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Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich
Williams Honors College, Honors Research Projects
The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.
Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit
Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit
Williams Honors College, Honors Research Projects
In this paper I discuss six philosophical theories of mathematics including logicism, intuitionism, formalism, platonism, structuralism, and moderate realism. I also discuss problems that arise within these theories and attempts to solve them. Finally, I attempt to harmonize the best features of moderate realism and structuralism, presenting a theory that I take to best describe current mathematical practice.