The context of problem solving is used to show that students exhibit a local coherence but not global coherence in their physics knowledge. When presented with a problem-solving task, students often activate a coherent set of knowledge called a schema to solve the problem. Although the schemas students develop in the physics course are usually sufficient in the class, they are often insufficient for solving complex problems. Complex problems require a deep understanding where students have integrated their qualitative knowledge and quantitative knowledge with related physics topics. We show that our students activate schemas consisting of small amounts of knowledge and these schemas are often isolated from other schemas.

Physics Education Research (PER) has shown students in introductory physics lack a deep understanding of physics principles and concepts. PER has also shown that conceptual understanding can be improved and problem solving skills may be taught through a modified research-based curriculum. Despite these improvements, students still have difficulty developing a coherent knowledge of physics or connecting related physics concepts. In addition, they view quantitative problems and qualitative questions as distinct types of tasks, possessing different types of knowledge and rules for responding.

Using methods physics instructors and physics education researchers can use to examine coherence in student knowledge, distinct schemas for qualitative and quantitative knowledge are identified and provide evidence for local coherence in student physics knowledge. After identifying some of these difficulties in student understanding, we examine how students connect their qualitative and quantitative knowledge after going through a concept-based curriculum. In addition, we compare performance on quantitative questions between a physics class using the traditional problem-solving recitation and a class using Tutorials in Introductory Physics.