Animated Contrasting Cases in Geometry

***Recently Funded by NSF***

Description Utilizing an innovative and theoretically grounded approach, this project will extend the work of cognitive scientists and mathematics educators who have previously documented the impact of comparison on students’ learning in algebra (Star et al., 2015), with the goal of transforming the learning that occurs in sixth grade geometry classrooms. The purpose of this research is two-fold: To design animated mathematics curricular materials for geometry that focus on directly comparing different approaches to solving the same geometry problem, and to examine the effects of these materials on student learning of geometry. Design-based research (Brown, 1992; Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003; Collins, 1992; Schoenfeld, 2006) will be used to develop and pilot the animated contrasting cases for geometry in collaboration with our district and school partners. An iterative process will be utilized to design, pilot, and revise the geometry cases to ensure their utility and credibility. A mixed-method approach will be used to provide evidence of effectiveness of the supplemental materials on students’ procedural and conceptual knowledge of geometry. Specifically, an explanatory sequential design (Creswell & Clark, 2010) will be used to determine if there are significant gains in student’s procedural and conceptual knowledge after engaging in the materials (quantitative) and then to explore students’ geometric thinking, after instruction with the animated contrasting cases, in greater detail (qualitative).

Intellectual Merit: The intellectual merit of this work lies in pioneering a new way of learning geometry, namely in establishing a scientific basis for using contrasting cases to explore multiple solution strategies of students. Further, because the geometry cases will be developed on a digital platform, the power of technology will be harnessed to provide students with visual animations to support their learning of geometry. This research will contribute significantly to: 1) investigating the degree to which the method of comparisons is viable for geometry, 2) advancing the knowledge about how students learn through comparisons, and 3) determining the effects of learning through comparisons on students’ procedural knowledge and conceptual understanding of geometry.

Broader Impacts: The geometry animated contrasting cases will promote a new way for learning geometry content that will be made available electronically so that schools across the US can implement the materials. These materials have the promise to deeply engage students in developing deep, connected understanding of geometry. The knowledge gained from this research may influence pre-service teacher preparation programs or teacher professional development through incorporating activities to expand teachers’ knowledge and capacity to use contrasting cases for improving student learning of geometry. Furthermore, the comparison approach to geometry ensures broad impact among the research community. Once the materials are fully developed, other researchers can use them to study this learning approach across different contexts or even analyzing their influence on different outcome measures. The research findings produced through this project will be shared at various stages at national conferences and through educational journals, including practitioner journals, and across the fields of educational psychology and mathematics education.

This project is supported by the National Science Foundation under Grant No. DRL 1907745 awarded to North Carolina State University. Any opinions, findings, and conclusions or recommendations expressed herein are those of the principal investigators and do not necessarily reflect the views of the National Science Foundation.