The Linear Algebra Project is developing, implementing, and disseminating curriculum and pedagogy for parallel courses in (a) undergraduate mathematics content and (b) learning theory as applied to the study of mathematics. The purpose of the research, partially funded by the National Science Foundation, is to investigate how parallel study of learning theories and advanced mathematics influences the thinking of individuals in both domains. We conjecture that strengthened understanding of mathematics and learning theory will be an outcome of the reflection promoted by this parallel study, and that the deeper insights will contribute to more effective instruction by those who become high school mathematics teachers and, consequently, better learning by their students in secondary mathematics. These courses are appropriate for mathematics majors, pre-service secondary mathematics education majors, and practicing mathematics teachers. The initial focus of the project is on Topics in Linear Algebra and on Theories for the Learning of Mathematics. We plan to adapt this approach to other undergraduate mathematics content areas. The learning theory course focuses most heavily on constructivist theories, though it also examines sociocultural and historical perspectives. A particular theory, APOS (Asiala et al., 1996), is directly related to their study of linear algebra. APOS (Action-Process-Object-Schema) has already been used in a variety of research studies focusing on the understanding of undergraduate mathematics. The study of topics in linear algebra focuses on standard material that is found in many advanced undergraduate linear algebra courses. This study of linear algebra is designed to highlight connections between collegiate linear algebra and secondar
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