caa a22 4500 445881712 CHVBK 20180317145545.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10649-011-9306-5 doi (NATIONALLICENCE)springer-10.1007/s10649-011-9306-5 How do mathematicians learn math?: resources and acts for constructing and understanding mathematics [Elektronische Daten] [Michelle Wilkerson-Jerde, Uri Wilensky] 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. Springer Science+Business Media B.V., 2011 Expert mathematicians nationallicence Topology nationallicence Proof nationallicence Reasoning nationallicence Knowledge resources nationallicence Wilkerson-Jerde Michelle Center for Connected Learning, Northwestern University, 2120 Campus Drive, Evanston, IL, USA aut Wilensky Uri Center for Connected Learning, Northwestern University, 2120 Campus Drive, Evanston, IL, USA aut Educational Studies in Mathematics Springer Netherlands 78/1(2011-09-01), 21-43 0013-1954 78:1<21 2011 78 10649 https://doi.org/10.1007/s10649-011-9306-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10649-011-9306-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wilkerson-Jerde Michelle Center for Connected Learning, Northwestern University, 2120 Campus Drive, Evanston, IL, USA aut NATIONALLICENCE 700 1- Wilensky Uri Center for Connected Learning, Northwestern University, 2120 Campus Drive, Evanston, IL, USA aut NATIONALLICENCE 773 0- Educational Studies in Mathematics Springer Netherlands 78/1(2011-09-01), 21-43 0013-1954 78:1<21 2011 78 10649 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer