Educational Studies in Mathematics
, Volume 78, Issue 1, pp 2143
First online:
How do mathematicians learn math?: resources and acts for constructing and understanding mathematics
 Michelle H. WilkersonJerdeAffiliated withCenter for Connected Learning, Northwestern UniversityLearning Sciences Program, Northwestern University Email author
 , Uri J. WilenskyAffiliated withCenter for Connected Learning, Northwestern UniversityLearning Sciences Program, Northwestern UniversityComputer Science and Electrical Engineering, Northwestern UniversityNorthwestern Institute on Complex Systems, Northwestern University
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In this paper, we present an analytic framework for investigating expert mathematical learning as the process of building a network of mathematical resources by establishing relationships between different components and properties of mathematical ideas. We then use this framework to analyze the reasoning of ten mathematicians and mathematics graduate students that were asked to read and make sense of an unfamiliar, but accessible, mathematical proof in the domain of geometric topology. We find that experts are more likely to refer to definitions when questioning or explaining some aspect of the focal mathematical idea and more likely to refer to specific examples or instantiations when making sense of an unknown aspect of that idea. However, in general, they employ a variety of types of mathematical resources simultaneously. Often, these combinations are used to deconstruct the mathematical idea in order to isolate, identify, and explore its subcomponents. Some common patterns in the ways experts combined these resources are presented, and we consider implications for education.
Keywords
Expert mathematicians Topology Proof Reasoning Knowledge resources Title
 How do mathematicians learn math?: resources and acts for constructing and understanding mathematics
 Journal

Educational Studies in Mathematics
Volume 78, Issue 1 , pp 2143
 Cover Date
 201109
 DOI
 10.1007/s1064901193065
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Expert mathematicians
 Topology
 Proof
 Reasoning
 Knowledge resources
 Authors

 Michelle H. WilkersonJerde ^{(1)} ^{(2)}
 Uri J. Wilensky ^{(1)} ^{(2)} ^{(3)} ^{(4)}
 Author Affiliations

 1. Center for Connected Learning, Northwestern University, 2120 Campus Drive, Evanston, IL, USA
 2. Learning Sciences Program, Northwestern University, 2120 Campus Drive, Evanston, IL, USA
 3. Computer Science and Electrical Engineering, Northwestern University, 2120 Campus Drive, Evanston, IL, USA
 4. Northwestern Institute on Complex Systems, Northwestern University, 2120 Campus Drive, Evanston, IL, USA