The Effect of Mathematics Research on Mathematics Majors' Mathematical Beliefs
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This is a dissertation about the beliefs that mathematics majors have about mathematics and how their beliefs are affected by the introduction of mathematics research. The mathematics research presented to the students dealt with counting regular orbits of an action. Research has shown that the beliefs that teachers hold about mathematics influences how they teach their classes. For example, it has been observed that some teachers who believe mathematics as a static field might teach a drill and memorization type of class. Four sections of an Introduction to Advanced Mathematics course were split into a two treatment and two control groups. There were a total of 40 students in the study; 22 in the treatment group and 18 in the control group. The treatment group received a three weeks intervention at the end of the semester in which basic modern algebra content was presented to the student to prepare them for presentations pertaining to the mathematics research. The study incorporated a pre/mid/post-survey format. The pre-survey was given at the beginning of the semester; the mid-survey was given before the beginning of the three week intervention; and the post-survey was given at the end of the semester after the intervention. Additional data in the form of written work and student interviews were collected to supplement survey data. There was no statistical difference between the treatment and control groups for each administration of the survey. However, there was a statistical difference between the post and mid-surveys at the .05 level and a statistical difference between the post and pre-surveys at the .02 level for the treatment group while the control group had significance levels of .12 and .09 respectively. Additionally the survey subscale Status of Mathematics had statistically significant differences at the .00 level between the post and mid-surveys and between the post and pre-surveys in the treatment group while there was no significant difference for the control group (p-values > .3). Supplemental data from student interviews and reflections showed mathematical growth and gave indications of students becoming interested in the idea of mathematics research. These results reveal that the introduction of mathematics research had a positive impact on what the students believe about mathematics and their appreciation for the subject.