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The burgeoning interest in early mathematics has led to an increasing interest in assessments of young children's mathematical competencies and the recent creation of new measures. This paper reviews 15 instruments designed to measure mathematics competencies of children preschool through the primary grades, including their theoretical frameworks, foci (including elaborate content analysis, describing not only how many items are included for each topic and what level of thinking they assess along learning trajectories), and psychometrics and examines their appropriateness for various uses in early childhood education settings. Several instruments are identified that meet the needs of the different goals that assessments serve, but they differ substantially in characteristics such as time and nature of administration and content coverage.