Making the Connection: Research and Teaching in Undergraduate Mathematics Education
Marilyn Paula Carlson, Chris Rasmussen
Mathematical Association of America, 2008 - Mathematics - 319 pages
The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.
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On Developing a Rich Conception of Variable
2b Using Definitions Examples and Technology 22
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abstract algebra accumulation functions activities angle bisector approach approximation arguments calculus calculus students Carlson chapter classroom cognitive concept image conjectures consider construct construct proofs context cosets course covariational curriculum definitions described develop differential equations difficulties discussion division Dubinsky Educational Studies example Figure formal graph Harel Hazzan help students infinite infinity input instructional instructional theory integral interaction interviews intuitive isomorphic key idea knowledge learners learning limit mathematical induction mathematical proof mathematical thinking mathematicians Mathematics Education multiple Oehrtman participants particular patterns pedagogical precalculus problem solving proof scheme prove question quotient groups Rasmussen rate of change reasoning representation Research in Mathematics Riemann sums role Selden sequence situations slope solution specific stereotype threat strategies structure student thinking Studies in Mathematics symbols tangent tangent vector tasks teacher techniques theorem topic transformation triangle undergraduate mathematics understanding variable Zandieh Zazkis