## Contrasting Cases in Geometry: Think Alouds with Students about Transformations

There is strong empirical evidence in support of learning from comparisons in mathematics education research (Rittle-Johnson & Star, 2007; Star, Pollack, et al., 2015; Star et al., 2016). Comparisons have produced gains in students’ procedural knowledge, flexibility, and conceptual knowledge of algebra (Lynch & Star, 2014; Star, Newton, et al., 2015; Star, Pollack, et al., 2015). The Animated Contrasting Cases in Geometry project seeks to extend this research and transform the learning of geometry for middle school students by designing a supplementary digital animated curriculum.

There is strong empirical evidence in support of learning from comparisons in mathematics education research. The Animated Contrasting Cases in Geometry project seeks to extend this research and transform the learning of geometry for middle school students by designing a supplementary digital animated curriculum. This paper focuses on the Transformations unit, which is one of four units.