Abstract:

In higher education, many courses have evolved into "gatekeeper" course. These courses are defined to be high-enrollment, low-completion courses which are cornerstones in general education. These courses often become graduation roadblocks and prevent students from attaining their educational goals. At the authors' home institution, Precalculus has become a gatekeeper course with approximately 40% of the students failing to complete the course, a failure rate commonly seen at many institutions of higher education. This paper details the development of a highly accurate neural network-based, predictive system that identifies students at the beginning of the semester as being "at-risk" of not completing the course. The predictors/inputs into the neural network offer pedagogical insights into how a student's “at-risk” classification might be mitigated via numerous techniques such as concurrent support courses, online tutorials, "just-in-time" instructional aids, study skills, motivational interviewing, and/or peer mentoring.

The predictive system utilizes a multilayered backpropagation neural network to classify correctly approximately 80% of precalculus students. The system correctly categorizes approximately 85% of the "at-risk" students and approximately 70% of the not "at-risk" students. Predictors stem from items on a statistically reliable questionnaire from NCSM (National Council of Supervisors of Mathematics), algebraic assumptions resulting from interviews with Precalculus instructors, and student admission information. Sixteen of the predictors were found to be statistically significant at the p<= 0.01 level (2-tailed). These precalculus success predictors may guide not only pedagogical and curricula development but possibly course sequencing and placement decisions per students' backgrounds.

Keywords:

Precalculus, neural network, student success, gatekeeper course.