Work in Progress: Determining a Mathematical Model to Study the Relationship Between Pedagogical Strategies and the Attainment of Student-learning Outcomes

One of the primary goals of an instructor is to present all the required course material and assess the students learning outcomes (SLOs) as often as possible. The assessment results provide the input to the instructor to adjust, improve, modify, or adopt new pedagogical strategies to achieve better results on SLOs. The intervention techniques or pedagogical strategies employed by the instructor to improve SLOs can be viewed as a controller to the dynamic system of teaching and learning. In a typical model-driven system design, we have inputs to and outputs from the dynamic system. Drawing an equivalence, the course learning objectives (CLOs) can be identified as the reference input and student SLOs as the output of this system. This dynamic system is a Multi-Input-Multi-Output (MIMO) system since the number of CLOs and SLOs are more than one. Feedback from the output provides an estimate of how far the input or the goal has been achieved. This feedback when compared to input offers an error that needs to be minimized so that the expected output is achieved by the system. The error minimization requires a controller which can be looked at as the intervention technique or pedagogical strategy employed by the instructor in this situation. However, an appropriate strategy can be established when we know not only how much the students have learned at any time but the rate at which they are learning a particular topic. Such a rate-based model is used in control system design and it is known, in its simplest form, as a linear model where only the first-order rate of each parameter is considered. Thus, a rate-based model of the student learning system would indicate where and how the efforts need to be applied to improve the students learning rate and consequently the SLOs. The preliminary testing of the model was conducted in a Basic Aerodynamics course, offered at Elizabeth City State University (ECSU). Course tests were administered over a quick interval of time to be able to calculate the learning rate. The Aviation Accreditation Board International (AABI) defined SLOs were used for this course. The weekly test results offered data for these SLOs. Besides the weekly test, each test had more than two questions on one SLO during the two-hour midterm exam and final exam. This provided a shorter time interval to calculate the slopes, which in this case corresponds to the learning rate. These are further combined with the weekly learning rate to compute the linear model. Once a linear mathematical model of the system is available, a suitable controller or pedagogical strategy can be determined using the conventional control system design methodology. The work-in-progress paper will discuss (i) a detailed approach to formulating a model that provides a relation between SLOs and pedagogical strategies; (ii) intervention techniques employed to reduce the gap in attaining SLO; (iii) technique to measure learning rate; and (iv) preliminary implementation results of the proposed approach in a college course.