Student Perception of Mathematical Modeling Before and After Completing a Two Joint Robot Computer Simulation Task (RTP)
Engineers frequently utilize computer simulation as part of their design processes to model and understand the behavior of complex systems. Simulation is also an important tool for developing students’ understanding of modeling and strengthening their intuition for problem solving in complex domains, especially in fields where mathematical calculations by hand may be tedious and time consuming. The use of simulation also allows for more accurate results, because values that otherwise require rounding are calculated quickly by computers. Computer simulations are cost-effective and easily shared as well.
This project uses a two-joint robot arm problem and accompanying computer simulation to demonstrate to AP BC Calculus students how and why we would use calculus concepts simultaneously in Cartesian and polar coordinate systems. High school students receive only very brief instruction in polar coordinates, and they spend the majority of their secondary education years dealing with functions in Cartesian space. As a result, the shift to polar coordinates is difficult, particularly when calculus students are asked conceptual questions dealing with objects in motion.
Numerous studies recognize the potential of pre-college engineering to provide context and improve students’ understanding of mathematics and science.The two-joint robot problem is commonly used in upper-level engineering courses with a prerequisite of differential equations and linear algebra. Engineering students may be required to design their own simulation or computer program that demonstrates the motion of a two-joint robot arm. These tasks as described require a level of complexity that is outside the scope of a high school AP BC Calculus course. We created a simulation and that approaches this problem geometrically with constraints in order to help students make connections and insights about this complex problem.
We developed the simulation in a way that allows students to experience mathematical modeling in an applications-based context. Mathematical modeling is a critical component of STEM education. It allows students to strengthen conceptual understanding, expand problem solving skills, and develop their understanding of the engineering design process. A small cohort of students in AP BC Calculus will complete an open-response survey of their perceptions on mathematical modeling before and after completing our simulation. We will compare student responses to a formal description of mathematical modeling to determine which aspects, if any, change after completing the simulation activity.
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