Title: Mathematics and Music
Description: This study looks at the use of integrated mathematics and music lessons at the high school level. Four lessons were taught by the researcher in both a research and a control class to determine how mathematically motivated music instruction affects students understanding of operations of functions, composition of functions, inverse functions and domain and range. A pretest-posttest was used to determine the effect of these lessons and a questionnaire was used to identify differences between groups and to help determine the effect of musical applications of mathematics on students’ mathematical perceptions, self-efficacy and grit. The pretest-posttest included both a standard mathematics section and a section involving non-musical applications. A gain score approach using independent sample t tests was used to determine the impact of the integrated instruction. The research group demonstrated significantly greater gains both overall and on the applications portion of the exam. Additional qualitative analysis was done to determine how the posttests differed between groups.

Three major differences were identified: the research group used function notation more frequently than the control group, the control group demonstrated confusion between composition of functions and inverse functions while the research group did not and the research group showed more mathematical work for the applications portion of the exam than the control group. Qualitative analysis was also done to identify trends in the questionnaire data. Among the major differences between groups was the increased willingness to work with mathematical applications in the future by the research group compared to the control group. The integrated instruction led to comparable and in some cases significantly better mathematics outcomes than the control group and led students to an increased willingness to work with mathematical applications both on the posttest and moving forward.