Learning Transfer in the Differentiation Using the Chain Rule and its Relationship to Motivation and Performance

Damji Heo, Purdue University

Abstract

Previous studies indicated that calculus courses are considered ‘weed-out’ courses as a lot of students in STEM majors struggle to pass. Instructors and researchers explored various instructional methods to facilitate calculus learning, however, more tailored instructional strategies are still needed. Inventing Contrasting Case is a strategy that has been proven effective in transfer, yet, its effect when combined with the motivational factor and across various content areas should be investigated further. Therefore, this study investigated the relationship between participants’ motivation, instruction condition, and the performance on the direct application and transfer problems using Calculus 1 content. The data was collected from undergraduate students in STEM majors at a Midwestern university who were required to complete a Calculus 1 course to attain their degree. Eighty-one students participated for the study. Participants were assigned to either the iCalCulus (iCC) group or the Tell and Practice (TP) group. The study consisted of two separate sessions. In Session 1, participants were provided with a motivation survey, calculus course experience survey, pre-requisite knowledge check test, ICC task or TP task, and post-test. Seven days later, participants took a delayed post-test (Sesson 2). Google Forms was used to create study materials. The results from Bayesian independent sample t-test analyses indicated that the iCC group did not outperform the TP group in direct application problems. In addition, the iCC group did not outperform the TP group in PFL problems in either test. However, the ICC group outperformed the TP group in the further PFL problems from the delayed post-test (BF01 = .096, p = .003). The results from Bayesian one-way ANCOVA analyses indicated that there was the moderate evidence that supports the effect of group condition on direct application, Preparation for Future Learning (PFL) performance from the post-test, while controlling for the average pre-requisite knowledge check test score and motivational level. The results also indicated that there was from moderate to strong evidence to support that group condition had an effect on PFL performance from the delayed post-test (Session 2), and the further PFL performance from both post-test and delayed post-test while controlling for the average pre-requisite knowledge check test score. In addition, motivational level was shown to not be an effective moderator between instructional condition and performance in PFL problems. The results from GLM repeated measure analyses showed the ICC strategy had a more significant effect on the participants regarding PFL performance and further PFL performance over time as there was a significant cross-over interaction effect between the time and the instruction condition (p = .012, η 2 p = .08 for PFL performance and p = .003, η 2 p = .11 for further PFL performance). The direction for potential future studies is addressed in the conclusion section including the importance of developing curriculum to train students’ transfer ability; and a new type of assessment to measure transfer is offered for consideration.

Degree

Ph.D.

Advisors

Menekse, Purdue University.

Subject Area

Mathematics education|Instructional Design|Community college education|Design|Education|Educational administration|Mathematics|Operations research

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