Mathematical generalization, the ability to create general rules, formulas, and strategies, is a key aspect of doing mathematics. Policy makers recommend making generalization a central component of mathematics instruction at every grade level from elementary school through undergraduate mathematics, with the Common Core State Standards highlighting generalization as a major goal in both the content and the practice standards. However, these recommendations pose serious challenges given students’ pervasive difficulties in creating and expressing generalizations. In a report on performance assessments from more than 60,000 secondary students, findings revealed only a 20% success rate in students’ creation of correct general statements (Rivera, 2008). Students’ challenges with mathematical generalizations also contributes to difficulties in mathematics achievement in many domains, including algebra, geometry, and combinatorics.

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GAMMA addresses these challenges by investigating how students generalize productively and how teachers can support more effective mathematical generalization. Through student interviews, paired teaching experiments, and mid-size design experiments, the project investigators explore these issues in algebra, precalculus, and combinatorics. Student participants range from middle school students through the undergraduate level. The diverse range of student ages and mathematical domains contribute to a robust model characterizing how students generalize in Grades 8-16. Our findings also identify instructional activities that can better support generalization in different settings, which will be of use to teachers, school districts, teacher educators, and university instructors. The knowledge generated from the project will support improved student performance in critical areas of undergraduate mathematics, thus contributing to a diverse and globally competitive STEM workforce.