Development of a Measure of Early Mathematics Achievement Based on Learning Trajectories

• In Event: Innovations in Designing, Implementing, and Evaluating Classroom Assessments Based on Learning Theories

Abstract

Purpose: To fill a gap in assessments of early mathematics, we developed and evaluated a comprehensive, theoretically-based instrument designed to measure the mathematical knowledge and skills of children from 2 to 8 years of age along research-based learning trajectories. The Research-based Elementary Math Assessment (REMA) uses an individual interview format with explicit protocol, coding, and scoring procedures. The developmental progressions of items in each of 20 topics, as well as the fit of individual items has been reported in earlier research. The REMA measures competence as a latent trait in Item Response Theory (IRT), yielding a score that locates children on a common ability scale with a consistent, justifiable metric (allowing accurate comparisons, even across ages and meaningful comparison of change scores, even when initial scores differ, Wright & Stone, 1979). Beyond correctness, the REMA also collects, codes, and scores children’s strategies. Strategies reflect the observed process for solving the item such as using counting all, counting on, or derived facts in solving arithmetic word problems. These strategies are recoded into three levels of sophistication for submission to the IRT model.

Methods: Participants were 2000+ children from schools serving diverse populations in multiple states. We submitted the REMA to different IRT models to evaluate one-, two-, and three-parameter models.

Results: The final instrument satisfactorily measured total mathematics ability as a coherent, unidimensional latent trait and possessed the properties of conjoint measurement, producing interval measures that are linear and additive. Indices of item and person reliability of .9 or higher support construct validity.

Implication: The REMA fills an existing gap in the measure of mathematics achievement in the early years, especially given its structuration according to learning trajectories inclusion of children’s strategies. Reports to teachers not only include the total mathematics score, but also each child’s level of thinking along the individual learning trajectories (for each topic) and the sophistication of children’s strategy use (teachers can dive deeply into children’s responses and specific strategies for individual problems), provide a wealth of diagnostic information.

Authors

• Julie Sarama, University of Denver

• Douglas H. Clements, University of Denver

• Crystal A Day-Hess, University of Denver

• Christopher Wolfe

• Shannon Stark Guss, University of Denver