Students’ Perceived Utility of Precision Taught Calculus

Introduction The recent research conducted on calculus courses suggested that conceptual exploration and science lab-like group work supports student engagement, understanding, and achievement (Hsu, Murphy, & Treisman, 2008; Oehrtman, 2009). These efforts also increase students' grades, but can leave students with the same misconceptions about the material regardless of pedagogical approach. Furthermore, few studies have investigated how to identify study misconceptions within exploratory calculus courses (Garfield & Ben-Zvi, 2007; Hsu et al., 2008; Nickerson & Bowers, 2008; Rasmussen & Marrongelle, 2008). Calculus instructors remain unclear which instructional methods to pair with these new activities, especially given the broad amount of context they are expected to cover. In this study we (1) explored a potential solution in order to help calculus instructors identify misconceptions prior to lab activities that occur in class. After noticing that some instruction time was not relevant for most of the class, we began wondering how we could determine what information students had coming into a given lecture day. Rather than large-scale assessments that were lengthy for students to complete and teacher to grade, we began looking at how daily formative assessment that occurs over material yet to be covered could help teachers identify material students struggled with and excelled at prior to the material being covered in the course. For example, by collecting a formative assessment over multiplying binomials the day prior to the class meeting where multiplying binomials would be used as a step to computing the derivate of a factored polynomial, instructors could make informed decisions about how to spend the class time. If 95% of the students indicated understanding how to multiply binomials, then the instructor could feel justified in jumping straight into the important material students have not covered. Or, if over half of the students had problems with multiplying, the instructor would feel justified in the spending time to do an example, or multiple examples, depending on the severity of the misunderstanding indicated. The main goal of this technique, which we term precision teaching, is to inform the instructor what concepts students struggle with in order make instructions activities tailored to this information. We also developed this dynamic instruction practice to create time to add the activities research suggests to the syllabus without sacrificing content. Given our experience, we acknowledge how precision teaching requires more preparation than traditional classes, but will argue the time is worth the outcomes. This study is a result of our work aimed to document the effects of precision teaching in a calculus course. We feel it is important to formally document the perceived utility of the teaching technique, to provide the justification for other calculus instructors on the merit of precision teaching. Teacher fidelity to the method is an important concern for the outcomes of any new pedagogy, as Kilpatrick (1997) highlights. Precision teaching was an instructional method based on the weekly decision cycle outlined below (figure 1). The amount of content to be covered each week was designated at the start of the unit. The day before the material will be covered in class, the students completed a pre-lecture writing activity, called a reading sheet. Reading sheets consisted of approximately five short answer writing questions about the principles and concepts in the section. Based on the mistakes on the writing assignments, lecture notes focused on these problematic areas; topics 80% of the class answered correctly were not addressed with formal class time. If a student is part of the 20% who incorrectly answer a question, their pre-lecture sheet was returned with detailed comments on their mistake, and they were encouraged to attend office hours for additional help. …