Table 3 Structural validity and external validity for identified mathematical assessments and screeners
Name of Measurement Tool (Related Papers) | Structural Validity | Internal Consistency | ||||
|---|---|---|---|---|---|---|
Method(s) | Results | Rating | Method(s) | Results | Rating | |
Mathematical assessments | ||||||
Academic Rating Scale (ARS)-adapted (Kilday et al., 2012) | NR | NR | NA | NR | NR | NA |
Ani Banani Test (ten Braak & Størksen, 2021) | CFA | 1 factor model RMSEA ≤ .03, CFI ≥ .96, TLI ≥ .95 | Acceptable | NR | NR | NA |
Arithmetic Calculation Efficiency Test (TECA) (Singer & Cuadro, 2014) | CFA | 1 factor model Tanaka index > .98 | Acceptable | NR | NR | NA |
Assessment of Algebraic Thinking (AAT) (Ralston et al., 2018) | IRT | Most item total correlations > .25 | Low | Cronbach alpha | α = > .70 | Acceptable |
Birthday Party-Long Version (English) (Lee, 2016) | CFA | 4 factor model RMSEA ≥ .05, CFI ≥ .96, TLI ≥ .91 | Mixed | Cronbach alpha | α = .76–.94 | Acceptable |
Birthday Party-Long Version (Spanish) (Lee, 2016) | NR | NR | NA | Cronbach alpha | α = .34–.86 | Mixed |
CIRCLE Progress Monitoring (CPM) Math Subtest (Assel et al., 2020) | CFA | 5 factor model RMSEA = .05, CFI = .98 | Acceptable | Cronbach alpha | α = .94 | Acceptable |
Cognitive Diagnostic Test (Li et al., 2020) | NR | NR | NA | NR | NR | NA |
Comprehensive Learning Test-Mathematics (CLT-M) (Lee et al., 2017) | PCA | 4 factor model that explained 66.4% of the cumulative variance | NA | 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) | CFA | 8 factor model RMSEA = .00–.05, SRMR = .003–023, CFI = .99–1.00 | Acceptable | Cronbach alpha | α = .69–.97 | Mixed |
DIFER School Readiness Test Battery Counting and Basic Numeracy (Csapó et al., 2014; Józsa et al., 2023) | Rasch Model | Infit MNSQ = .97–.98 Outfit MNSQ = 1.20–1.99 | Acceptable Mixed | Cronbach alpha | α = .74–.94 | Acceptable |
Early Arithmetic, Reading and Learning Indicators (EARLI) – Numeracy measures (Cheng et al., 2017; Lei et al., 2009) | Unidimensionality | Evidence of unidimensionality for 5 groups of items | NA | Cronbach alpha | α = .82–.98 | Acceptable |
Early Grade Mathematics Assessment (EGMA) (Ketterlin-Geller et al., 2018; Perry, 2020) | EFA | 1 factor model, RMSEA = .07–.10, TLI = .70–.85 | Low | Cronbach alpha | α = .74–.88 | Acceptable |
Early Learning Outcomes Measure (ELOM) (Anderson et al., 2021; Snelling et al., 2019) | CFA | 1 factor model, RMSEA = .01, CFI = 1.00, SRMR = .01 | Acceptable | IRT | Person reliability = .63–.75 | Acceptable |
Early Measurement Assessment Tool (EMAT) (Ceylan & Aslan, 2023) | MIRT | 1 dimension, 2 parameter model, RMSEA = .03, SRMR = .05, CFI = .99 | Acceptable | Cronbach alpha | α = .82–.95 | Acceptable |
Early Years Toolbox-Early Numeracy (Howard et al., 2022) | Unidimensionality | Evidence of unidimensionality for 70 items | NA | NR | NR | NA |
Evaluación Neuropsicológica Infantil-Preescolar (ENI-P)- Numerical Abilities Test (Beltrán-Navarro et al., 2018) | NR | NR | NA | Cronbach alpha | α = .48–.96 | Mixed |
Galileo Early Maths-Revised (Kowalski et al., 2018) | NR | NR | NA | NR | NR | NA |
Heidelberger Rechen Test (HRT) 1–4 (Hassler Hallstedt & Ghaderi, 2018) | NR | NR | NA | NR | NR | NA |
KeyMath-Revised (Rhodes et al., 2015) | CFA | 1 factor model, RMSEA = .03, CFI, .91 | Mixed | Split half reliability | r = .56–75 | Mixed |
Kieler Kindergartentest Mathematik (KiKi) (Van Hoogmoed et al., 2022) | IRT | 3 factor model, BIC = 8704, CAIC = 8762 | NA | NR | NR | NA |
