Research, practice and theory in didactics of mathematics: Towards dialogue between different fields

Bartolini, Maria Giuseppina; Bazzini, Luciana

doi:10.1023/b:educ.0000006169.86495.49

Cited by 11 publications

(3 citation statements)

References 19 publications

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“…So, in a sense, historical research is moving away from a monolithic image of mathematics. Bartolini-Bussi and Bazzini (2003) describe also the problematic relationship between historians and didacticians. In some cases mathematics educators consider history as a solution of the problem of involving students in mathematics, thus the transposition into classrooms was carried out mainly relying on the glamour and neglecting a careful set up of methodologies and objectives.…”

Section: A Denser Geometric Progressionmentioning

confidence: 95%

Using History to Teach Mathematics: The Case of Logarithms

Panagiotou¹

2010

Sci & Educ

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Many authors have discussed the question why we should use the history of mathematics to mathematics education. For example, Fauvel (For Learn Math, 11(2): 3-6, 1991) mentions at least fifteen arguments for applying the history of mathematics in teaching and learning mathematics. Knowing how to introduce history into mathematics lessons is a more difficult step. We found, however, that only a limited number of articles contain instructions on how to use the material, as opposed to numerous general articles suggesting the use of the history of mathematics as a didactical tool. The present article focuses on converting the history of logarithms into material appropriate for teaching students of 11th grade, without any knowledge of calculus. History uncovers that logarithms were invented prior of the exponential function and shows that the logarithms are not an arbitrary product, as is the case when we leap straight in the definition given in all modern textbooks, but they are a response to a problem. We describe step by step the historical evolution of the concept, in a way appropriate for use in class, until the definition of the logarithm as area under the hyperbola. Next, we present the formal development of the theory and define the exponential function. The teaching sequence has been successfully undertaken in two high school classrooms.

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Section: A Denser Geometric Progressionmentioning

confidence: 95%

Using History to Teach Mathematics: The Case of Logarithms

Panagiotou¹

2010

Sci & Educ

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“…In addition, research objects in mathematics education are characterized by a high level of complexity, which is due to the interdisciplinary nature of the discipline (Wittmann 1995;Bartolini-Bussi and Bazzini 2003). Furthermore, the objects studied are characterized by different intra-or interpersonal relationships on micro (individual), meso (e.g., group, class, school) and macro level (e.g., country level or educational system).…”

Section: Special Features Of Mmr In Mathematics Educationmentioning

confidence: 99%

Planning and Conducting Mixed Methods Studies in Mathematics Educational Research

Buchholtz

2019

ICME-13 Monographs

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In this chapter, central ideas of Mixed Methods Research are presented in which qualitative and quantitative research methods are combined or integrated. In addition to the explanation of common Mixed Methods terminology, the chapter provides an overview of the most important aspects that must be reflected in the planning and conduction of a mixed-methodological research project. On the basis of considerations on the nature of the research object and specific conditions of mathematics education research, methodological aspects of the research question, research design and data analysis are described. The chapter concludes with considerations on the challenges of Mixed Methods, as well as recommendations on the step-by-step approach to a Mixed Methods Research project.

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“…(School) Practice and (content-related educational) science need to be seen as two relatively autonomous institutions and fields of work, between which there are no direct possibilities of influence or change (see about this Bartolini-Bussi & Bazzini, 2003;Krainer, 2003;Scherer & Steinbring, 2006;Steinbring, 1994Steinbring, , 1998a. Each of the two fields is subject to its own expectations and aims, as well as to system-internal requirements and norms, which cannot be invalidated from the outside in order to apparently be able to directly interfere into and to purposefully regulate within the other field.…”

Section: Mathematics Education Research and Mathematicalmentioning

confidence: 99%

Changed views on mathematical knowledge in the course of didactical theory development—independent corpus of scientific knowledge or result of social constructions?

Steinbring

2008

ZDM Mathematics Education

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The study tries to show one line of how the German didactical tradition has evolved in response to new theoretical ideas and new-empirical-research approaches in mathematics education. First, the classical mathematical didactics, notably 'stoffdidaktik' as one (besides other) specific German tradition are described. The critiques raised against 'stoffdidaktik' concepts [for example, forms of 'progressive mathematisation', 'actively discovering learning processes' and 'guided reinvention' (cf. Freudenthal, Wittmann)] changed the basic views on the roles that 'mathematical knowledge', 'teacher' and 'student' have to play in teaching-learning processes; this conceptual change was supported by empirical studies on the professional knowledge and activities of mathematics teachers [for example, empirical studies of teacher thinking (cf. Bromme)] and of students' conceptions and misconceptions (for example, psychological research on students' mathematical thinking). With the interpretative empirical research on everyday mathematical teaching-learning situations (for example, the work of the research group around Bauersfeld) a new research paradigm for mathematics education was constituted: the cultural system of mathematical interaction (for instance, in the classroom) between teacher and students.

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Research, practice and theory in didactics of mathematics: Towards dialogue between different fields

Cited by 11 publications

References 19 publications

Using History to Teach Mathematics: The Case of Logarithms

Using History to Teach Mathematics: The Case of Logarithms

Planning and Conducting Mixed Methods Studies in Mathematics Educational Research

Changed views on mathematical knowledge in the course of didactical theory development—independent corpus of scientific knowledge or result of social constructions?

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