A Theoretical Framework for Physics Education Research: Modeling Student Thinking

Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations and through which different theoretical models of student thinking can be compared. Much that is known in the behavioral sciences is robust and observationally based. In this paper, I draw from a variety of fields ranging from neuroscience to sociolinguistics to propose an over-arching theoretical framework that allows us to both make sense of what we see in the classroom and to compare a variety of specific theoretical approaches. My synthesis is organized around an analysis of the individual's cognition and how it interacts with the environment. This leads to a two level system, a knowledge-structure level where associational patterns dominate, and a control-structure level where one can describe expectations and epistemology. For each level, I sketch some plausible starting models for student thinking and learning in physics and give examples of how a theoretical orientation can affect instruction and research.Comment: 63 pages, Varenna school lecture

Using math in physics: 5. Functional dependence

When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary). How much a change in one variable or parameter is associated with a change in another depends on how they appear in the equation: their functional dependence. Understanding this sort of relationship is rarely taught in introductory mathematics classes, and students who have not yet learned to blend conceptual ideas with mathematical symbols may not see the relevance and power of this idea. We need to explicitly teach functional dependence as part of our effort to help students to learn to use math productively in science.Comment: 5 pages, 4 figure

Introducing students to the culture of physics: Explicating elements of the hidden curriculum

When we teach physics to prospective scientists and engineers we are teaching more than the "facts" of physics - more, even, than the methods and concepts of physics. We are introducing them to a complex culture - a mode of thinking and the cultural code of behavior of a community of practicing scientists. This culture has components that are often part of our hidden curriculum: epistemology - how we decide that we know something; ontology - how we parse the observable world into categories, objects, and concepts; and discourse - how we hold a conversation in order to generate new knowledge and understanding. Underlying all of this is intuition - a culturally created sense of meaning. To explicitly identify teach our hidden curriculum we must pay attention to students' intuition and perception of physics, not just to their reasoning.Comment: 4 pages, Physics Education Research Conference 2010 Plenary tal

Using math in physics -- 1. Dimensional analysis

Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think with math. Teaching dimensional analysis (DA). figuring out what measurements were combined to create a symbolic quantity, is a valuable first step in helping them learn to appreciate this difference. In this paper I discuss some of the issues associated with learning dimensional analysis and show some ways we can modify our instruction to help. This paper is one of a series on how to help students develop the scientific thinking skills required for learning to use math in science.Comment: 5 pages, 3 figure

Problem Solving and the Use of Math in Physics Courses

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend to blend conceptual physics with mathematical symbolism in a way that profoundly affects the way equations are used and interpreted. Research with university physics students in classes from algebra-based introductory physics indicates that the gap between what students think they are supposed to be doing and what their instructors expect them to do can cause severe problems.Comment: Invited talk presented at the conference, World View on Physics Education in 2005: Focusing on Change, Delhi, August 21-26, 2005. To be published in the proceeding