Table 2 Overview of the measurement tools identified through the systematic review (N, number; A, arithmetic; SSM, shape, space, and measure)
Name of Measurement Tool (Original Authors) | Age Range (Years) | Country (Languages) | Measure Type; Format | Measure Mode; Administrator | Number of Items: Measurement Tasks | Areas of Maths Development | ||
|---|---|---|---|---|---|---|---|---|
N | A | SSM | ||||||
Mathematical assessments | ||||||||
Academic Rating Scale (ARS)-adapted (Kilday et al., 2012) | 3–5 | USA (English) | Observation; paper-based | Individual or group; teacher | 12 items: number sense; numerical operations; geometry; measurement | Y | Y | Y |
Ani Banani Test (ten Braak & Størksen, 2021) | 4–7 | Norway (Norwegian) | Child-direct; tablet-based (child uses) | Individual; researcher/trained assessor | 18 items: numeracy; geometry; problem solving | Y | Y | Y |
Arithmetic Calculation Efficiency Test (TECA) (Singer & Cuadro, 2014) | 6–11 | Uruguay (Spanish) | Child-direct; paper-based | Group; researcher/trained assessor | 144 items: addition; subtraction; multiplication; division | - | Y | - |
Assessment of Algebraic Thinking (AAT) (Ralston et al., 2018) | 6–11 | USA (English) | Child-direct; paper-based | Group; teacher | 25 items: open number sentences; equivalence; work with variables; efficient numerical calculation; generalisation; numerical patterns; figural patterns; generalising figural patterns | Y | Y | Y |
Birthday Party- Long Version (Ginsburg & Pappas, 2016) | 3–5 | USA (English; Spanish) | Child-direct; computer-based (child uses) | Individual; teacher | 30–36 items: number and operations; shape; space; pattern | Y | Y | Y |
CIRCLE Progress Monitoring (CPM) Math Subtest (Assel et al., 2020) | 4–5 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 27 items: rote counting; Shape naming; number naming; shape discrimination; counting; simple addition and subtraction word problems | Y | Y | Y |
Cognitive Diagnostic Test (Li et al., 2020) | 3–6 | China (English) | Interview; paper-based | Individual; researcher/trained assessor | 38 items: cardinality concept; set comparison; addition and subtraction within 10; combine; result-unknown change; change-unknown change; consistent language comparison; inconsistent language comparison; addition and subtraction inverse reasoning; additive composition reasoning; one-to-many correspondence reasoning | Y | Y | - |
Comprehensive Learning Test-Mathematics (CLT-M) (Lee et al., 2017) | 5–14 | South Korea (Korean) | Child-direct; computer-based (child uses) | Individual; researcher/trained assessor | 5 subtests (number of items NR): whole number computation; numeral comparing/magnitude; numeral comparing/distance; enumeration of dot group; number line estimation | Y | - | - |
Comprehensive Research-Based Early Math Ability Test (CREMAT) (Clements et al., 2022) | 6–8 | USA (English) | Child-direct; computer-based (child uses) | Individual; teacher | 42 items: measurement; length; area | - | - | Y |
Curriculum Based Measures for Kindergarten- Grade 3 (Lee & Lembke, 2016) | 5–9 | USA (English) | Child-direct; tablet-based (child uses) | Individual; researcher/trained assessor | 8 tasks (number of items NR): counting; missing number; quantity discrimination; next number; number identification; computation; concepts; number facts | Y | Y | - |
DIFER School Readiness Test Battery Counting and Basic Numeracy (Csapó et al., 2014) | 6–7 | Hungary (Hungarian) | Child-direct; computer-based (child uses) | Individual; researcher/trained assessor | 13 items: number; number relations; basic mathematical thinking | Y | Y | - |
Early Arithmetic, Reading and Learning Indicators (EARLI) – Numeracy measures (DiPerna et al., 2007) | 3–4 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 58 items: number recognition; shape recognition; measurement concepts | Y | - | Y |
Early Grade Mathematics Assessment (EGMA) (RTI International, 2014) | 6–10 | 14 LMICs (Various)a | Child-direct; paper-based | Individual; researcher/trained assessor | 77 items: number identification; quantity discrimination; missing number; addition; subtraction; multiplication; division; shape recognition | Y | Y | Y |
