About CLEAR Calculus
Assessments
Project CLEAR Calculus is using three primary instruments to asses the impact on student learning and instructor assessment.
The Limit Models Assessment (LMA)
The LMA provides quantitative comparisons of the cognitive models employed by students in courses using CLEAR Calculus materials with other calculus students and enables us to monitor long term shifts in students’ models. We developed the LMA following Model Analysis Theory from physics education research drawing an analogy from quantum mechanics to model the structure of student thinking as a mixture of previously identified cognitive models with varying probabilities of being activated (Bao & Reddish, 2001; Bao, Hogg, & Zollman, 2001). Our prior research (e.g. Martin & Oehrtman, 2010a, 2010b; Oehrtman, 2002, 2003, 2008, 2009) has resulted in detailed characterizations and indicators of students’ conceptual models for limits as applied throughout calculus, which serves as the qualitative foundation for the LMA.
The Calculus Concepts Assessment (CCA)
The CCA is used to measure shifts in students’ understanding of the central concepts of calculus. We will also correlate students’ normalized gains with the predominance of approximation models as assessed by the post-course LMA to determine if the development of approximation models is related to conceptual gains.
The Exam Characterization Framework (ECF)
The ECF was recently created from a national MAA study of calculus courses (Tallman & Carlson, 2012) and characterizes exams according to 3 dimensions: item orientation, item representation, and item format. Each dimension is broken down into several categories/levels. For example, for item orientation, exam items could require students to engage in a low level cognitive activity such as recall a definition or apply a procedure or exam items might require students to engage in a higher level activity such as applying their understanding to a contextual problem or relating different concepts together. Collecting exams and adapting the ECF will allow us to determine if there is a shift in instructor exams of items at a higher cognitive level than just recalling definitions and rote procedure.