(207e) Improved Homework Effectiveness in a Problem-Solving Course

The effectiveness of homework in a junior-level, problem-solving course, specifically a kinetics and reaction engineering course, was assessed as the course format, homework grading basis and homework feedback mechanism were modified. Development of problem-solving mastery is central in the learning outcomes for this course. The learning literature establishes that (a) to develop mastery, students must acquire component knowledge and skills, practice integrating them and know when to apply what they have learned, and (b) goal-directed practice coupled with targeted feedback is critical to developing problem-solving mastery.

In this study, the distribution of total exams scores for students who completed 90% or more of the assigned homework (high completion group) compared to that for students who completed less than 90% of the homework (lower completion group) was used as a measure of homework effectiveness. Initially, the course was taught using a traditional lecture format with weekly homework assignments being graded and contributing to the students’ course grades. Feedback consisted of returning “graded” assignments, posting a correct solution and providing office hours where students could seek assistance on pending homework and feedback on completed homework. Under these conditions, homework was completely ineffective; the difference in total exams scores between the high completion group and the lower completion group was not statistically significant. Results like these are not uncommon and have lead to questions on the usefulness of homework and to the development of automated homework systems.

The course was then changed to a flipped format; videos corresponding to the former in-class lectures were provided to the students for pre-class use. Much of the class meeting time was then used to engage students in learning activities that afforded them opportunities to practice problem solving in class with immediate instructor feedback and prior to being required to submit homework. Homework was still graded and contributed to the students’ final course grades, and additional feedback again consisted of returning “graded” assignments, posting a correct solution and providing office hours. After flipping the course, homework appeared to be significantly more effective: the total exams scores of the high completion group were approximately one letter grade equivalent higher than the scores for the lower completion group. The precise reason for the increase in homework effectiveness is not known.

While the flipped format afforded additional problem-solving practice, the instructor suspected that students approached homework with the wrong goal. Specifically, their goal was to obtain the correct answer. The fact that their homework was graded on correctness and counted toward their overall course grade justified and reinforced their focus on obtaining a correct answer. Indeed, a focus on obtaining the correct answer on homework is deeply ingrained after many years of having homework graded and counted toward final course scores. By mimicking worked examples, students can efficiently obtain a correct solution, but in doing so, they often fail to learn when to apply and how to integrate their component knowledge on their own. For homework to be most effective, the students’ focus and goal must be learning how to obtain the answer, not just obtaining it.

On the basis of the preceding reasoning, the course was again modified so that homework assignments were graded on the basis of apparent effort, and not on being correct. At the same time, each homework assignment was followed-up with the required submission of a self-corrected solution. The corrections were assigned immediately after the homework was originally due and the correct solution had been posted. Effectively, this approach attempted to have the students self-generate feedback on their homework. They still were provided with a correct solution, but their homework was not graded. Instead, they were expected to determine where and why their solution diverged from the correct solution.

This change did not improve the effectiveness of homework as had been intended. The difference between the high completion group and the lower completion group remained nearly the same. The instructor believed that the students’ focus was still improperly directed. When they corrected the homework they submitted, they used the posted solution to determine where they went wrong, but they didn’t reflect upon why they had gone wrong. Instead, they simple replicated the posted solution from that point on to complete their required corrections.

Most recently four changes to the course were implemented in an attempt to appropriately shift the students’ focus as they completed homework assignments. First, for each of the six major type of problems considered in the course, explicit, in-class instruction on the identification of the problem type was introduced. Second, at the same time, a generalized procedure for solving each type of problem was explicitly presented together with the instruction on problem-type identification. Third, scaffolding that emphasized the generalized procedure for solving each problem type was incorporated into related in-class, problem-solving activities. Finally, instead of requiring students to submit a corrected homework solution, students were required to submit a homework wrapper. The homework wrappers ask the students to write a few sentences assessing the problem-solving strategy that they conceptualized in comparison to the generalized procedure that was discussed and practiced in class. After these four changes were implemented, the effectiveness of homework again increased substantially. The total exams scores of the high completion group were approximately one and one-half letter grade equivalents higher than the scores for the lower completion group.

The results of this study suggest that conventional homework can be very useful in helping students develop problem-solving mastery. They suggest that homework, at least initially for a given problem type, should be viewed and implemented as an opportunity for goal-directed practice and targeted feedback, and not as a summative assessment instrument. The results further suggest that when homework wrappers are coupled with explicit instruction on generalized problem solution strategies, they may enable students to self-generate constructive and targeted feedback on their problem-solving efforts. An additional benefit of this approach is that amount of grading support needed can be decreased substantially when homework is graded on effort.