Developing Skeptical Reverence for Mathematics

Julie Gainsburg

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Conference: 2012 ASEE Annual Conference & Exposition
Location: San Antonio, Texas
Publication Date: June 10, 2012
Start Date: June 10, 2012
End Date: June 13, 2012
ISSN: 2153-5965
Conference Session: Using Applications and Projects in Teaching Mathematics
Tagged Division: Mathematics
Page Count: 17
Page Numbers: 25.436.1 - 25.436.17
DOI: 10.18260/1-2--21194
Permanent URL: https://peer.asee.org/21194
Download Count: 479

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Julie Gainsburg California State University, Northridge

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Julie Gainsburg is Associate Professor of secondary education at California State University, Northridge, where she has taught credential and graduate-level courses for pre-service and in-service mathematics teachers since 2003, when she earned her Ph.D. in curriculum and teacher education from Stanford University. In addition to studying mathematics-teacher development, she has studied the mathematical behavior and development of civil engineers and drawn implications for K-12 mathematics education.

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Abstract

Developing Skeptical ReverenceThe tendency of K-12 students to view mathematics as an activity that only takes place inschools has been hypothesized to cause educational trouble, including a lack of studentmotivation and thus less learning, and students’ inability to apply what mathematics they dolearn to solving problems outside of school or in other subjects. Many adults have not outgrownthe idea that mathematics is not really useful in their everyday activity or work. Despiteengineering’s reputation as math-intensive, even the engineering community debates the amountof (school) mathematics individual engineers actually need to know to perform everyday work,especially in light of the increasing role of computers.That debate inspired a prior study, in which I showed that a key component of the expertise ofcivil engineers was their ability to use mathematics to serve their problem-solving purposes.This required a keen understanding of the powers and limitations of formal and informalmathematical tools. Only rarely could mathematical procedures be applied wholesale (as theyusually are in school); engineering expertise included flexibly selecting and adapting—occasionally even overriding—mathematical procedures to model real phenomena. I termed thissomewhat hybrid disposition towards mathematics skeptical reverence: a fine balance betweenseeing mathematics as an indispensible tool and understanding its limitations.The current study investigates how engineers develop their perspective on the relationshipbetween mathematics and engineering and this disposition of skeptical reverence. This questionis critical for engineering education: Young engineers who see little connection betweenmathematics and engineering, who perhaps believe that “real engineers don’t use math,” wouldseem unlikely to learn to use the mathematics well. Yet, those who view engineering as theroutine application of known mathematical procedures or believe that mathematics serves as theultimate authority for engineering decisions will be equally hobbled in their efforts to attainengineering expertise.This study draws on the sociocultural research tradition that frames learning as a personaltransition within and across communities of practice. I targeted individuals at various stages ofthe transition between the communities of practice of school and engineering work, and Iexplored their evolving perceptions of the role of mathematics in engineering. Assuming themathematical disposition of skeptical reverence is productive and desirable for engineers, Iaimed to back-map the development of that disposition, through interviews, engineering-courseobservations, and “think-aloud” problem-solving sessions. The greater study involved 20participants, ranging from freshmen in an undergraduate civil-engineering program to veterancivil engineers and instructors. This paper focuses on the development of the 10 students: 2-3 ateach of the four years of the undergraduate program. Using qualitative-data-analysis methods, Icharacterize the students’ mathematical dispositions and how these differed among students indifferent years of the program. I discuss implications for engineering education as well as K-12.

Citation
Format

Gainsburg, J. (2012, June), Developing Skeptical Reverence for Mathematics Paper presented at 2012 ASEE Annual Conference & Exposition, San Antonio, Texas. 10.18260/1-2--21194

TY  - CPAPER
AB  -                             Developing Skeptical ReverenceThe tendency of K-12 students to view mathematics as an activity that only takes place inschools has been hypothesized to cause educational trouble, including a lack of studentmotivation and thus less learning, and students’ inability to apply what mathematics they dolearn to solving problems outside of school or in other subjects. Many adults have not outgrownthe idea that mathematics is not really useful in their everyday activity or work. Despiteengineering’s reputation as math-intensive, even the engineering community debates the amountof (school) mathematics individual engineers actually need to know to perform everyday work,especially in light of the increasing role of computers.That debate inspired a prior study, in which I showed that a key component of the expertise ofcivil engineers was their ability to use mathematics to serve their problem-solving purposes.This required a keen understanding of the powers and limitations of formal and informalmathematical tools. Only rarely could mathematical procedures be applied wholesale (as theyusually are in school); engineering expertise included flexibly selecting and adapting—occasionally even overriding—mathematical procedures to model real phenomena. I termed thissomewhat hybrid disposition towards mathematics skeptical reverence: a fine balance betweenseeing mathematics as an indispensible tool and understanding its limitations.The current study investigates how engineers develop their perspective on the relationshipbetween mathematics and engineering and this disposition of skeptical reverence. This questionis critical for engineering education: Young engineers who see little connection betweenmathematics and engineering, who perhaps believe that “real engineers don’t use math,” wouldseem unlikely to learn to use the mathematics well. Yet, those who view engineering as theroutine application of known mathematical procedures or believe that mathematics serves as theultimate authority for engineering decisions will be equally hobbled in their efforts to attainengineering expertise.This study draws on the sociocultural research tradition that frames learning as a personaltransition within and across communities of practice. I targeted individuals at various stages ofthe transition between the communities of practice of school and engineering work, and Iexplored their evolving perceptions of the role of mathematics in engineering. Assuming themathematical disposition of skeptical reverence is productive and desirable for engineers, Iaimed to back-map the development of that disposition, through interviews, engineering-courseobservations, and “think-aloud” problem-solving sessions. The greater study involved 20participants, ranging from freshmen in an undergraduate civil-engineering program to veterancivil engineers and instructors. This paper focuses on the development of the 10 students: 2-3 ateach of the four years of the undergraduate program. Using qualitative-data-analysis methods, Icharacterize the students’ mathematical dispositions and how these differed among students indifferent years of the program. I discuss implications for engineering education as well as K-12.   
AU  - Julie Gainsburg
CY  - San Antonio, Texas
DA  - 2012/06/10
PB  - ASEE Conferences
TI  - Developing Skeptical Reverence for Mathematics
UR  - https://peer.asee.org/21194
DO  - 10.18260/1-2--21194
ER  -