| Summary: | In this thesis we approach the concept of Rate of Change as a mathematical model, and we apply it to a few physics problems. Its main goal is to help students to bridge concepts form mathematical models and the real life applications. We begin with a review of measurements, proportionality and similarity based on Euclidean geometry; then, we review linear and affine functions, and we introduce a mathematical model for the average and instantaneous rate of change. This mathematical model is applied to problems from physics following the four representations of functions: verbal, algebraic, tabular and graphical. By doing so, the main point is to show a unifying theme for mathematics and sciences, and the strong connections between the two. This thesis is intended to be a guide for teachers and students in Algebra and Calculus classes. The thesis consists of three main parts: a review of Euclidian geometry concepts and functions related to proportional reasoning, average rate of change and instantaneous rate of change with applications in physics problems.
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