What is the TEMA-3? The Test of Early Mathematics Ability explained

The TEMA-3, short for the Test of Early Mathematics Ability, Third Edition, is an individually administered, "norm-referenced" test of mathematical thinking for children ages 3 years 0 months through 8 years 11 months. Norm-referenced means a child's performance is compared with that of a large, representative sample of same-age peers rather than judged against a fixed pass mark. Written by Herbert P. Ginsburg and Arthur J. Baroody and published by PRO-ED in 2003, the TEMA-3 takes about 40 minutes and measures both the informal math ideas children develop on their own and the formal skills they are taught in school. This article explains what the test covers, how it is scored, how the results connect to teaching, and where it fits alongside other assessments.

The distinctive feature of the TEMA-3 is its split between "informal" and "formal" mathematics. Informal mathematics is the knowledge young children build through everyday experience before anyone teaches them written arithmetic. Counting a handful of crackers, judging that seven blocks are more than three, and adding small quantities with fingers or objects are all informal skills. Formal mathematics is the school-taught layer that sits on top: reading and writing numerals, memorizing number facts, and carrying out written calculations.

According to the publisher, the test measures informal and formal concepts and skills across six areas.

• Numbering skills: verbal counting and using counting to determine how many items are in a set.

• Number-comparison facility: judging which of two numbers or quantities is larger.

• Numeral literacy: reading and writing written numerals.

• Mastery of number facts: recalling basic addition, subtraction, and multiplication facts.

• Calculation skills: carrying out mental and written arithmetic procedures.

• Understanding of concepts: grasping the ideas behind the procedures, such as what counting or place value actually mean.

Items span a wide developmental range. In a study led by mathematical-cognition researcher Michele Mazzocco, the authors note that typical TEMA-3 items for a 6-year-old include counting, reading and writing two-digit numbers, adding and dividing quantities with manipulatives, comparing the magnitude of written numbers, and solving mental addition problems with one-digit numbers.

PRO-ED states that the TEMA-3 is designed for children between ages 3-0 and 8-11, and that it is also useful with older children who have learning problems in mathematics. An examiner might use it, for example, with a 10-year-old whose math skills are suspected to fall well below grade level, though scores for children outside the normative age range must be interpreted with extra care.

The test comes in two parallel forms, A and B, each containing 72 items. Parallel forms are separate versions built to the same blueprint so that a child can be retested without simply remembering the answers. The distributor PAR notes that scores on Form A and Form B can be used interchangeably, which makes the pair useful for measuring progress across a school year or before and after an intervention.

Administration is one-on-one and takes roughly 40 minutes. The kit includes picture books, worksheets, and hands-on manipulatives such as counters and blocks, so much of the session feels like structured play rather than a paper-and-pencil exam. Testing follows "basal" and "ceiling" rules: researchers who use the instrument describe establishing a basal of five consecutive correct answers and stopping after five consecutive errors, so each child only faces items near his or her own level. The TEMA-3 is a Level B instrument, meaning it should be purchased and administered by professionals with formal training in assessment, such as school psychologists, diagnosticians, and special educators.

The child's raw performance converts to an overall standard score, which researchers using the test also refer to as the math ability score. In the Mazzocco study cited above, this age-referenced normative score is described as having a mean of 100 and a standard deviation of 15, the same metric most intelligence and achievement tests use. A score near 100 is typical for the child's age, roughly two thirds of children score between 85 and 115, and scores well below 85 flag possible difficulty. The test also yields percentile ranks along with age and grade equivalents.

The publisher reports solid measurement properties for a test of such young children. The normative sample consists of 1,219 children whose characteristics approximate the 2001 U.S. Census, internal consistency reliabilities are all above .92, and immediate and delayed alternate-form reliabilities fall in the .80s and .90s. An independent review of the TEMA-3 by Stacy Bliss in the Journal of Psychoeducational Assessment describes it as a norm-referenced parallel-forms test intended to identify the level of mathematical ability of children from 3-0 through 8-11 and evaluates its technical adequacy in detail.

The usual cautions still apply. Any single testing session with a preschooler carries measurement error, attention and mood matter at this age, and a score is an estimate with a confidence interval around it rather than a fixed property of the child.

One reason educators like the TEMA-3 is that it was built to connect assessment with instruction. The kit includes a supplementary book, Assessment Probes and Instructional Activities, which the publisher describes as a collection of remedial techniques and teaching tasks tied to the skills covered by each test item. After identifying which items a child missed, an examiner can follow up with the matching probes to explore why the error occurred and then hand teachers concrete activities that target the weak skill.

This makes the TEMA-3 more than a ranking tool. PRO-ED lists its intended uses as identifying strengths and weaknesses, measuring progress, evaluating programs, screening for readiness, discovering the bases for poor school performance in mathematics, identifying gifted students, and guiding instruction and remediation. In practice, the score answers the question "how does this child compare with peers?" while the item-level profile and probes answer the more useful question "what exactly should we work on next?"

