caa a22 4500 445881895 CHVBK 20180317145546.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10649-010-9277-y doi (NATIONALLICENCE)springer-10.1007/s10649-010-9277-y Can slope be negative in 3-space? Studying concept image of slope through collective definition construction [Elektronische Daten] [Deborah Moore-Russo, AnnaMarie Conner, Kristina Rugg] Developing deep conceptual understanding of what Ma (1999) calls fundamental mathematics is a well-accepted goal of teacher education. This paper presents a microanalysis of an intriguing episode within a course designed to encourage such understanding. An adaptation of Krummheuer's (1995) elaboration of Toulmin's (1958/2003) diagrams is used to examine video recordings and transcripts of a group of graduate students in secondary mathematics education grappling with the idea of a three-dimensional line having negative slope. The graduate students' understandings of slope are examined using an expansion of Stump's (1999, 2001b) categories of conceptions of slope. The episode ends in an interesting impasse, in which the graduate students agree to pursue the idea no further, purposely ignoring the question of negative slope, despite the clear intention of the task. The analysis explores the argumentation, factors of the learning environment, and conceptions of slope that may have contributed to this impasse. Springer Science+Business Media B.V., 2010 Secondary mathematics teachers nationallicence Slope nationallicence Teacher education nationallicence Concept image nationallicence Argumentation nationallicence Moore-Russo Deborah University at Buffalo, The State University of New York, 566 Baldy Hall, Buffalo, NY, USA aut Conner AnnaMarie University of Georgia, 105 Aderhold Hall, 30602, Athens, GA, USA aut Rugg Kristina University at Buffalo, The State University of New York, 566 Baldy Hall, Buffalo, NY, USA aut Educational Studies in Mathematics Springer Netherlands 76/1(2011-01-01), 3-21 0013-1954 76:1<3 2011 76 10649 https://doi.org/10.1007/s10649-010-9277-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10649-010-9277-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Moore-Russo Deborah University at Buffalo, The State University of New York, 566 Baldy Hall, Buffalo, NY, USA aut NATIONALLICENCE 700 1- Conner AnnaMarie University of Georgia, 105 Aderhold Hall, 30602, Athens, GA, USA aut NATIONALLICENCE 700 1- Rugg Kristina University at Buffalo, The State University of New York, 566 Baldy Hall, Buffalo, NY, USA aut NATIONALLICENCE 773 0- Educational Studies in Mathematics Springer Netherlands 76/1(2011-01-01), 3-21 0013-1954 76:1<3 2011 76 10649 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer