Developing workable attributes for psychometric models based on the Q-Matrix

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Tatsuoka, C., Clements, D. H., Sarama, J., Izsák, A., Orrill, C. H., de la Torre, J., Khasanova, E., Tatsuoka, K. K. (2016). Developing workable attributes for psychometric models based on the Q-Matrix. In A. Izsák, J. T. Remillard, & J. Templin (Eds.), Psychometric methods in mathematics education: Opportunities, challenges, and interdisciplinary collaborations (Monograph #15) (pp. 73–96). Reston, VA: National Council of Teachers of Mathematics.


This chapter examines how three projects have responded to challenges of identifying and validating workable attributes in developing mathematics assessments that are based on the Q-matrix. A main result spanning all three projects is that identifying workable attributes requires extended investigation and expertise, both in the targeted cognition and in psychometric modeling. The first section of the chapter presents a synthesis of issues that the three projects have encountered in identifying and validating workable attributes. The second and third sections provide an extended example from one project that is developing assessments of elementary mathematics. The second section illustrates some statistical considerations in employing Q-matrix-based psychometric models, and the third section explains how the project refined both attributes and items in developing an assessment of geometric measurement for first-grade students.