We used two survey instruments to measure student outcomes from inquiry-based learning in undergraduate mathematics and to compare these outcomes between various student groups, in particular, between IBL and non-IBL students. The attitudinal survey was designed to detect the quality of and changes in students’ mathematical beliefs, affect, learning goals, and mathematical problem-solving strategies. The learning gains survey (SALG-M) measured students’ experiences of class activities and their cognitive, affective and social gains from a college mathematics class. The surveys addressed the following questions • • • • • What learning gains do students report from an IBL mathematics class? How do students experience IBL class activities? How do students’ class experiences account for their gains? What kind of beliefs, affect, goals and strategies do IBL students report at the start of a mathematics course? How do these approaches change during a college mathematics course? How do these changes relate to or explain students’ learning gains? For each of these outcomes—learning gains, experiences, attitudinal measures, and changes—how do the outcomes for IBL students differ from those of non-IBL students, and among IBL student sub-groups?
The survey instruments provided us with large student data sets from four campuses, gathered during the two academic years 2008-2010. They offered us a comprehensive picture of students’ approaches to learning college mathematics as well as of their experiences and gains from IBL classes. Moreover, the survey data could be used to analyze differences in reported learning approaches, classroom experiences and learning outcomes among various student groups. In addition to structured questions, students also could write about their experiences and gains in the open-ended survey questions. Both the open-ended survey answers and student interview data were used to validate, confirm, and fill in the picture of student outcomes obtained from the structured survey responses. A3.2 Study sample
The data were gathered on all four campuses in a variety of undergraduate courses. These included courses entitled: • • • • (Honors) Analysis 1-3, (Honors) Calculus 1-3, Cryptology Discrete mathematics,
Cite as: Assessment & Evaluation Center for Inquiry-Based Learning in Mathematics (2011). (Report to the IBL Mathematics Project) Boulder, CO: University of Colorado, Ethnography & Evaluation Research.
Appendix A3: Survey Methods • • • • • • • • • Explorations in mathematics, Exploratory calculus, Group theory, Introduction to proofs, Introduction to real analysis, Multivariate calculus 1-2, Number theory, Probability, Real analysis 1.
They covered the full range of introductory to advanced mathematics courses. Mathematics courses specifically developed for elementary and middle school or secondary school pre-service teachers represented another type of course in the sample. This kind of survey data was obtained from two campuses. Additional smaller data sets came from a geometry course designed (but not required) for prospective high school mathematics teachers at one campus. In all, we collected surveys from 82 college mathematics sections, of which 65 were IBL sections and 17 non-IBL sections. Data obtained with our surveys consisted of an attitudinal presurvey, a learning gains post-survey, and a combined post-survey including both the attitudinal and the learning gains questions. We received pre-surveys from 1245 students, learning gains post-surveys from 200 students, and combined post-surveys from1165 students. Combining the pre-survey data with the post-survey data produced us information from 800 individually matched surveys. These surveys included responses from 412 IBL math track students (i.e., students who studied mathematics as their major or minor subject), 156 non-IBL math track students, 208 IBL pre-service...