Student Perception of Mathematical Modeling Before and After Completing a Two Joint Robot Computer Simulation Task

Laurel Johnston; Noah Salzman

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Conference: 2020 ASEE Virtual Annual Conference Content Access
Location: Virtual On line
Publication Date: June 22, 2020
Start Date: June 22, 2020
End Date: June 26, 2021
Conference Session: Pre-college Engineering Education Division Technical Session 19
Tagged Division: Pre-College Engineering Education
Page Count: 18
DOI: 10.18260/1-2--35228
Permanent URL: https://peer.asee.org/35228
Download Count: 592

Paper Authors

biography

Laurel Johnston Boise State University

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Laurel Johnston is a master's student in the STEM Education program at Boise State University. She has over eight years of teaching experience in high school science and mathematics. She enjoys integrating engineering concepts in the classroom to help increase student engagement and understanding.

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biography

Noah Salzman Boise State University

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Noah Salzman is an Assistant Professor at Boise State University, where he is a member of the Electrical and Computer Engineering Department and IDoTeach, a pre-service STEM teacher preparation program. His work focuses on the transition from pre-college to university engineering programs, how exposure to engineering prior to matriculation affects the experiences of engineering students, and engineering in the K-12 classroom. He has worked as a high school science, mathematics, and engineering and technology teacher, as well as several years of electrical and mechanical engineering design experience as a practicing engineer. He received his Bachelor of Science degree in Engineering from Swarthmore College, his Master's of Education degree from the University of Massachusetts, and a Master's of Science in Mechanical Engineering and Doctorate in Engineering Education from Purdue University.

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Abstract

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.

Citation
Format

Johnston, L., & Salzman, N. (2020, June), Student Perception of Mathematical Modeling Before and After Completing a Two Joint Robot Computer Simulation Task Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--35228

TY - CPAPER
AB - 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.

AU - Laurel Johnston
AU - Noah Salzman
CY - Virtual On line
DA - 2020/06/22
PB - ASEE Conferences
TI - Student Perception of Mathematical Modeling Before and After Completing a Two Joint Robot Computer Simulation Task
UR - https://peer.asee.org/35228
DO - 10.18260/1-2--35228
ER -