Abstract:

The importance of calculus in engineering applications makes it an interesting area for research and educational development. This study examines the effects of ongoing pedagogical interventions in a first-year calculus course, and offers alternative strategies that could have greater potential to improve academic performance. This is a mandatory, first-year calculus course for engineering students - with an annual enrollment of approximately 1,500. The course accounts for 7.5 credits, or 25% of the estimated workload. On completion, candidates would be familiar with basic numerical methods for solving nonlinear equations, differential equations, and integration.

At the turn of the century, failure rates were at extremely high levels, prompting professors to investigate the situation. A research study in 2002 identified correlations between student attitudes, behaviors, and examination grades, which included identical data collection procedures that would take place twelve years later. In this period, high schools revised their curricula, and a voluntary mathematics refresher course aimed to ease the transition from secondary school to university. Tutoring services were similarly improved, and a collection of instructional videos enabled greater flexibility for those with part time work or family obligations.

Survey data, along with self-reported grades from the high school and grades in the calculus course, constituted our data. The survey was comprised of 32 items in four sequences: the first featured background data, while the remainder items addressed study behaviors, exercises, and tutorial experiences. Students responded to questions, or indicated their level of agreement by clicking a box on a nine-point scale. Contrary to expectations, none of the aforementioned measures yielded noticeable changes in either attitude or achievement.

Poor performers reported less effort in contrast to their successful peers, and weak performers struggled to keep pace with the general progression. For some, simply getting a pass with minimal effort appeared to be the goal. Students committed to simply memorizing facts and methods earned poorer grades, compared to those practicing deep learning strategies: there was an intent to make sense of the material, correlated with a greater capacity to keep pace. Typical student concerns included reduced motivation and increased fear, both constituting overly negative motives in the realm of learning.

Our study found that a heavy workload and speedy progression overruled well-intended measures, such that cramming before the exam prevailed. The project team decided to search for a theoretical framework to explain these underlying mechanisms, in turn creating so many issues. Critical realism as an ontological framework posits that outcomes, as seen in our case, are rooted in larger contextual units than a single case – for example, workload and learning cultures that were part of the entire study program. This position offers both intriguing and relevant assumptions about causal mechanisms of the current study and beyond.

Keywords:

Calculus, academic achievement, critical realism.