Early Learning Outcomes Measure (ELOM) (Snelling et al., 2019) | 4–5 | South Africa (Afrikaans, English, Setswana, isiZulu; isiXhosa) | Child-direct; paper-based | Individual; researcher/trained assessor | 8 items: counting; addition and subtraction; sorting and classification; spatial vocabulary; measurement vocabulary | Y | Y | Y |
Early Measurement Assessment Tool (EMAT) (Ceylan & Aslan, 2023) | 4–8 | Türkiye (Turkish) | Child-direct; paper-based | Individual; researcher/trained assessor | 38 items: length; area; volume; angle | - | - | Y |
Early Years Toolbox-Early Numeracy (Howard et al., 2022) | 3–5 | Australia (English) | Child-direct; tablet-based (child uses); | Individual; teacher | 79 items: number sense; cardinality and counting; numerical operations; spatial and measurement constructs; patterning | Y | Y | Y |
Evaluación Neuropsicológica Infantil-Preescolar (ENI-P)-Numerical Abilities Test (Beltrán-Navarro et al., 2018) | 2–4 | Mexico (Spanish) | Child-direct; paper-based; | Individual; researcher/trained assessor | 26 items: magnitude comparison; counting; subitising; basic calculation | Y | Y | - |
Galileo Early Maths-Revised (Kowalski et al., 2018) | 3–5 | USA (English) | Observation; computer-based | Individual or group; teacher | 22 items: number writing; shape recognition; counting; sorting; measurement comparison; ordinality; more and less; addition; sharing; division; pattern recognition | Y | Y | Y |
Heidelberger Rechen Test 1–4 (Hassler Hallstedt & Ghaderi, 2018) | 6–10 | Sweden (Swedish) | Child-direct; tablet-based (child uses) | Individual; researcher/trained assessor | 121 items: addition; subtraction; missing term; count amount; tap rate | Y | Y | - |
KeyMath-Revised (Connolly, 1988) | 7–10 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 258 items: numeration; geometry; addition; subtraction; measurement; time and money; rational numbers; multiplication; division; mental computation; estimation; interpreting data; problem solving | Y | Y | Y |
Kieler Kindergartentest Mathematik (KiKi) (Van Hoogmoed et al., 2022) | 4–6 | Germany; Netherlands (German; Dutch) | Child-direct; paper-based | Individual; researcher/trained assessor | 31–32 items: sets, numbers, and operations; measurement; space and shape; change and relationships; data and chance | Y | Y | Y |
Mathematical and Arithmetic Competence Diagnostic (MARKO-D) (Ricken et al., 2013) | 6–7 | Germany; South Africa (German; English; Afrikaans; isiZulu; Sesotho) | Child-direct; paper-based | Individual; researcher/trained assessor | 55 items: counting; ordinality; cardinality; part-part-whole; relationality | Y | - | - |
Mathematical Profile (MathPro) Test (Karagiannakis & Noël, 2020) | 6–12 | Belgium (Dutch) | Child-direct; computer-based (child uses) | Individual; researcher/trained assessor | 212–339 items: dot magnitude comparison; single and multidigit number magnitude comparison; number dictation; next number; previous number; subitising; enumeration; addition facts retrieval; multiplication facts retrieval; mental calculations; number lines 0–100; number lines 0–1000; squares; building blocks; word problems; calculation principles; numerical patterns | Y | Y | Y |
Mathematical Reasoning Test (Nunes et al., 2015) | 7–9 | UK (English) | Child-direct; paper-based | Group; teacher | 17 items: additive composition; additive reasoning; multiplicative reasoning | - | Y | - |
mCLASS: Math (Lee et al., 2010) | 5–9 | USA (English) | Interview; computer-based (child uses) | Individual; researcher/trained assessor | 5 domains (number of items NR): counting; addition; subtraction; multiplication; written numbers | Y | Y | - |
Neuropsychological Test Battery for Number Processing and Calculation in Children – Revised (NUCALC- R)b (von Aster et al., 2006) | 7–12 | Brazil; Germany; Greece (Brazilian Portuguese; German; Greek) | Child-direct; paper-based | Individual; researcher/trained assessor | 100 items: counting dots; counting backwards; dictation of numbers; positioning numbers; oral comparison; perceptive estimation; contextual estimation; written comparison; mental calculation; problem solving | Y | Y | - |
