Robotics: Enhancing Pre-College Mathematics Learning with  Real-world Examples

Ravi T. Shankar; Don Ploger; Agnes Nemeth; Steven Alan Hecht

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Conference: 2013 ASEE Annual Conference & Exposition
Location: Atlanta, Georgia
Publication Date: June 23, 2013
Start Date: June 23, 2013
End Date: June 26, 2013
ISSN: 2153-5965
Conference Session: Mathematics Division Technical Session 1
Tagged Division: Mathematics
Page Count: 18
Page Numbers: 23.1050.1 - 23.1050.18
DOI: 10.18260/1-2--22435
Permanent URL: https://peer.asee.org/22435
Download Count: 645

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Paper Authors

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Ravi T. Shankar Florida Atlantic University

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Dr. Ravi Shankar is a professor in the computer and electrical engineering and computer science (CEECS) department in the college of engineering and computer science (COECS) at Florida Atlantic University (FAU) at Boca Raton, Fla. He is the director of a college-wide center on systems integration. He has a Ph.D. from the University of Wisconsin, Madison, Wisc., and an M.B.A. from FAU. He is a registered Professional Engineer in the State of FL, a Senior member of IEEE, and a fellow of the American Heart Association.

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Don Ploger Florida Atlantic University

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Dr. Don Ploger, Ph.D., is an Associate Professor with the College of Education. He and Dr. Shankar have worked together in developing Robotics courses for high school students. Dr. Ploger brings two important perspectives to this collaborative research. First, from an engineering education perspective, he emphasizes the importance of communicating essential knowledge to non-engineers. The second perspective comes from the mathematics education research literature. There is a well-established paradox: students often fail to apply familiar methods when they attempt to solve novel problems. Coordinating these perspectives has facilitated the collaboration across disciplines.

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Agnes Nemeth Florida Atlantic University

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Steven Alan Hecht Ph.D. Nova Southeastern University

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Abstract

Robotics: Enhancing Pre-College Mathematics Learning with Real-world ExamplesIntroduction: Seventeen ninth grade students worked in teams to build low cost robots, programthem, and use them to draw various geometric shapes on a canvas of 6’ x 6’, all during a regularsemester long course. The course was designed to enhance their interest in engineering and math,while providing a social context of competition and cooperation.Background: Studies in the mathematics education research indicate that students may be able torecall certain facts, but fail to use those facts in solving novel problems. Some students do noteven recognize that solving such problems is important. Students often “give clear evidence ofknowing certain mathematics but then proceed to act as if they are completely ignorant of it."Bringing engineering technology into the mathematics classroom can help students understandthe subject matter more deeply than in traditional mathematics instruction. We need to helpexpand our students’ mathematical toolbox: they need to learn the rules, concepts & formulas tosolve mathematical problems. Students who only encounter the abstract nature of mathematicsoften describe it as a boring and dry subject and state that they never learn anything that theycould use in real life. When practicum and pure thought are inextricably intertwined, that is realmath instruction. Teaching math with robots combines these two sides of mathematics.Approach: We were immensely helped by the Open Source software and hardware from Arduinowhich allows one to use low cost off-the-shelf components to assemble and program rapidly amicrocontroller-based system. We extended this to build robots. The robot software andhardware were prototyped a priori by engineering college students, so we knew that the flow forhigh school students would be predictable and repeatable, and that robots built would be robust.Discussion: Real life word problems are extremely difficult for students because they have toread, understand, and visualize the problems. Students in general are used to one step problemsolving and are perplexed when they encounter a problem that they have to plan, define thevariables, and step by step solve. Application of mathematical skills is much more complicatedthan practicing the skills in isolation. When designing curricula, assessments, and professionaldevelopment, there is a need to connect the mathematical instruction and practices to real lifecontent. When students are making mathematical models, robots can enable them to visualize theresults of varying assumptions, explore consequences, and compare predictions with data. Theyare able to use the robots to explore and deepen their understanding of concepts. However, aquestion might arise whether engineering errors might mask the lesson. Low cost robots mayhave systematic errors due to manufacturing tolerance and in linear distance and angular rotationcovered. These are random with respect to each other and are estimated to cause less than + 10%error for our robot. We found that the students were able to ignore this low degree of error andfocus on the big picture. We also discussed this (and sensitized them to it) in the class.Conclusion: Problem solving is not only part of math instruction but an extremely vital part ofour everyday life. A lack of understanding prevents a student from engaging in the mathematicalpractices. Mathematically proficient students can apply the mathematics they know to solveproblems arising in everyday life, society, and the workplace. Robotics may aid in this process.References:Arduino (2012). Arduino website for open source tools useful to build robots and otherembedded systems. Retrieved September 21, 2012 from http://www.arduino.cc/Figure: Our Low cost ($100) RobotFigure: A high school team’s plotting of a Star

