E. F. Redish, R. E. Scherr & J. Tuminaro, published in a slightly abbreviated version in The Physics Teacher, 44, p 293 (May 2006).
Abstract: Problem solving is the heart and soul of most college physics and many high school physics courses. The “big idea” is that physics tells you more about a physical situation than you thought you knew — and you can quantify it if you use fundamental physical principles expressed in mathematical form. Often, the results of your problem solving can lead you to understand and rethink your intuitions about the physical world in new and more productive ways. As a result, physics is a great place (some of us would claim the best place) to learn how to use mathematics effectively in science.
As physics teachers, we often stress the importance of problem solving in learning physics. Unfortunately, many of our students appear to find problem solving very difficult. Sometimes they generate ridiculous answers and seem satisfied with them. Sometimes they can do the calculations but not interpret the implications of the results. Sometimes, despite apparent success in problem solving, they seem to have a poor understanding of the physics that went into the problems.1 We give them explicit instructions on how to solve problems (“draw a picture,” “find the right equation,” …) but it doesn’t seem to help.
We might respond that they need to take more math prerequisite classes, but in the algebra-based physics class at the University of Maryland, almost all of the students have taken calculus and earned an A or a B. Many of them have been successful in classes such as organic chemistry, cellular biology, and genetics. Why do they have so much trouble with the math in an introductory physics class?
As part of a research project to study learning in algebra-based physics,2 the Physics Education Research Group at the University of Maryland videotaped students working together on physics problems. Analyzing these tapes gives us new insights into the problems they have in using math in the context of physics. One problem is that they have inappropriate expectations as to how to solve problems in physics (some of it learned, perhaps, in math classes). This is discussed elsewhere.3 A second problem seems to lie with the instructors. As instructors, we may have misconceptions about how people think and learn, and this has important implications about how we interpret what our students are doing.
In this paper, we want to consider one example of students working on a physics problem that showed us in a dramatic fashion that we had failed to understand the work the students needed to do in order to solve an apparently “simple” problem in electrostatics. Our critical misunderstanding was failing to realize the level of complexity that we had built into our own “obvious" knowledge about physics.
As physics teachers, we often stress the importance of problem solving in learning physics. Unfortunately, many of our students appear to find problem solving very difficult. Sometimes they generate ridiculous answers and seem satisfied with them. Sometimes they can do the calculations but not interpret the implications of the results. Sometimes, despite apparent success in problem solving, they seem to have a poor understanding of the physics that went into the problems.1 We give them explicit instructions on how to solve problems (“draw a picture,” “find the right equation,” …) but it doesn’t seem to help.
We might respond that they need to take more math prerequisite classes, but in the algebra-based physics class at the University of Maryland, almost all of the students have taken calculus and earned an A or a B. Many of them have been successful in classes such as organic chemistry, cellular biology, and genetics. Why do they have so much trouble with the math in an introductory physics class?
As part of a research project to study learning in algebra-based physics,2 the Physics Education Research Group at the University of Maryland videotaped students working together on physics problems. Analyzing these tapes gives us new insights into the problems they have in using math in the context of physics. One problem is that they have inappropriate expectations as to how to solve problems in physics (some of it learned, perhaps, in math classes). This is discussed elsewhere.3 A second problem seems to lie with the instructors. As instructors, we may have misconceptions about how people think and learn, and this has important implications about how we interpret what our students are doing.
In this paper, we want to consider one example of students working on a physics problem that showed us in a dramatic fashion that we had failed to understand the work the students needed to do in order to solve an apparently “simple” problem in electrostatics. Our critical misunderstanding was failing to realize the level of complexity that we had built into our own “obvious" knowledge about physics.
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