Number Sense Test (Malofeeva et al., 2004) | 3–5 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 165 items: counting; number identification; number-object correspondence; ordinality; comparison; addition; subtraction | Y | Y | - |
Numeracy-Caregiver report questionnaire (Pushparatnam et al., 2021) | 4–6 | 8 LMICs (Various)c | Interview; paper-based | Individual; researcher/trained assessor with parent | 24 items: verbal counting; set production’ mental addition; numeral identification; spatial sense; measurement vocabulary | Y | Y | Y |
Numeracy-Child direct assessment (Pushparatnam et al., 2021) | 4–6 | 10 LMICs (Various)d | Child-direct; paper-based | Individual; researcher/trained assessor | 42 items: verbal counting; set production; mental addition; numeral identification; spatial sense; measurement vocabulary | Y | Y | Y |
Observing and Analysing Children’s Mathematical Development (OAMD) (Bunck et al., 2017) | 5–9 | Netherlands (Dutch) | Observation & interview; paper-based | Individual; researcher/trained assessor | 18 items: counting; numbers; addition/subtraction; multiplication/division | Y | Y | - |
Parent ratings of numeracy skills (Lin et al., 2021) | 3–5 | USA (English) | Observation; paper-based; | Individual or group; Parent | 11 items: Verbal counting; Simple arithmetic; Numeral identification | Y | Y | - |
Quantitative Reasoning Test (Nunes et al., 2015) | 5–6 | UK (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 32 items: Additive composition; Inverse relations; Additive reasoning; Multiplicative reasoning | - | Y | - |
Research-Based Early Maths Assessment (REMA) (Clements et al., 2008) | 4–5 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 199 items: comparing and ordering; counting; arithmetic; recognition of number and subitising; composing number; geometry; comparing shape; identifying shape; turns; representing shape; composing shape; measuring; patterning | Y | Y | Y |
Research-Based Early Maths Assessment- Short Form (REMA-SF)e (Weiland et al., 2012) | 4–5 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 19 items: counting; comparing number and sequencing; recognition of number and subitising; numerals; composition of number; arithmetic; shape; patterning shape; compose shape | Y | Y | Y |
School Achievement Test- 2nd Edition- Arithmetic Subtest (Viapiana et al., 2016) | 6–14 | Brazil (Brazilian Portuguese) | Child-direct; paper-based | Individual; researcher/trained assessor | 202 items: number recognition, composition, and writing; counting; sequencing; arithmetic; decimals; fractions | Y | - | - |
Teacher Rating Scale – Early Numeracy (TRS-EN) (Vessonen et al., 2023) | 3–4 | Finland (Finnish) | Observation; paper-based | Individual or group; teacher | 22 items: counting; numerical relations; basic arithmetic skills | Y | Y | - |
Teaching Strategies GOLD (Heroman et al., 2010) | 1–4 | USA (English) | Observation; paper-based | Individual; teacher | 7 items: number concepts and operations; spatial relationships and shapes; measurement and comparison; pattern knowledge | Y | Y | Y |
Test of Early Number and Arithmetic (TENA) (Bojorque et al., 2015) | 4–5 | Ecuador (Spanish) | Child-direct; paper-based | Individual; researcher/trained assessor | 54 items: quantifiers; one-to-one correspondence; order relations more than/less than; counting; quantity identification and association with numerals; ordering; reading and writing numerals; addition; subtraction | Y | Y | - |
The International Development and Early Learning Assessment (IDELA)-Emergent Numeracy (Save the Children, 2019) | 3–6 | 78 countriesf | Child direct; paper-based | Individual; researcher/trained assessor | 7 domains (number of items NR): size and length comparison; shape identification; number identification; numerical knowledge; addition and subtraction; puzzle | Y | Y | Y |
The Utrecht Test of Early Numeracy (ENT) Test (Van Luit et al., 1994; Van de Rijt et al., 2003) | 4–8 | 8 European countries (Various)g | Child-direct; paper-based | Individual; researcher/trained assessor | 40 items: comparison; classification; making correspondence; seriation; using number words; synchronous and shortened counting; resultative counting; general knowledge of numbers | Y | Y | - |
