Evaluating the effectiveness of experiential learning with concrete-representational-abstract instructional technique in a college statistics and algebra course.

摘要

A student underprepared for college-level mathematics and requiring college algebra and statistics may need as many as three to six mathematics courses. College algebra is an at-risk course since it has a drop, fail, and withdrawal (DFW) rate of 40--60% (Adelman, 2004; Small, 2010). The study evaluated the effectiveness of a college algebra class where statistics is integrated into its curriculum, denoted CA/S course. The integration occurred through the author-developed experiential concrete-representational-abstract (E-CRA) instructional method, a derivative of the Kolb experiential learning model and the concrete-representational-abstract (CRA) instructional method (Kolb, 1984; Witzel, 2005). When learning new algebra and statistics topics, students brought in their own data or used real-world data, created and reflected on different representations of the data, learned the mathematics equations and functions that explain the data in the abstract stage, and then utilized mathematical modeling to further understand the data and use the model for prediction purposes. The variables, attitudes towards statistics, statistics self-efficacy, mathematics anxiety, algebra skills, statistical numeracy and reasoning skills, and persistence, were analyzed for the students in the CA/S course. Students in CA/S course (n=19) showed improved statistics self-efficacy, (p=.002), and statistical numeracy and reasoning skills, (p=.053), from the beginning to the end of the semester. When controlling for developmental mathematics, students in CA/S reported a stronger (i.e., practical significance p=.053) statistical self-efficacy than students in a comparable group who did not take CA/S. At the end of the study, CA/S students possessed two statistical numeracy and reasoning skills that were significantly stronger than the students in the comparable group (p=.032, p=.006). No statistical significance was found for the other research variables. The research found that the CA/S curriculum utilizing the E-CRA instructional method yield positive outcomes related to the affective domain of the CA/S students. Students' self-efficacy became significantly stronger, possibly contributing to the improvement of the students' abilities to perform statistical numeracy and reasoning skills. Lesson plans are included as well as suggestions for implementation and recommendations for future study.