Bereichsspezifische Beliefs zur Schulanalysis

Witzke, Ingo; Spies, Susanne

doi:10.1007/s13138-016-0106-4

Cited by 13 publications

(5 citation statements)

References 21 publications

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“…In this work, we are particularly interested in domain-specific beliefs (i.e., those that refer to a specific mathematical domain -in our case, calculus). The basis for our work can be traced back to the article "Domain-Specific Beliefs of School Calculus" by Witzke and Spies (2016). In this article, the authors discussed, among other things, that some domain-specific beliefs in school calculus are more dominant than others, according to the way calculus is taught at school and the way students receive and construct the knowledge.…”

Section: Beliefs For Enabling Perspectives On Calculusmentioning

confidence: 99%

“…The content is structured in terms of typical belief systems of mathematics according to different educational perspectives on calculus, namely, the formal-abstract perspective, the empirical-concrete perspective, the "toolbox" perspective, and the application perspective. These four perspectives are the result of a reduction of the orientations mentioned in the study by Witzke and Spies (2016) -the logical-structural orientation and the abstract-terminological orientation merge into the formal-abstract perspective, and the toolbox orientation and the symbolic orientation form the "toolbox" perspective. This is a subjective selection from the perspective of the authors of this paper, based on their experience with calculus teaching.…”

Section: Structure Of the Seminar And The Bookmentioning

confidence: 99%

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Beliefs-oriented subject-matter didactics

Dilling,

Stoffels,

Witzke

2024

LUMAT

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This paper presents a modified approach to subject-matter didactics, in which the focus is not on the content itself, but on the students' view of the content. The introduction deals with an overview of subject-matter didactics and the notion of beliefs used in this paper. The main portion of the paper deals with presenting the concepts of a book and a seminar based on the student-centered subject-matter didactics approach. For the first qualitative evaluation, selected reflections of students are analyzed. Finally, initial findings are summarized and an outlook is provided.

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Section: Beliefs For Enabling Perspectives On Calculusmentioning

confidence: 99%

Section: Structure Of the Seminar And The Bookmentioning

confidence: 99%

Beliefs-oriented subject-matter didactics

Dilling,

Stoffels,

Witzke

2024

LUMAT

Self Cite

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“…There are a lot of different descriptions and definitions of the belief concept in literature (Goldin, 2003;Green, 1971;Grigutsch, Raatz & Törner, 1998;Pajares, 1992;Schoenfeld, 1985;Stoffels, 2020;Thompson, 1992), furthermore a lot of research works mention that there is no consent on a definition of belief (Bräunling, 2017;Pehkonen, 1995;Rolka, 2006). Still, there seems to be no satisfactory answer to these theoretical problems; instead, a lot of research dealing with beliefs focus on exploring beliefs of different bearer groups, e.g., teachers and students (Törner, 2018), or the diversity of beliefs in different mathematical fields, establishing the concept of domain-specific beliefs (Eichler & Erens, 2015;Witzke & Spies, 2016).…”

Section: How To Frame (Researchers') Beliefs: Interaction Vs Reflectionmentioning

confidence: 99%

How to deal with and utilize (mathematics (education)) researchers’ beliefs

Stoffels

2024

LUMAT

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This paper addresses the desideratum identified by Törner (2018), that researchers' beliefs are rarely addressed in the research literature dealing with beliefs. For this purpose, firstly a suitable theoretical framework is outlined that links the concept of belief with the research perspectives of researchers. Secondly, examples are given of how beliefs were, can and should be addressed in corresponding research on beliefs. Finally, it is shown in which ways explicating beliefs of mathematics education researchers might made their research, as well as their teaching more effective.

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“…In a study on beliefs of school-calculus, Witzke and Spies (2016) were able to show that concepts such as continuity or differentiability are rarely used and understood by students. The development of such concepts can be supported by the 'embodied approach to the calculus' described by Tall (2013).…”

Section: The Software Graph Printer and 3d-printed Graphs Of Functionsmentioning

confidence: 99%

The Use of 3D-Printing Technology in Calculus Education: Concept Formation Processes of the Concept of Derivative with Printed Graphs of Functions

Dilling

Witzke

2020

Digit Exp Math Educ

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3D-printing technology has become increasingly important in recent years, offering many possibilities for mathematics teaching and learning. From our point of view, the field of calculus seems to be particularly suitable for the use of 3D-printing. Using the example of 3D-printed graphs of functions, the use of this technology in calculus is discussed within the three approaches of Grundvorstellungen, Subjective Domains of Experience and Empirical Theories. An empirical study, based on the qualitative content analysis according to Philipp Mayring, examines the influence of the models on concept formation processes in the context of derivatives. The focus is on the following research question: "What are the characteristics of concept formation processes of the concept of derivative in the context of 3D-printed graphs of functions?" Keywords 3D-printing. Derivative. Calculus. Grundvorstellung. Subjective domains of experience. Printed graphs of functions 3D-Printing in Mathematics Education 3D-printing technology is a relatively new tool with potential for mathematics education. It can be described as an additive manufacturing method allowing for digital models constructed with CAD-software to be transformed layer by layer into a real model made out of liquid plastic (see Gibson et al. 2014). Witzke and Hoffart (2018) detail three options for using the 3D-printing technology in the classroom. First, there is the possibility to reproduce Digital Experiences in Mathematics Education

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Bereichsspezifische Beliefs zur Schulanalysis

Cited by 13 publications

References 21 publications

Beliefs-oriented subject-matter didactics

Beliefs-oriented subject-matter didactics

How to deal with and utilize (mathematics (education)) researchers’ beliefs

The Use of 3D-Printing Technology in Calculus Education: Concept Formation Processes of the Concept of Derivative with Printed Graphs of Functions

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