## UMD PERG PhD Dissertations: Michael C. Wittmann

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# Making sense of how students come to an understanding of physics: An example from mechanical waves

## Abstract

While physics education research (PER) has traditionally focused on introductory physics, little work has been done to organize and develop a model of how students come to make sense of the material they learn. By understanding how students build their knowledge of a specific topic, we can develop effective instructional materials. In this dissertation, I describe an investigation of student understanding of mechanical and sound waves, how we organize our findings, and how our results lead to the development of curriculum materials used in the classroom.

The physics of mechanical and sound waves at the introductory level (using small-amplitude approximation in the dispersionless system) involves fundamental concepts that are difficult for many students. These include: distinguishing between medium properties and boundary conditions, recognizing local phenomena (e.g. superposition) in extended systems, using mathematical functions of two variables, and interpreting and applying the mathematics of waves in a variety of settings. Student understanding of these topics is described in the context of wave propagation, superposition, use of mathematics, and other topics. Investigations were carried out using the common tools of PER, including free response, multiple choice, multiple-response, and semi-guided individual interview questions.

Student reasoning is described in terms of primitives generally used to simplify reasoning about complicated topics. I introduce a previously undocumented primitive, the object as point primitive. We organize student descriptions of wave physics around the the idea of patterns of associations that use common primitive elements of reasoning. We can describe students as if they make an analogy toward Newtonian particle physics. The analogy guides students toward describing a wave as if it were a point particle described by certain unique parts of the wave. A diagnostic test has been developed to probe the dynamics of student reasoning during the course of instruction.

We have replaced traditional recitation instruction with curriculum materials designed to help students come to a more complete and appropriate understanding of wave physics. We find that the research-based instructional materials are more effective than the traditional lecture setting in helping students apply appropriate reasoning elements to the physics of waves.