School psychologists, early childhood specialists, and researchers use the TEMA-3 in several situations. The most common is early identification of mathematics difficulty. A kindergartner who cannot count a small set or compare quantities may be at risk for a persistent math learning disability, sometimes called "dyscalculia," and a low TEMA-3 score is one signal that a fuller evaluation is warranted. A screener or a single test score is never a diagnosis by itself. At the other end, an unusually high score can support identification of advanced early math ability, and the publisher explicitly lists gifted identification among the test's uses. Parents weighing broader ability testing for young children can read our guide to IQ tests for kids at https://www.riotiq.com/articles/specific-iq-tests-and-formats/iq-tests-for-kids for context on what such scores mean at early ages.

Early math skills deserve this attention because they forecast later achievement. In a well-known 2007 study in Developmental Psychology, Greg Duncan and colleagues analyzed six longitudinal data sets and found that school-entry math skills were the strongest predictor of later academic achievement, ahead of early reading and attention skills. The associations were modest in absolute terms, so an early score is a probability shift rather than a destiny, but the pattern has been influential in pushing schools toward earlier math assessment. Consistent with that picture, a 2023 study in Cognitive Development found that preschoolers' TEMA-3 performance contributed to their arithmetic skills years later in elementary school. Readiness-oriented instruments like the one covered in our article on the Bracken School Readiness Assessment at https://www.riotiq.com/articles/specific-iq-tests-and-formats/what-is-the-bracken-school-readiness-assessment measure related territory from the concept side.

The TEMA-3 is an "achievement" measure: it samples what a child currently knows and can do in mathematics. For students older than 8-11 who need a diagnostic math assessment, examiners typically move to a broader instrument; our article on the KeyMath-3 at https://www.riotiq.com/articles/specific-iq-tests-and-formats/what-is-the-keymath-3 covers the leading option for ages 4 through 21.

Achievement tests differ from ability tests. An IQ test estimates general reasoning capacity, including "fluid reasoning," the ability to solve novel problems that do not depend on taught content. The two usually correlate, and comparing them is informative: a child with strong reasoning scores and a low TEMA-3 score may have an instructional gap or a specific math difficulty rather than a general cognitive one.

For adults who want a rigorous measure on the ability side, the RIOT IQ test (the Reasoning and Intelligence Online Test), developed by RIOT IQ with psychometrician Dr. Russell T. Warne, assesses test takers 18 and older with 15 subtests across six cognitive indices: verbal reasoning, fluid reasoning, spatial ability, working memory, processing speed, and reaction time. It takes about 52 minutes and reports scores on the familiar mean-100, standard-deviation-15 scale. Like any online measure, it does not replace an individually administered diagnostic evaluation. It does offer a carefully normed estimate of the reasoning abilities that math learning draws on. You can take it at https://www.riotiq.com/.

The TEMA-3 is normed for children from 3 years 0 months through 8 years 11 months. The publisher notes it can also be informative with older children who have significant math learning problems.

No. It is a test of mathematics achievement, measuring learned informal and formal math skills. IQ tests measure broader reasoning abilities, though scores on the two kinds of tests tend to correlate.

The overall standard score has a mean of 100 and a standard deviation of 15, so scores from about 90 to 110 are average, scores above 115 are well above average, and scores below about 85 suggest a need for follow-up.

About 40 minutes, administered one-on-one. Basal and ceiling rules keep each child working only on items near his or her own level.

Not by itself. A low score can flag risk for a mathematics learning disability, but a diagnosis requires a comprehensive evaluation that also considers cognitive ability, instruction history, and performance over time.

Both are individually administered math assessments. The TEMA-3 focuses on early informal and formal number skills for ages 3-0 to 8-11, while the KeyMath-3 covers a wider curriculum range for students from about age 4 through 21.

1. PRO-ED. (2003). TEMA-3: Test of Early Mathematics Ability-Third Edition. proedinc.com

2. Western Psychological Services. (n.d.). (TEMA-3) Test of Early Mathematics Ability, Third Edition. wpspublish.com

3. Bliss, S. (2006). Test reviews: Ginsburg, H., & Baroody, A. (2003). Test of Early Mathematics Ability-Third Edition. Journal of Psychoeducational Assessment, 24(1), 85-98. eric.ed.gov

4. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. apa.org

5. Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS ONE, 6(9), e23749. pmc.ncbi.nlm.nih.gov

6. Akhavein, K., Clark, C. A. C., Nelson, J. M., Espy, K. A., & Finch, J. E. (2023). The longitudinal contributions of preschool executive functions and early math abilities to arithmetic skills in elementary school. Cognitive Development, 68, 101388. doi.org

7. Texas Statewide Leadership for Autism Training. (n.d.). Test of Early Mathematics Ability - Third Edition. txautism.net

Hero photo: Close-up of a classroom counting frame with rows of blue, red, green, and natural wooden beads, a child's painted rainbow on the window behind. Photo by Onderwijsgek (cropped), CC BY-SA 3.0, via Wikimedia Commons.