In physics equations, each symbol represents a physical quantity, and mathematical expressions define relationships between these physical quantities. How do physicists and physics students make sense of these abstract equations? I will describe a theoretical approach to this question that marries ideas and methods of functional grammar and perceptual symbol systems. In summary, the way physicists use mathematics shares many elements that are similar to the grammar of human languages. Moreover, these elements seem to play a similar cognitive and symbolic purposes as their equivalent linguistic structures. Consequently, although many mathematical expressions may validly describe a given physics situation, few are contextually appropriate. I will present a several studies that reveal how physics students interpret mathematical structure. For example, different forms of the same equation influence students’ models of the physical reality that the equation describes. I will discuss the implications of this research for how students learn to interpret mathematics in physics.
Refreshments will be served half an hour before the start of the colloquium in Weniger 305.