Homework has been a central topic of study for over 80 years. This study investigated 1) the opinions of a class of introductory college mathematics students on the purpose of homework in their class, 2) their professor's opinion on the purpose of mathematics in the class and whether any differences between the students' and the teacher's opinion had any effects on the students, and 3) whether time-spent on homework correlated positively with grade expectation in the class. Research took place over a one year period, involving first-year engineering students taking multi-variable calculus. Students were given a survey, asking a number of questions, including: what they believed to be the purpose of homework, how many hours per week they spent on homework, and what they expected would be their grade in the course. Their professor was then interviewed in email correspondence and provided her views on the purpose of homework and its relationship to learning and examinations. This study found that the vast majority of students in the class viewed homework as practice and review of ideas already presented in lecture. Their professor also thought the purpose of homework was for practice and review, but had other purposes, including the application of learned material to thought-provoking problems, and integrating old knowledge with new knowledge. As a possible effect, the few students who selected higher cognitive purposes of homework, such as the synthesis of new ideas not previously presented, and the evaluation of one's own understanding, tended to expect higher grades than their peers. Lastly, the correlation between grade expectation and time spent on homework was positive up until a point, whereafter the correlation became negative. This point coincided with the expected amount of time to spend on homework given by the professor, but whether this was the cause of the change in correlation was not proven. It did indicate, however, that the assumption that homework had a purely positive correlation with grade expectation at the collegiate level was tenuous.