Approaches to qualitative research in mathematics education: examples of methodology and methods

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Resumen Este estudio está enmarcado en la argumentación matemática en el salón de clases. Tuvo como propósito identificar funciones que cumple la refutación de aserciones en argumentaciones colectivas. Esto se llevó a cabo mediante la implementación de un enfoque teórico metodológico fundamentado en el modelo argumentativo de Toulmin (2003), el cual permitió el estudio de las argumentaciones colectivas y sus estructuras dentro del salón de clases. Conjunto con lo establecido en la teoría se encontró cómo la refutación tiene un poder persuasivo sobre los argumentos de los estudiantes, ésta otra función de la refutación.
Qualitative research methods in mathematics education. Monograph 9
  • A R Teppo
Qualitative empirical methods in mathematics education -Discussions and reflections
  • G Kaiser
Kaiser, G. (Ed.). (2003a). Qualitative empirical methods in mathematics education -Discussions and reflections -Volume 1 [Special Issue]. Zentralblatt für Didaktik der Mathematik, 35(5), 188-232.
Theoretical categories for investigations in the social history of mathematics education and some characteristic patterns
  • G Schubring
Schubring, G. (1989). Theoretical categories for investigations in the social history of mathematics education and some characteristic patterns. In C. Keitel (Ed.), Mathematics, education, and society (pp. 6-8). Paris: UNESCO.
A history of school mathematics, 2 Volumes
  • G Stanic
Stanic, G. (ed). (2003). A history of school mathematics, 2 Volumes. Reston, VA: NCTM.
Fried Ben Gurion University of the Negev ?
  • N Michael
Michael N. Fried Ben Gurion University of the Negev ? 2015, Michael N. Fried
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Die Vernachl?ssigung der Kausalkategorie in der qualitativen Sozialforschung ist hochgradig problematisch, da die Kategorie der Kausalit?t mit dem Konzept sozialen Handelns eng verknüpft ist. Ohne Zweifel ist aber in sozialwissenschaftlichen Gegenstandsbereichen die Analyse von Kausalbeziehungen mit besonderen Schwierigkeiten und methodologischen Herausforderungen belastet, die in dem Beitrag mit Hilfe von Mackies Konzept der “INUS”-Bedingungen diskutiert werden. Diese Probleme lassen sich mit den beiden bislang für die qualitative Forschung vorgeschlagenen Verfahren der Kausal-analyse auf der Basis komparativer Methoden, der “Analytischen Induktion” und der “Qualitativen Komparativen Analyse” allein nur sehr unvollkommen bearbeiten, vielmehr erfordern sie eine Verbindung fallkontrastierender Methoden mit explorativen Forschungsstrategien, die das lokale Akteurswissen im Feld als Ressource zur Entdeckung bislang unbekannter Handlungsbedingungen nutzt. The disregard of causal inference in the methodological literature about qualitative research is highly problematic, since the category of causality is closely linked to the concept of social action. However, it is also clear that causal analysis is burdened with certain difficulties and methodological challenges in the realm of social research. Some of these problems are discussed in this article using Mackie—s concept of 3 “INUS”-conditions. Thereby it will be shown that strategies of causal analysis based on comparative methods proposed for qualitative research, namely “Analytic Induction” and “Qualitative Comparative Analysis” have great difficulties in dealing adequately with these problems. They can only be solved, if case-comparative methods are combined with explorative research strategies which support the researcher in gaining access to the local knowledge of the research field.
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This paper is a commentary on the problem of networking theories. My commentary draws on the papers contained in this ZDM issue and is divided into three parts. In the first part, following semiotician Yuri Lotman, I suggest that a network of theories can be conceived of as a semiosphere, i.e., a space of encounter of various languages and intellectual traditions. I argue that such a networking space revolves around two different and complementary “themes”—integration and differentiation. In the second part, I advocate conceptualizing theories in mathematics education as triplets formed by a system of theoretical principles, a methodology, and templates of research questions, and attempt to show that this tripartite view of theories provides us with a morphology of theories for investigating differences and potential connections. In the third part of the article, I discuss some examples of networking theories. The investigation of limits of connectivity leads me to talk about the boundary of a theory, which I suggest defining as the “limit” of what a theory can legitimately predicate about its objects of discourse; beyond such an edge, the theory conflicts with its own principles. I conclude with some implications of networking theories for the advancement of mathematics education.