Fostering a Conceptual Understanding in Undergraduate Materials Education: A Multivariable Animated Spreadsheet Approach
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Fostering a Conceptual Understanding in Undergraduate Materials Education: A Multivariable Animated Spreadsheet Approach
Scott A. Sinex1 and Joshua B. Halpern2 1 Department of Physical Sciences & Engineering, Prince George's Community College, Largo, Maryland 2 Department of Chemistry, Howard University, Washington, District of Columbia ABSTRACT We describe how students explore materials science concepts using animated interactive spreadsheets. An engaging pedagogy is created in the classroom using spreadsheets in a way that initially camouflages mathematical complexity, which can later be revealed and taught. Use of off-the-shelf spreadsheet software, including freeware makes these spreadsheets universally available. INTRODUCTION Many topics in materials science involve mathematical relationships that are illustrated graphically in textbooks. The graphical capabilities of spreadsheets allow for an animated multivariable approach to many mathematical relationships. Further, by camouflaging the mathematics, a more conceptual route can be taken in the classroom. In this article, we demonstrate a number of concepts from sophomore-level materials science via animated interactive spreadsheets or Excelets. The spreadsheets are all computationally-based (formulae, no programming) and hence easily modified as well. Not only are the topics transformed into a dynamic learning situation but they also allow for discovery-based learning through the mode of “what if” questioning posed by the instructor. The collection of Materials Science Excelets that we have developed can be freely downloaded [1]. The collection contains over thirty interactive spreadsheets covering a variety of topics appropriate for sophomore-level materials science or freshmen chemistry or physics. Gabel [2] has outlined a number of items that improve conceptual understanding. Discovery learning and mathematical problem solving (mathematical modeling) are two of these that are solidly addressed by the animated interactive spreadsheets. Use in a collaborative learning environment covers another item from Gabel’s list. Further science process (predicting, interpreting, concluding) and algebraic thinking are added by their use. Students also learn to use Excel, or its Open Office equivalent for analyzing data and graphing. THE BEHAVIOR OF LIGHT AT THE INTERFACE BETWEEN MATERIALS Let’s consider the Fresnel equation for the determination of the reflection coefficient, R, as given by equation 1: (n - n )2 R= 1 2 2 (1) (n1 + n 2 )
where n1 and n2 are the indices of refraction of the two mediums. Instead of giving or presenting the Fresnel equation to students, why not let them explore the relationship (figure1 from the Optical Interaction Excelet) by varying the index of refraction for the medium? Students also observe that what is not reflected is transmitted, T, through the material and can further explore the absorption of light in the medium. Students should discover that T = 1 – R. What if the index of refraction of medium 2 increased, how does the refl
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