnostic accuracy Predictive (Third Grade Maths Achievement; 3 years) | Sensitivity = .69 Specificity = .67 Estimate = 5.01 | Low Low NA |
Numeracy Screener (Bugden et al., 2021; Hawes et al., 2019; Nosworthy et al., 2013) | Test–retest (M = 89.55 days) | r = .61–.72 | Mixed | Diagnostic accuracy Concurrent (WJ-III-Maths) Divergent (WJ-III-Reading) Predictive (school maths grades; 1 year) | Sensitivity = .62 Specificity = .87 r = .22–.25 r = .15–.19 r = .23–.31 | Low Acceptable Low Low Low |
Preschool Early Numeracy Skills Screener- Brief Version (PENS-B) (English Version) (Purpura et al., 2015) | NR | NR | NA | Concurrent (TEMA-3) Divergent (GRTR; EOWPVT) | r = .73 r = .60–.63 | AcceptableAcceptable |
Preschool Early Numeracy Skills Screener- Brief Version (PENS-B) (Greek Version) (Tsigilis et al., 2023) | Marginal reliability index | .79–.82 | Acceptable | NR | NR | NA |
Preschool Numeracy Indicators (Floyd et al., 2006) | Test–retest (M = 26.5 days) | r = .32–.92 | Mixed | Concurrent (BBCS-R; WJ-III-AP; TEMA-3) | r = .29–70 | Mixed |
Primary Math Assessment Diagnostic (PMA-D) (Brendefur et al., 2018) | NR | NR | NA | NR | NR | NA |
Primary Math Assessment Screener (PMA-S) (Brendefur et al., 2018) | NR | NR | NA | NR | NR | NA |
Symbolic Magnitude Processing (SYMP) Test (Brankaer et al., 2017) | Test–retest (interval NR) | r = .62–.77 | Mixed | Diagnostic accuracy Concurrent (standardized maths test) | TD children (≥ 35th percentile on standardized maths test) consistently outperformed MLD children (≤ the 10th percentile), except 10–11 years r = .16–.40 | Acceptable Low |
Universal Screening of Math Skills/Despiste Universal de Competências Matemáticas (DUCMa) (Cruz et al., 2024) | Test–retest (start and end of school year) | r = .39–.72 | Mixed | Predictive (school maths grades; 1 year) | r = .27–.45 | Low |
Measurement tools widely used to assess criterion validity | ||||||
Test of Early Mathematics Abilities-3rd Version (TEMA-3; Ginsburg & Baroody, 2003) | Test–retest (2 weeks) | r = .82–.93 | Acceptable | Concurrent (KeyMath-R/NU; WJ-III-Math; DAB-3; YCAT) | r = .54–.91 | Mixed |
Woodcock-Johnson III Achievement Tests Maths (WJ-III-ACH Maths) (Schrank et al., 2001) | Test–retest (1 day) | r = .91–.95 | Acceptable | Concurrent (Kaufman Test of Educational Achievement maths sub-tests; WIAT maths sub-tests) | r = .29–.70 | Mixed |