Achievement in problem solving and metacognitive thinking strategies among undergraduate calculus students

Abstract

The purpose of this study was to investigate problem solving in the field of calculus. The study investigated the metacognitive thinking strategies employed by lecturers that were considered as subject matter specialist. The study developed and operationalized a metacognitive thinking strategies model. This model was then tested for its reliability and its predictive nature towards problem solving skills in nonroutine calculus problems. A questionnaire was then administered among 480 first year undergraduate students who were selected randomly. The rate of return was about 90%. Using principal component analysis (PCA) the study successfully identified seven underlying dimensions of metacognitive thinking strategies. They are Self-efficacy, Define, Explore, Accommodate, Strategize, Execute and Verify. Finally, the researcher applied multiple regression analysis to evaluate the predictive ability of the identified predictor and the performance on routine and non-routine calculus problems. The study found that problem solving skills is acquired through practice and utilization of thinking strategies which is the corner stone on which advance mathematical ideas and particularly calculus are build on. This study revealed that there are six meaningfully predictive factors of calculus problem solving performance. It found that “strategize” is the major predictive of calculus problem solving performance, followed by “accommodate, self-efficacy, define, explore and then execute”. Further analysis revealed that Strategies, Accommodate and Self- Efficacy were considered most significant with substantial practical importance. With these findings, educators will be able to clinically evaluate a person's ability to regulate, monitor and control his or her own cognitive processes. Instructional strategies can then be developed for those individuals having difficulty functioning in the learning environment.