For engineering undergraduates, mastering and retaining the material taught in the introductory mathematics sequence is essential to successful completion of their baccalaureates in engineering. "Spaced retrieval" is one factor that cognitive scientists have shown to affect mastery and retention of a subject. In spaced retrieval, once a concept is introduced, students practice the concept in multiple sessions distributed across the semester rather than massed in a single session at the time the concept is taught. Research in cognitive psychology has established that the act of retrieving a piece of information from memory increases the likelihood that the information will be retained at a later date, this is referred to as the retrieval practice effect. Moreover, any given number of retrievals will have greater impact if they occur non-consecutively versus consecutively (the spacing effect). This project will study the effect of spaced versus massed practice in two introductory engineering mathematics courses at the University of Louisville.
In many mathematics classes, practice problems are massed (the opposite of spaced); that is, all of the problems related to a specific learning objective are assigned consecutively, and students complete all the problems over a fairly short period of time. For many engineering students, retaining mathematical knowledge from one course to the next is a requirement for success. The transfer of knowledge from one course to the next is an area faculty and researchers regularly identify as problematic. This project will use the online homework and tutorial system MyMathLab, to manipulate spacing of practice problems covering a subset of objectives in a sequence of two math courses: "Introduction to Calculus for Engineers" and "Engineering Analysis I." The students will be pseudo-randomly assigned to treatment and control groups to ensure comparable distribution of student characteristics across groups, including race, gender, high school GPA, and ACT math score. The study's research questions are: 1) Is overall performance in the second course better for students for whom some practice problems in the first course were spaced than for students for whom all practice problems were massed?; and 2) Is objective-specific mathematical knowledge better retained when accompanying practice problems are spaced versus massed? If results indicate positive effects from spacing, the findings could motivate the use of spacing in foundational mathematics courses to reduce the number of students transferring out of STEM majors due to inadequate mathematical knowledge. Since the analysis will include demographic data, the project has the potential to identify whether spacing retrieval has a different impact on students from a number of diverse groups.