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Shankar, R. T., & Ploger, D., & Nemeth, A., & Hecht, S. A. (2013, June), Robotics: Enhancing Pre-College Mathematics Learning with Real-world Examples Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--22435

TY - CPAPER
AB - Robotics: Enhancing Pre-College Mathematics Learning with Real-world ExamplesIntroduction: Seventeen ninth grade students worked in teams to build low cost robots, programthem, and use them to draw various geometric shapes on a canvas of 6’ x 6’, all during a regularsemester long course. The course was designed to enhance their interest in engineering and math,while providing a social context of competition and cooperation.Background: Studies in the mathematics education research indicate that students may be able torecall certain facts, but fail to use those facts in solving novel problems. Some students do noteven recognize that solving such problems is important. Students often “give clear evidence ofknowing certain mathematics but then proceed to act as if they are completely ignorant of it.&quot;Bringing engineering technology into the mathematics classroom can help students understandthe subject matter more deeply than in traditional mathematics instruction. We need to helpexpand our students’ mathematical toolbox: they need to learn the rules, concepts &amp; formulas tosolve mathematical problems. Students who only encounter the abstract nature of mathematicsoften describe it as a boring and dry subject and state that they never learn anything that theycould use in real life. When practicum and pure thought are inextricably intertwined, that is realmath instruction. Teaching math with robots combines these two sides of mathematics.Approach: We were immensely helped by the Open Source software and hardware from Arduinowhich allows one to use low cost off-the-shelf components to assemble and program rapidly amicrocontroller-based system. We extended this to build robots. The robot software andhardware were prototyped a priori by engineering college students, so we knew that the flow forhigh school students would be predictable and repeatable, and that robots built would be robust.Discussion: Real life word problems are extremely difficult for students because they have toread, understand, and visualize the problems. Students in general are used to one step problemsolving and are perplexed when they encounter a problem that they have to plan, define thevariables, and step by step solve. Application of mathematical skills is much more complicatedthan practicing the skills in isolation. When designing curricula, assessments, and professionaldevelopment, there is a need to connect the mathematical instruction and practices to real lifecontent. When students are making mathematical models, robots can enable them to visualize theresults of varying assumptions, explore consequences, and compare predictions with data. Theyare able to use the robots to explore and deepen their understanding of concepts. However, aquestion might arise whether engineering errors might mask the lesson. Low cost robots mayhave systematic errors due to manufacturing tolerance and in linear distance and angular rotationcovered. These are random with respect to each other and are estimated to cause less than + 10%error for our robot. We found that the students were able to ignore this low degree of error andfocus on the big picture. We also discussed this (and sensitized them to it) in the class.Conclusion: Problem solving is not only part of math instruction but an extremely vital part ofour everyday life. A lack of understanding prevents a student from engaging in the mathematicalpractices. Mathematically proficient students can apply the mathematics they know to solveproblems arising in everyday life, society, and the workplace. Robotics may aid in this process.References:Arduino (2012). Arduino website for open source tools useful to build robots and otherembedded systems. Retrieved September 21, 2012 from http://www.arduino.cc/Figure: Our Low cost ($100) RobotFigure: A high school team’s plotting of a Star
AU - Ravi T. Shankar
AU - Don Ploger
AU - Agnes Nemeth
AU - Steven Alan Hecht Ph.D.
CY - Atlanta, Georgia
DA - 2013/06/23
PB - ASEE Conferences
TI - Robotics: Enhancing Pre-College Mathematics Learning with Real-world Examples
UR - https://peer.asee.org/22435
DO - 10.18260/1-2--22435
ER -