The course described here is still under development. The written materials from the course are still rough and will be rewritten during the Spring Semester of 1996. Mathematics 407 is a capstone course for any interested mathematics major, but particularly for those students who intend to pursue a single-subject credential in Mathematics. The goals of the course are to enable students to build connections among the mathematical areas they have studied and between undergraduate mathematics and school mathematics, to develop their understanding of mathematics as an integrated discipline, and to strengthen their oral and written communication skills in mathematics.
Writing is a major component of the course.
There will be regular journal prompts given on connecting undergraduate and 7-12 content. Each student will also submit regular write-ups of mathematical investigations which include communication of process as well as final product. The experience of using different representations for the same situation leads to a useful intuitive understanding of the idea of isomorphism. Algorithmic Thinking Focusing on the process of developing, interpreting, and analyzing algorithms develops insight into the nature of mathematics. This kind of sense-making is challenging, but the power it provides is a compelling reason for learning mathematics.