Criterion referenced tests are designed to find out whether a child has a set of skills, rather than how a child compares to other children of the same age (normed tests.) The test designers analyze the component parts of specific academic skills, say number understanding, and then write test items that will measure whether the child has all the component parts of the skill.
A test of reading skills would seek to discover whether a child can identify the specific sounds consonants make before it would evaluate whether a student can answer comprehension questions. The questions in a criterion referenced test would seek to find if the student has all those skills, not whether the student does as well as other third grade children.
The Key Math Tests are criterion referenced achievement tests that provide both diagnostic information and achievement scores in math.
Other criterion referenced tests include the Peabody Individual Achievement Test (PIAT,) and the Woodcock Johnson Test of Individual Achievement.