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PROBLEM SOLVING AND THE USE OF MATH IN PHYSICS COURSES

Source: www.physics.umd.edu
Topic: Problem Solving

Sort Desciption: Mathematics is an essential element of physics problem solving but experts often fail to ..... employs only a fraction of their problem-solving resources. ...

Content Inside: 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 proceedings. 1 PROBLEM SOLVING AND THE USE OF MATH IN PHYSICS COURSES EDWARD F. REDISH Department of Physics University of Maryland College Park MD 20742-4111 USA 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 dia- lect 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. 1. We use math differently in physics Mathematics is commonly referred to as the language of science and we typically re- quire our physics students to take mathematics as prerequisites to their study of physics. As instructors we are often surprised by how little math our students seem to know despite successful performances in their math classes. When students appear to have trouble with math in our physics classes we might ask them to study more math. But using math in science (and particularly in physics) is not just doing math. It has a differ- ent purpose representing meaning about physical systems rather than expressing ab- stract relationships and it even has a distinct semiotics the way meaning is put into symbols from pure mathematics. It almost seems that the language of mathematics we use in physics is not the same as the one taught by mathematicians. There are many notable differences. 1.1. Physicists and mathematicians label constants and variables differently In mathematics as typically taught the choice of symbols t ...

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