The research methods being used to study active learning are improving. They are looking at outcomes beyond a single course at one institution. Here's a summary of a study that explored some larger impacts.
“This study examined the impact of inquiry-based learning (IBL) in college mathematics on undergraduates' subsequent grades and course selection at two institutions.” (p. 183) The researchers explain their choice of grades and course selection as outcome measures. “Students' course grades and course-taking patterns—their choices to pursue (or not) subsequent courses in a discipline—offer broad and arguably objective measures for evaluating the effects of an educational intervention.” (p. 184) The intervention can be deemed a success if student grades are higher in subsequent courses and if the experience in one course motivates them to take subsequent courses when those courses are not required.
The intervention under study here was inquiry-based learning. IBL approaches in the math courses involved in this study “engage students in exploring mathematical problems, proposing and testing conjectures, developing proofs or solutions, and explaining their ideas.” (p. 184) The approach involves students working together on problems and their solutions. The study examined subsequent grades and course selections of students after taking a course that used IBL approaches or after a course where those approaches were not used. To confirm that students were indeed experiencing different instructional approaches, the researchers spent more than 300 hours observing in the 42 course sections involved in the study. There were differences in how faculty used IBL approaches, but despite this variation there were several factors that differentiated IBL sections from non-IBL sections. “On average, about 60% of the time in IBL courses was spent on student-centered activities such as small-group work, student presentation of problems at the board, or whole-class discussion, while in non-IBL courses over 85% of class time consisted of the instructor talking.” (p. 185)
The research design is robust, with a variety of variables controlled and manipulated. The sample is large. Design details are fully explained in the study. The researchers targeted three math courses, each offered in both IBL and non-IBL sections.
As for the results, in all three of the target courses, “IBL students' grades were as good or better than their non-IBL peers'. In two cases IBL students' grades were statistically significantly better.” (p. 190) They write more about these findings in the discussion section. “Overall, the effect of IBL on students' subsequent grades and course-taking was modest when comparing IBL and non-IBL students in their entirety. Certainly no harm was done; IBL students succeeded at least as well as their peers in later courses. This result challenges instructors' common concern that material omitted to accommodate the slower pace of IBL courses may hinder student success in later courses.” (pp. 194-195)
Researchers disaggregated these overall results and looked specifically at the IBL effects by gender and achievement, and this is where the results show more significant differences. Women in the non-IBL sections succeeded at rates similar to those of men, but they reported less mastery of the material and lower confidence at the end of the course than men did. They also took fewer subsequent math courses. In the IBL sections, course success rates were the same, but the women reported similar intellectual and affective gains. They also took more math courses subsequently.
As for achievement, “taking an IBL course did not erase achievement differences among students, but did flatten them. In non-IBL courses, initial patterns of achievement difference were preserved; previously low-achieving students gained no ground.” (p. 196) Low-achieving students who took an IBL section boosted their grades in subsequent math courses by between .3 and .5 GPA points.
Researchers conclude by pointing out an interesting irony. Those using student-centered approaches like IBL are frequently asked to provide evidence that the approach garners benefits. Those who use lecture approaches “have seldom undergone similar evidence-based scrutiny.” (p. 197) “Our study indicates that the benefits of active learning experiences may be lasting and significant for some student groups, with no harm done to others. Importantly, ‘covering' less material in inquiry-based sections had no negative effect on students' later performance in the major.” (p. 197)
Reference: Kogan, M., and Laursen, S. L. (2014). Assessing long-term effects of inquiry-based learning: A case study from college mathematics. Innovative Higher Education, 39 (3), 183-199.