Developing Mathematical Intuition by Building Estimation Skills

Rebecca Bourn; Sarah C. Baxter

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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 4
Tagged Division: Mathematics
Page Count: 10
Page Numbers: 23.405.1 - 23.405.10
DOI: 10.18260/1-2--19419
Permanent URL: https://sftp.asee.org/19419
Download Count: 448

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Paper Authors

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Rebecca Bourn Tribeca Flashpoint Media Arts Academy

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Dr. Bourn designed the math curriculum for the Core Studies Program at the Tribeca Flashpoint Media Arts Academy.
She received her PhD in Applied Mathematics from the University of Virginia School of Engineering and Applied Science.

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biography

Sarah C. Baxter University of South Carolina

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Professor Baxter is an Associate Professor in the Department of Mechanical Engineering at the University of South Carolina. She received her PhD in Applied Mathematics from the University of Virginia School of Engineering and Applied Science.

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Abstract

Developing Mathematical Intuition by Building Estimation SkillsOpen-ended problems are challenging for many students because they have not yet developed amathematical intuition. It is difficult for them to see patterns or associate one type of problemwith another and they have few intuitive skills to judge the quality and “correctness” of theiranswers. These can be significant obstacles for students who don’t define themselves asmathematicians, but whose careers require mathematics to support the use of technology as wellas build physical intuition. One approach to improving mathematical intuition is in improvingestimations skills. In particular, learning to estimate can help bridge the gap between “f(x)” andthe real world, encourage critical thinking, and help students learn to solve open-ended problems.In this paper we outline a simple estimation exercise that was presented to two `applied math’student populations: Media Arts students and beginning Mechanical Engineering students.Students in Media Arts were asked to design an open-air concert space in a downtown city plaza.They developed estimates for appropriate physical structures such as a surrounding fence, andconcert parameters such as crowd capacity (space per person). Engineering students were askedto estimate the volume of an interior courtyard of a three-story city building in order to estimatecosts of an HVAC system, and the area of an awning suspended over the open roof area, as analternative approach to environmental control. Both groups worked in teams and presentedresults in report format. The paper discusses the challenges for both groups, voluntary studentfeedback, and the results of a set of pre and post-project concept based exercises.Exercises that build estimation skills have been used to help enhance basic arithmetic skills inthe early grades. Later, Fermi questions such as `How many drops of water are in Lake Erie?”,can strengthen the use of unit conversion sequences and help teach abstract problem solving.These approaches have limited success, however, when applied to media arts students, whosegoals are technology-based careers in the film, music, and game industries, and to beginningmechanical engineering students who envision careers in engineering design. Both groups prefermath that is immediately and transparently applicable to their career paths. With powerful andinexpensive calculators, learning even simple math seems like a waste of time, and they havelearned to trust without question, the output of user-friendly software. These projects, whichhave an immediate ‘real’ world feel, help answer the question of ‘what can I do with this?’,encourage iteration and refinement of solutions, which are critical math skills for design andinnovation, and help students make the connection between math classes and their major field.

Citation
Format

Bourn, R., & Baxter, S. C. (2013, June), Developing Mathematical Intuition by Building Estimation Skills Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--19419

TY  - CPAPER
AB  -         Developing Mathematical Intuition by Building Estimation SkillsOpen-ended problems are challenging for many students because they have not yet developed amathematical intuition. It is difficult for them to see patterns or associate one type of problemwith another and they have few intuitive skills to judge the quality and “correctness” of theiranswers. These can be significant obstacles for students who don’t define themselves asmathematicians, but whose careers require mathematics to support the use of technology as wellas build physical intuition. One approach to improving mathematical intuition is in improvingestimations skills. In particular, learning to estimate can help bridge the gap between “f(x)” andthe real world, encourage critical thinking, and help students learn to solve open-ended problems.In this paper we outline a simple estimation exercise that was presented to two `applied math’student populations: Media Arts students and beginning Mechanical Engineering students.Students in Media Arts were asked to design an open-air concert space in a downtown city plaza.They developed estimates for appropriate physical structures such as a surrounding fence, andconcert parameters such as crowd capacity (space per person). Engineering students were askedto estimate the volume of an interior courtyard of a three-story city building in order to estimatecosts of an HVAC system, and the area of an awning suspended over the open roof area, as analternative approach to environmental control. Both groups worked in teams and presentedresults in report format. The paper discusses the challenges for both groups, voluntary studentfeedback, and the results of a set of pre and post-project concept based exercises.Exercises that build estimation skills have been used to help enhance basic arithmetic skills inthe early grades. Later, Fermi questions such as `How many drops of water are in Lake Erie?”,can strengthen the use of unit conversion sequences and help teach abstract problem solving.These approaches have limited success, however, when applied to media arts students, whosegoals are technology-based careers in the film, music, and game industries, and to beginningmechanical engineering students who envision careers in engineering design. Both groups prefermath that is immediately and transparently applicable to their career paths. With powerful andinexpensive calculators, learning even simple math seems like a waste of time, and they havelearned to trust without question, the output of user-friendly software. These projects, whichhave an immediate ‘real’ world feel, help answer the question of ‘what can I do with this?’,encourage iteration and refinement of solutions, which are critical math skills for design andinnovation, and help students make the connection between math classes and their major field.
AU  - Rebecca Bourn
AU  - Sarah C. Baxter
CY  - Atlanta, Georgia
DA  - 2013/06/23
PB  - ASEE Conferences
TI  - Developing Mathematical Intuition by Building Estimation Skills
UR  - https://sftp.asee.org/19419
DO  - 10.18260/1-2--19419
ER  -