### Abstract:

For several years researchers have investigated how teachers’ beliefs
impact a classroom. Equally important to consider when striving to improve
education are the beliefs held by the students. College Algebra is an important
class for many collegiate students, and gaining an insight into their beliefs about
mathematics and desires for a mathematics classroom could prove to be essential
in developing a class that benefits the students. This study focused on discovering
desired classroom characteristics for College Algebra students and the connection
between their mathematical beliefs and those classroom characteristics. Eleven
College Algebra students were given a 60-item survey detailing their beliefs about
mathematics. Following the survey, participants were interviewed and asked
questions regarding their mathematical dispositions, past experiences,
expectations, and ideal class. The results showed that a student’s belief about the
source of knowledge as either a passive or active endeavor was most indicative of
their definition of an ideal class. Students with survey results indicating a belief
that learning mathematics should be a passive process described an ideal class
centered on the teacher’s lecture. Participants found to believe learning math
should be an active process were more likely to depict an ideal class involving
student exploration and discovery.
Key