Tools for Early Assessment in Math Danish Version (DK-TEAM) (Sjoe et al., 2019) | 3–6 | Denmark (Danish) | Child-direct; tablet-based (assessor uses) | Individual; researcher/trained assessor | 19 items: patterns and pre-algebraic thinking; recognising shapes; comparing shapes; counting; comparing and ordering numbers; numerals; composing numbers | Y | Y | Y |
Screeners | ||||||||
Arabic number-writing task (Moura et al., 2015) | 6–10 | Brazil (Brazilian Portuguese) | Child-direct; paper-based | Individual; researcher/trained assessor | 28 items: Write dictated 1–4-digit numbers | Y | - | - |
Assessing Student Proficiency of Early Number Sense (ASPENS) (Clarke et al., 2011) | 5–7 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 4 tasks (number of items NR): numeral identification; Magnitude comparison; Missing numbers; Basic arithmetic facts and base 10 | Y | Y | - |
Basic Number Processing Test (BNPT) (Olkun et al., 2016) | 6–9 | Türkiye (Turkish) | Child-direct; tablet-based (child uses) | Individual; researcher/trained assessor | 71 items: canonic dot counting; symbolic number comparison; mental number line | Y | - | - |
Birthday Party- Short Version (Ginsburg & Pappas, 2016) | 3–5 | USA (English) | Child-direct; computer-based (child uses) | Individual; teacher | 13–21 items: number and operations; shape; space; pattern | Y | Y | Y |
Dyscalculia screener (Butterworth, 2003) | 6–14 | UK (English) | Child-direct; computer-based (child uses) | Individual; researcher/trained assessor | 4 domains (number of items NR): dot enumeration; number comparison; addition; multiplication | Y | Y | - |
Dyscalculia Test (Eteng-Uket, 2023) | 7–13 | Nigeria (Nigerian) | Child-direct; paper-based | Individual; researcher/trained assessor | 85 items: number sense; arithmetic operations; computation; working memory | Y | Y | - |
Early Measurement Curriculum-Based Measures (EM-CBM) (Clarke et al., 2023) | 6–7 | USA (English) | Child-direct; paper and tablet-based (assessor uses) | Individual; researcher/trained assessor | 120 items: length-comparison; length-measurement; iteration-application; iteration-conceptual | - | - | Y |
Early Numeracy (EN)-Test (Koponen et al., 2011) | 5–8 | Finland (Finnish, Swedish) | Child-direct; paper-based | Group; researcher/trained assessor | 48- 64 items: symbolic and non-symbolic number knowledge; understanding mathematical relations; counting; basic arithmetic | Y | Y | - |
Early Numeracy Screener (Lopez-Pedersen et al., 2021) | 6–7 | Norway (Norwegian) | Child-direct; paper-based | Group; teacher | 52 items: numerical relational skills; counting skills; arithmetic skills | Y | Y | - |
Early Numeracy Skill Indicators (Methe et al., 2008) | 5–6 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 4 tasks (number of items NR): counting on fluency; match quantity fluency; number recognition fluency; ordinal position fluency | Y | - | - |
House of Numbers (HoN) (Chatzaki et al., 2024) | 5–6 | Germany (German) | Child-direct; paper-based | Individual; researcher/trained assessor | 24 items: counting; mental number line; cardinality and decomposition; class inclusion and embeddedness; relationality | Y | - | - |
Indicators of Basic Early Math Skills (IPAM) (Jiménez & de León, 2019) | 6–7 | Spain (Spanish) | Child-direct; Paper-based | Group; researcher/trained assessor | 5 tasks (number of items NR): quantity discrimination; missing number; single-digit computation; multi-digit computation; place value | Y | Y | - |
Math Essential Skill Screener- Elementary Version (MESS-E) (Erford et al., 1998) | 6–8 | USA (English) | Child-direct; paper-based | Individual or group; researcher/trained assessor | 27 items: writing numerals; addition; subtraction; time; money; fractions; word problems (addition and subtraction) | Y | Y | - |
Mathematical School Readiness (MSR) (Mejias et al., 2019) | 6–7 | Belgium (French) | Child-direct; paper-based | Individual; researcher/trained assessor | 3 items: number writing; Number comparison; Arithmetic problem solving | Y | Y | - |
