Curriculum Embedded Assessment: An Examination of the Array Model for Observing Unitizing

Unitizing, a cognitive support for number sense, describes how students conceptualize quantities in terms of units. Given the importance of this skill, a formative assessment tool was developed for array multiplication problems, including arrays that model the distributive property found in typical classroom curricula. Video of 77 fourth grade students from a major metropolitan area solving array multiplication tasks were classified by unitizing ability on tasks in the range of additive and early stages of multiplicative thinking. Unitizing is the ability to recursively modify units understanding to create and coordinate the relationships between different units. Scoring is based on unit coordination schemes identified in the array problem solutions’ written record, gestures and verbal explanations. New gestures were identified as well as actions specific to scoring the array item type to add to the body of unit coordination work. Findings suggest that students who cannot coordinate two levels of units in an interiorized fashion are more affected by a partially covered array diagram in problem solution. The available tools and the strategic choices students made in the open response problems influenced opportunities to make inferences about student thinking. Implications for classroom use, the design of instructional materials, and professional development are shared.