Abstract
In this paper we describe and discuss how mathematical values influence researchers’ choices when practicing mathematics. Our paper is based on a qualitative investigation of mathematicians’ practices, and its goal is to gain an empirically grounded understanding of mathematical values. More specifically, we will analyze the values connected to mathematicians’ choice of problems and their choice of argumentative style when communicating their results. We suggest that these two situations can be understood as relating to the three mathematical values: recognizability, formalizability and believability. Furthermore, we discuss three meta-issues concerning the general nature of mathematical values, namely (1) the origin of mathematical values, (2) the extent to which different values change over time and (3) the situatedness of mathematical values; that is the extent to which mathematical values depend on the specific context in which you are located. We conclude the chapter by recommending a methodological pluralism in future investigations of mathematical values.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barany, M. J. & MacKenzie, D. (2014). Chalk: Materials and concepts in mathematics research. In C. Coopmans, M. Lynch, J. Vertesi & S. Woolgar (Eds.), Representation in scientific practice revisited (pp. 107–129). Cambridge, MA: The MIT Press.
Bishop, A. J. (this volume). What would the mathematics curriculum look like if instead of concepts and techniques, values were the focus?
Burton, L. (2004). Mathematicians as enquirers: Learning about learning mathematics. Boston: Kluwer Academic Publishers.
Charmaz, K. (2006). Constructing grounded theory. London, Thousand Oaks: Sage Publications.
Ernest, P. (2016). Mathematics and values.
Ferreirós, J. (this volume). Purity as a value in the German-speaking area.
Geist, C., Löwe, B. & Kerkhove, B. V. (2010). Peer review and knowledge by testimony in mathematics. In B. Löwe & T. Müller (Eds.). Philosophy of mathematics: Sociological aspects and mathematical Practice PhiMSAMP (pp. 155–178). Texts in Philosophy 11, London: College Publications.
Greiffenhagen, C. W. K. (2014). The materiality of mathematics: Presenting mathematics at the blackboard. The British Journal of Sociology, 65(3), 502–528.
Hersh, R. (1991). Mathematics has a front and a back. Synthese, 88(2), 127–133.
Hilbert, D. (1902). Grundlagen der Geometrie. Unpublished lectures, Göttingen: Mathematisches Institut.
Inglis, M. & Aberdein, A. (this volume). Diversity in proof appraisal.
Inglis, M., & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43(4), 358–390.
Inglis, M., Mejia-Ramos, J.-P., Weber, K., & Alcock, L. (2013). On mathematicians’ different standards when evaluating elementary proofs. Topics in Cognitive Science, 5, 270–282.
Johansen, M. W. (2013). What’s in a diagram? On the classification of symbols, figures and diagrams. In L. Magnani (Ed.), Model-Based Reasoning in Science and Technology. Theoretical and Cognitive Issues (pp. 89–108). Heidelberg: Springer.
Johansen, M. W. & Misfeldt, M. (2014). Når matematikere undersøger matematik—og hvilken betydning det har for undersøgende matematikundervisning. MONA, 2014(4), 42–59.
Mancosu, P. (2005). Visualization in logic and mathematics. In P. Mancosu, K. F. Jørgensen & S. A. Pedersen (Eds.), Visualization, explanation and reasoning styles in mathematics (pp. 13–30). Dordrecht: Springer.
Misfeldt, M. (2005). Media in mathematical writing. For the Learning of Mathematics, 25(2), 36–42.
Misfeldt, M. (2011). Computers as medium for mathematical writing. Semiotica, 186, 239–258.
Misfeldt, M. & Johansen, M. W. (2015). Research mathematicians’ practices in selecting mathematical problems. Educational Studies in Mathematics, 89(3), 357–373.
Müller-Hill, E. (2011). Die epistemische Rolle formalisierbarer mathematischer Beweise. Formalisierbarkeitsorientierte Konzeptionen mathematischen Wissens und mathematischer Rechtfertigung innerhalb einer sozio-empirisch informierten Erkenntnistheorie der Mathematik. Bonn: Rheinischen Friedrich-Wilhelms-Universität i Bonn. Ph.D. Dissertation. Retrieved 18. sep. 2014 from: http://hss.ulb.uni-bonn.de/2011/2526/2526.pdf.
Pasch, M. & Dehn, M. (1926 [1882]). Vorlesungen über neuere Geometrie. (2nd ed.) Die Grundlehren der mathematischen Wissenschaften 23, Berlin: Springer.
Strauss, A. L., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park: Sage Publications.
Sundström, R. (this volume). The notion of fit as a mathematical value.
Tymoczko, T. (1979). The four-color problem and its philosophical significance. The Journal of Philosophy, 76(2), 57–83.
Weber, K. (2013). On the sophistication of naïve empirical reasoning: Factors influencing mathematicians’ persuasion ratings of empirical arguments. Research in Mathematics Education, 15, 100–114.
Weber, K., Inglis, M., & Mejia-Ramos, J.-P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition. Educational Psychologist, 49, 36–58.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Johansen, M.W., Misfeldt, M. (2016). An Empirical Approach to the Mathematical Values of Problem Choice and Argumentation. In: Larvor, B. (eds) Mathematical Cultures. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-28582-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-28582-5_15
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-28580-1
Online ISBN: 978-3-319-28582-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)