Applied precalculus: An innovative approach to the learning and teaching of precalculus mathematics.

摘要

his study proposes a new model for the development of mathematical thinking and studies the implementation of this model in a precalculus course. This model, called the tri-cyclic model, is composed of three interdependent cycles: the abstract-concrete cycle, the conceptual-procedural cycle, and the seminar-intense individual effort-collaborative work cycle. The course studied was Applied PreCalculus, a college precalculus course which embodied the tri-cyclic model. The first two-thirds of the paper establishes the model and identifies how it was implemented in the Applied PreCalculus course design and implementation. The last third of the paper provides extensive analysis comparing the student performance of Applied PreCalculus students with their counterparts in the standard course. More than 500 students were evaluated in the analysis section.;Applied PreCalculus outperformed their counterparts on the 220-point common final examination with medians of 174 and 150, respectively. Moreover, the distribution of Applied PreCalculus scores was heavily right-skewed with a mean of 170 and a standard deviation of 27 points. These values expressed a statistically significant improvement (p