Number line assessment (Clarke et al., 2020) | 5–7 | USA (English) | Child-direct; tablet-based (child uses) | Individual; researcher/trained assessor | 26 items: number line estimation 0–20 and 0–100 | Y | - | - |
Number Line Assessment 0–100 (Sutherland et al., 2021) | 5–6 | USA (English) | Child-direct; tablet-based (child uses) | Individual; researcher/trained assessor | 26 items: number line estimation 0–100 | Y | - | - |
Number Sense Screener (NSS) (Jordan et al., 2010, 2012; Kiziltepe, 2019) | 5–6 | USA; Türkiye (English; Turkish) | Child-direct; paper-based | Individual; researcher/trained assessor | 26–33 items: counting knowledge and principles; number recognition; number knowledge; non-verbal addition and subtraction; addition and subtraction story problems; addition and subtraction number combinations | Y | Y | - |
Number Sets Test (Geary et al., 2009) | 5–6 | USA (English) | Child-direct; paper-based | Individual; Researcher/ trained assessor | 84 items: comparing set sizes to 5 and 9 | Y | - | - |
Numeracy Screener (Nosworthy et al., 2013) | 5–9 | Canada (English) | Child-direct; paper-based | Individual; Researcher/ trained assessor | 112 items: symbolic magnitude comparison; non-symbolic magnitude comparison | Y | - | - |
Preschool Early Numeracy Skills Screener- Brief Version (PENS-B) (Purpura et al., 2015) | 3–5 | USA; Greece (English; Greek) | Child-direct; paper-based | Individual; researcher/trained assessor | 24 items: counting; set comparison; numeral identification; set to numerals; number order; relative size; story problems; number comparison; number combinations; ordinality | Y | Y | - |
Preschool Numeracy Indicators (Floyd et al., 2006) | 3–6 | USA (English) | Child-direct; paper-based | Individual; researcher/trained assessor | 5 tasks (number of items NR): one-to-one correspondence; counting fluency; oral counting fluency; number naming fluency; quantity comparison fluency | Y | - | - |
Primary Math Assessment Diagnostic (PMA-D) (Brendefur et al., 2018) | 5–8 | USA (English) | Child-direct; computer-based (child uses) | Individual; researcher/trained assessor | 64 items: number identification; number recognition; number sequence; quantity discrimination; fact fluency addition; fact fluency subtraction; number sentences; bar model; join; separate; part-whole; transitivity; composing; decomposing; rotation | Y | Y | Y |
Primary Math Assessment Screener (PMA-S) (Brendefur et al., 2018) | 5–8 | USA (English) | Child-direct; computer-based (child uses) | Individual; researcher/trained assessor | 6 items: number sequencing; number facts; relational thinking; context; measurement; spatial reasoning | Y | Y | Y |
Symbolic Magnitude Processing (SYMP) Test (Brankaer et al., 2017) | 6–11 | Belgium (Dutch) | Child-direct; paper-based | Group; researcher/trained assessor | 2 tasks: one-digit symbolic comparison (digits between 1 and 9); two-digit symbolic comparison (digits between 11 and 99) | Y | - | - |
Universal Screening of Math Skills/ Despiste Universal de Competências Matemáticas (DUCMa) (Cruz et al., 2024) | 4–6 | Portugal (Portuguese) | Child-direct; paper-based | Group or individual; researcher/trained assessor | 8 tasks: cardinality; number recognition; number writing; counting; subitising; quantity discrimination; addition; subtraction | Y | Y | - |
Measurement tools widely used to assess criterion validity | ||||||||
Test of Early Mathematics Abilities-3rd Version (TEMA-3; Ginsburg & Baroody, 2003) | 3–8 | USA; Singapore; China; Spain; Türkiye (English; Mandarin; Spanish; Turkish) | Child-direct; paper-based | Individual; researcher/trained assessor | 72 items: informal mathematics-numbering; number comparisons; calculations; concepts. formal mathematics-numeral literacy; number facts; calculation; concepts | Y | Y | - |
Woodcock-Johnson III Achievement Tests Maths (WJ-III-ACH Maths) (Schrank et al., 2001; Woodcock et al., 2001) | 5–19 | USA; Spain (English; Spanish) | Child-direct; paper-based | Individual; researcher/trained assessor | 4 sub-tests: calculation (C); maths fluency (MF); applied problems (AP); quantitative concepts (QC) Four sub-tests grouped into three clusters: Broad Math (C; MF; AP); Math Calculation Skills (C; MF); Math Reasoning (AP; QC) | Y | Y | Y |