Comprehensive Mathematical Abilities Test
(CMAT)
OVERVIEW:
WHAT IS IT?
The CMAT is a norm-referenced individual assessment of mathematical skills.
CMAT has 4 principle uses: determine strengths and weaknesses, identify students
who are significantly above and below their peers, make predictions about the
student’s future performance, and serve as a measurement device in research
studies investigating math abilities.
WHO IS IT USED FOR?
CMAT was built for use with students between the ages of 7-0 and 18-11 and/or
grade levels between 3-12. Questions in the subtests vary in mathematical ability,
and can be used to test students’ knowledge in one subtest content area, a few, or all
of the CMAT can be used to understand a student’s overall mathematical ability.
NORM SAMPLE
The CMAT was normed on a national sample of over 1600 students in 17 different
states. All students were either in a public or private school. The normative group
was tactically selected based on age, gender, race, ethnic group membership,
geographic location, community size, and socioeconomic status. Students with
disabilities were included in the sample. Each student was administered the CMAT
according to it’s protocol.
BIASES
Potential item bias was studied and found to be insignificant. Not only was bias
studied at the test level, but also individual item bias was examined by comparing
item difficulty across demographic subgroups and by determining item curve
characteristics.
CMAT CONTENT:
1.
2.
3.
4.
5.
6.



SUBTESTS
Addition (AD)
7. Algebra (AL)
Subtraction (SU)
8. Geometry (GE)
Multiplication (MU)
9. Rational Numbers (RN)
Division (DI)
10. Time (TI)
Problem Solving (PS)
11. Money (MO)
Charts, Tables & Graphs (CTG)
12. Measurement (ME)
COMPOSITES
Core Composites
o General Mathematics- AD, SU, MU, DI, PS, CTG
o Basic Calculations – AD, SU, MU, DI
o Mathematical Reasoning- PS, CTG
Supplemental Composite
o Advanced Calculations AL, GE, RN
o Practical Applications- TI, MO, ME
Global Mathematics Ability- All Subtest
ADMINISTERING the CMAT:
MATERIALS
Examiner’s Manual
Picture Booklet
Profile/Examiner Booklet
Student Response Booklet 1
Student response Booklet 2
Pencil with erasers
Scratch paper
Calculator if the subtest allows one
STARTING POINTS
Each subtest’s starting point is different varying in age. All ages younger than 10-0
will start on item 1 with the exception of algebra and geometry, which students
under the age of 10-0 will not take.
BASAL & CEILING
Both the basal and ceiling are 3 for all subtests. On every subtest, the test ends when
3 items in a row are scored incorrect. Student may not establish a basal – do not
discontinue – proceed until a CEILING is established.
ADMINISTRATION
Test administrator reads the scripted directions before each subtest. These directio
ns are found in the Profile/Examiner Booklet, written in green. Subtests should be
administered in the order that they appear, however they are not required to be.
You do not need to use all subtest. Some may only be interested in the composite
tests; some may be interested in specific subtests. You should constantly praise and
encourage the student throughout the test. Avoid comments that reflect accuracy.
Do not discourage students from guessing. Signs, commas and other designations
are required only if necessary to convey the correct meaning. Administer CMAT in
quiet, comfortable, not distracting environment. Keep student at easy and on task.
Do this by establishing rapport, explaining the purpose of the test as a pleasurable
undertaking. Allow students to work at their own pace, but closely monitor their
work. Repeat items for understanding, if necessary.
SCORING
The CMAT is easy to score. Simply 1 point for every correct answer and 0 points for
every incorrect answer. All correct answers added together will give you the raw
scores of the subtests. The CMAT provides percentiles, standard scores, and age and
grade equivalents, which can all be interpreted in the appendix of the CMAT
Examiner’s Manual. The raw scores are converted to aged-based standard scores
and percentiles using the normative tables in Appendix A, or to grade-based
standard scores and percentiles in Appendix B. Raw scores can also be converted to
age or grade-based equivalents in Appendix E.
 Standard Scores- CMAT’s subtests scores have a mean of 10 and a standard
deviation of 3. This score allows the examiner to make comparisons across
subtest.
 Composite Quotients- This has a mean of 100 and a standard deviation of 15
and is a standard score calculated by adding all of the subtest scores
together.








PSYCHOMETRICS:
RELIABILITY
The CMAT has 3 sources of error variance; content sampling, time sampling, and
interscorer differences. The CMAT measured a high degree of reliability across all 3
sources. Reliability was determined using standard methods for estimating the
internal consistency of the subtests and composites. Reliability estimates are
uniformly high, with all composites and most subtest reliability values exceeding or
rounding to .90.
VALIDITY
The CMAT manual provides clear evidence for validity. Strong evidence of contentdescription validity, criterion-prediction validity, and construct-identification
validity is provided, including correctional research with individual and group
mathematics tests, intelligence tests, and measures of academic ability.
OVERALL QUALITY:









CAUTIONS & LIMITATIONS
Calculators are only permitted on subtests 5 thought 12.
Test is used to measure math abilities ONLY, and a student should not be
penalized for poor reading or handwriting.
Do not time students
Stop testing if the student tires or loses interest. Continue testing at another
time.
You do not need to use all subtest. Some may only be interested in the
composite tests; some may be interested in specific subtests.
Limited age group between 7-18
This test would not be useful for assessing students who may have a
disability, unless the student potentially has a specific learning disability in
math.
SIMILAR VALID AND RELIABLE MATH ASSESSMENTS
Test of Early math Abilities (TEMA): The Test of Early Math Abilities (TEMA3) measures the mathematics performance of children between the ages of 30 and 8-11 in numbering skills, number-comparison facility, numeral
literacy, mastery of number facts, calculation skills, and understanding of
concepts.
KeyMath III: measures a student’s understanding and application of critical
math concepts. The KeyMath III is given to students between the ages of 4-6
through 21-11.
MY CONCLUSION
The CMAT is proven to be very a reliable, valid, and unbiased test. It is a great tool to
assess and measure various mathematical abilities and skill levels a student may
possess. Overall, it would be an adequate test to use when seeking information on a
students strengths or weaknesses in math to determine a better educational
placement for the success of the student.