Mathematical and Arithmetic Competence Diagnostic (MARKO-D) (Bezuidenhout, 2018; Fritz et al., 2014; Henning et al., 2021) | Rasch model | All items within acceptable MNSQ values | NA | IRT | Person reliability = .87–.91 | Acceptable |
Mathematical Profile (MathPro) Test (Karagiannakis & Noël, 2020) | NR | NR | NA | Cronbach alpha | α = .42–.95 | Mixed |
Mathematical Reasoning Test (Nunes et al., 2015) | PCA | 1 factor model that explained 73.5% of the variance | NA | Cronbach alpha | α = .75 | Acceptable |
mCLASS: Math (Ginsburg et al., 2016) | NR | NR | NA | NR | NR | NA |
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 | NR | NR | NA |
Number Sense Test (Malofeeva et al., 2004) | NR | NR | NA | Cronbach alpha | α = .93–.97 | Acceptable |
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) | NR | NR | NA | Cronbach alpha | α = .74–.86 | Acceptable |
Parent ratings of numeracy skills (Lin et al., 2021) | CFA | 1 factor model, RMSEA = .00, CFI = 1.00, TLI = 1.00 | Acceptable | Cronbach alpha | α = .93 | Acceptable |
Quantitative Reasoning Test (Nunes et al., 2015) | PCA | 1 factor model that explained 73.5% of the variance | NA | Cronbach alpha | α = .69–.90 | Mixed |
Research-Based Early Maths Assessment (REMA) (Clements et al., 2008; Dong et al., 2023) | Rasch model vs. error variance | Separation index = 6.66 | NA | Cronbach alpha IRT | α = .71–.89 Person reliability = .93 | Acceptable Acceptable |
Research-Based Early Maths Assessment- Short Form (REMA-SF) (Weiland et al., 2012) | Rasch model | Infit MNSQ = .73–1.46 Outfit MNSQ = .57–1.46 | AcceptableAcceptable | Cronbach alpha IRT | α = .71–.79 Person reliability = .68–.76 | Acceptable Mixed |
School Achievement Test- 2nd Edition- Arithmetic Subtest (Viapiana et al., 2016) | CFA | 2 factor model TLI = .99, RMSEA = .04, SMRS = .04 | Acceptable | Cronbach alpha | α = .95 | Acceptable |
Teacher Rating Scale – Early Numeracy (TRS-EN) (Vessonen et al., 2023) | CFA | 3 factor model, RMSEA = .05–.06, CFI = .95–.99, TLI = .94–.99 Family socio-economic status factors not related to teachers’ ratings | Acceptable | Cronbach alpha | α = .92–.95 | Acceptable |
Teaching Strategies GOLD (Burts & Kim, 2014; Lambert et al., 2014, 2015) | CFA | 6 factor model, SRMR = .03, CFI = .93, RMSEA = .07 | Low | Cronbach alpha | α = .94–.97 | Acceptable |
Test of Early Number and Arithmetic (TENA) (Bojorque et al., 2015) | NR | NR | NA | Cronbach alpha | α = .89–.91 | Acceptable |
The International Development and Early Learning Assessment (IDELA)- Emergent Numeracy (Pisani et al., 2018, 2022; Shavitt et al., 2022; Wolf et al., 2017) | CFA | 1 factor model, RMSEA = .02, TLI = .99 | Acceptable | Cronbach alpha | α = .52–.92 | Mixed |
The Utrecht Test of Early Numeracy (ENT) Test (Aunio et al., 2006; David et al., 2015) | NR | NR | NA | Cronbach alpha | α = .79–.90 | Acceptable |
Tools for Early Assessment in Math Danish Version (DK-TEAM) (Sjoe et al., 2019) | NR | NR | NA | NR | NR | NA |
Screeners | ||||||
Arabic number-writing task (Moura et al., 2015) | NR | NR | NA | KR-20 coefficient Split half reliability | KR-20 = .91 r = .94 | Acceptable Acceptable |
Assessing Student Proficiency of Early Number Sense (ASPENS) (Brafford et al., 2023; Sutherland et al., 2021) | NR | NR | NA | NR | NR | NA |
Basic Number Processing Test (BNPT) (Olkun et al., 2016) | NR | NR | NA | Cronbach alpha KR-20 coefficient | α = .72–.96 KR-20 = .69–.72 | Acceptable 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) | Unidimensionality | Evidence of unidimensionality for 3 factors | Acceptable | KR-20 coefficient Split half reliability | KR-20 = .93 r = .92–.89 | Acceptable Acceptable |
