This study explores an iterative design research experiment of a flipped mathematics classroom over the span of five curricular units involving big ideas of transcendental and polynomial functions. Transcendental and polynomial functions involve an algebraic, analytic, and graphical approach to the concepts and procedures of exponential, logarithmic, power, cubic, quadratic, linear, and rational functions. The Compleat design research methodology (Middleton, Gorard, Taylor, & Bannan-Ritland, 2008) was used to explore a series of instructional sequences that an instructor implemented in a flipped classroom while teaching big ideas of transcendental and polynomial functions.
The experiment occurred over the course of a sixteen-week semester. Data analysis was constructed from a triangulation of relevant data from student constructions in the form of written documents, whole-group and small-group discussions from the video recordings, and the instructor’s personal reflective notes. The hypothetical learning trajectory served as the empirical basis upon which reflections occurred and meaningful modifications were made to the original prototype. Segmenting the content helped decrease the extraneous cognitive load by reducing the burden on students’ working memory in order to make instructional activities more meaningful and effective. More time was allocated in class for basic algorithmic processes prior to the implementation of the higher-order instructional tasks in phase five to account for the increasing intrinsic cognitive load in the instructional tasks. Micro-level practice-based concerns and improvements to the prototype as well as the creation of a theoretical and empirically-based instructional model were natural consequences to the design experiment
