TOMAGS-2: Test of Mathematical Abilities for Gifted Students - Second Edition

Gail R. Ryser • Susan K. Johnsen
SKU: 14885
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Gail R. Ryser • Susan K. Johnsen

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Ages: Grades 1 through 6
Testing Time: 30 to 60 minutes
Administration: Individual or group


The Test of Mathematical Abilities for Gifted Students–Second Edition (TOMAGS-2) is a standardized, norm-referenced test used to identify students in Grades 1 through 6 who are gifted in mathematics. Specifically, the TOMAGS-2 measures students’ ability to use mathematical reasoning and problem solving and is aligned with the current Common Core State Standards for Mathematics. The test can be administered to individuals or to small groups. The TOMAGS-2 now has three levels: the Primary level for Grades 1 and 2, the Intermediate level for Grades 3 and 4, and the new Advanced level for Grades 5 and 6.

New Features

  • An all-new demographically representative standardization sample was collected in 2014–2018.
  • Only one set of norms for general education students (which includes a small percentage of students with exceptionalities and disabilities) is reported.
  • New studies of the floors, ceilings, and item gradients index scores are included.
    The results indicate that the test has consistently excellent ceilings, even for the
    oldest and brightest students who take the test.
  • New studies of test bias (both differential item functioning and subgroup comparison studies) indicated that the test possesses little or no bias in regard to gender, race, or ethnicity.
  • New reliability and validity studies, including diagnostic accuracy analyses, were done, which are considered the most rigorous techniques for establishing a test’s validity. These analyses involve the computation of sensitivity and specificity indexes and the receiver operating characteristic/area under the curve (ROC/AUC) statistic.

Technical and Statistical Characteristics of the TOMAGS-2

The TOMAGS-2 was normed on a weighted sample of 1,137 students from 16 states and Washington, DC. Its raw scores can be converted to percentile ranks and index scores. The Examiner’s Manual includes a comprehensive discussion of the test’s theoretical and research-based foundation, item development, standardization, administration and scoring procedures, norms tables, and guidelines for using and interpreting the test’s results.

TOMAGS-2 internal consistency reliability coefficients are .84, .87, and .84 for the Primary, Intermediate, and Advanced levels, respectively. Test–retest reliability coefficients are .90, .80, and .79.

Validity studies demonstrate the test’s ability to differentiate students who are gifted in mathematical ability from students who are not. Specifically, a TOMAGS-2 Primary index cutoff score of 108 resulted in a sensitivity of .86, a specificity of .81, and a ROC/AUC of .90 in differentiating mathematically gifted students from non-mathematically-gifted students. An Intermediate index cutoff score of 108 produced a sensitivity of .78, a specificity of .82, and a ROC/AUC of .89; and an Advanced index cutoff score of 115 resulted in a sensitivity of .89, a specificity of .76, and a ROC/AUC of .91.

Complete TOMAGS-2 Kit includes: Examiner’s Manual, 75 Student Booklets (25 each for the Primary, Intermediate, and Advanced levels), and 75 Examiner Record Forms (25 for each level), all in a sturdy storage box. (©2020)