Early Measurement Curriculum-Based Measures (EM-CBM) (Clarke et al., 2023) | NR | NR | NA | NR | NR | NA |
Early Numeracy (EN)- Test (Hellstrand et al., 2020) | CFA | 4 factor model, RMSEA = .03, CFI = .89- .94, TLI = .88- .97 Consistent across language groups | Mixed | Cronbach alpha | α = .91–.95 | Acceptable |
Early Numeracy Screener (Lopez-Pedersen et al., 2021) | CFA | 3 factor model RMSEA = .05, CFI = .94, TLI = .93 | Mixed | Cronbach alpha | α = .79–.94 | Acceptable |
Early Numeracy Skill Indicators (Methe et al., 2008) | NR | NR | NA | KR-20 coefficient | KR-20 = .53–.83 | Mixed |
House of Numbers (HoN) (Chatzaki et al., 2024) | Rasch model | Infit = .82–1.20 Outfit = .62–1.57 | Acceptable Mixed | IRT | Person reliability = .82 | Acceptable |
Indicators of Basic Early Math Skills (IPAM) (de León et al., 2021; 2022) | CFA | 1 factor model RMSEA = .00- .05, CFI = 1.00, SRMR = .01- .02 | Acceptable | NR | NR | NA |
Math Essential Skill Screener- Elementary Version (MESS-E) (Erford et al., 1998) | Exploratory PCA | 1 factor model Eigenvalue = 10.80, % of variance = 37.2% | NA | KR-20 coefficient | KR-20 = .92 | Acceptable |
Mathematical School Readiness (MSR) (Mejias et al., 2019) | Unidimensionality | Evidence of unidimensionality for 3 tasks, r = .28–.49 | Mixed | Cronbach alpha | α = .63–.95 | Mixed |
Number Line Assessment 0–20, 0–100 (Clarke et al., 2020) | NR | NR | NA | Cronbach alpha | α = .83–.93 | Acceptable |
Number Line Assessment 0–100 (Sutherland et al., 2021) | NR | NR | NA | NR | NR | NA |
Number Sense Screener (NSS) (English Version) (Jordan et al., 2010, 2012) | Rasch model | Infit = .79–1.31 Outfit = .42–2.17 | AcceptableLow | Cronbach alpha | α > .80 | Acceptable |
Number Sense Screener (NSS) (Turkish Version) (Aktulun, 2019; Kiziltepe, 2019) | Rasch model | Infit = .81–1.35 Outfit = .60–1.39 | AcceptableAcceptable | Cronbach alpha | α = .83–.88 | Acceptable |
Number Sets Test (Geary et al., 2009) | NR | NR | NA | NR | NR | NA |
Numeracy Screener (Bugden et al., 2021; Hawes et al., 2019; Nosworthy et al., 2013) | NR | NR | NA | NR | NR | NA |
Preschool Early Numeracy Skills Screener- Brief Version (PENS-B) (English Version) (Purpura et al., 2015) | Correlation with latent factor score | r = .94 | Acceptable | Cronbach alpha Split half reliability | α = .93 r = .90 | Acceptable Acceptable |
Preschool Early Numeracy Skills Screener- Brief Version (PENS-B) (Greek Version) (Tsigilis et al., 2023) | CFA | 2 factor model, RMSEA = .04, CFI = .99 | Acceptable | NR | NR | NA |
Preschool Numeracy Indicators (Floyd et al., 2006) | NR | NR | NA | NR | NR | NA |
Primary Math Assessment Diagnostic (PMA-D) (Brendefur et al., 2018) | NR | NR | NA | Cronbach alpha | α = .82- .93 | Acceptable |
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) | NR | NR | NA | NR | NR | NA |
Universal Screening of Math Skills/ Despiste Universal de Competências Matemáticas (DUCMa) (Cruz et al., 2024) | CFA | 1 factor model per sub-scale, RMSEA = .00–.10, CFI = .97–1.00, TLI = .96–1.00 | Mixed | KR-20 coefficient | KR-20 = .80–.90 | Acceptable |
Measurement tools widely used to assess criterion validity | ||||||
Test of Early Mathematics Abilities- 3rd Version (TEMA-3; Ginsburg & Baroody, 2003) | Discrimination Index | r = .45–.68 | Acceptable | Cronbach alpha | α = .92–.96 | Acceptable |
Woodcock-Johnson III Achievement Tests Maths (WJ-III-ACH Maths) (Schrank et al., 2001) | CFA | 9 factor model with 3 maths-related clusters (Broad Math; Math Calculation; Math Reasoning) Correlations between achievement clusters, r = .50–.70 | Acceptable | Split half reliability | r = .86–.93 | Acceptable |