Grundfragen des Mathematikunterrichts

Wittmann, Erich Ch.

doi:10.1007/978-3-322-91539-9

Cited by 67 publications

(28 citation statements)

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“…The EIS principle is part of almost all German mathematics education textbooks. Information on the mathematics education learning contents paralleled the respective German mathematics education literature applied later in the participants’ teacher education programs (Wittmann, 1981; Hasemann, 1986; Hefendehl-Hebeker, 1996; Zech, 1996; Padberg, 2009; Eichelmann et al, 2012). …”

Section: Methodsmentioning

confidence: 99%

Integrated learning: ways of fostering the applicability of teachersâ€™ pedagogical and psychological knowledge

2015

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In teacher education, general pedagogical and psychological knowledge (PPK) is often taught separately from the teaching subject itself, potentially leading to inert knowledge. In an experimental study with 69 mathematics student teachers, we tested the benefits of fostering the integration of pedagogical content knowledge (PCK) and general PPK with respect to knowledge application. Integration was fostered either by integrating the contents or by prompting the learners to integrate separately taught knowledge. Fostering integration, as compared to a separate presentation without integration help, led to more applicable PPK and greater simultaneous application of PPK and PCK. The advantages of fostering knowledge integration were not moderated by the student teachers’ prior knowledge or working memory capacity. A disadvantage of integrating different knowledge types referred to increased learning times.

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Section: Methodsmentioning

confidence: 99%

Integrated learning: ways of fostering the applicability of teachersâ€™ pedagogical and psychological knowledge

2015

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“…The question arises of how this reform model has been received and implemented by mathematics teachers in the German-speaking part of Switzerland. To assess how familiar these teachers are with didactic principles and reform initiatives, the teacher questionnaire administered to the teachers of the TIMSS 1999 Video Study sample in the context of the Swiss Video Study included a question asking how often they organized their lessons according to three didactic principles: (1) operative didactics ([guided]) problem-based knowledge construction; e.g., Aebli, 1983;Wittmann, 1981); (2) the genetic-socratic exemplary approach (e.g., Wagenschein, 2008) and (3) the model of extended forms of teaching and learning (ETL). As Fig.…”

Section: The Role Of Instructional Reformmentioning

confidence: 99%

Expertise in Mathematics Instruction: Advancing Research and Practice from an International Perspective

Kaiser

2010

Expertise in Mathematics Instruction

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This chapter draws on data and findings from several video studies to describe the quality of mathematics teaching in Switzerland. The focus is on features of instructional practice and quality as core components of classroom behavior that reflect the teacher's expertise in creating optimal learning opportunities. The didactic triangle is used as the basis for describing the profile of expertise in Swiss mathematics instruction in terms of three interdependent dimensions of instructional quality. A core element of this pofile can be identified in Swiss mathematics teachers' particular strengths in the culture of communication, support and relationships. Findings also paint a generally positive picture of the culture of teaching, learning and understanding (e.g., methods and choreography of teaching) in Swiss mathematics classrooms. However, the culture of objectives, materials and tasks proves to be rather average in international comparison in several respects (level of mathematical content, characteristics of the problems set and the way they are worked on in lessons). In particular, there seems to be room for improvement in the specific context of the didactics of mathematics (e.g., the level of cognitive and mathematical challenge) Abstract This chapter draws on data and findings from several video studies to describe the quality of mathematics teaching in Switzerland. The focus is on features of instructional practice and quality as core components of classroom behavior that reflect the teacher's expertise in creating optimal learning opportunities. The didactic triangle is used as the basis for describing the profile of expertise in Swiss mathematics instruction in terms of three interdependent dimensions of instructional quality. A core element of this profile can be identified in Swiss mathematics teachers' particular strengths in the culture of communication, support and relationships. Findings also paint a generally positive picture of the culture of teaching, learning and understanding (e.g., methods and choreography of teaching) in Swiss mathematics classrooms. However, the culture of objectives, materials and tasks proves to be rather average in international comparison in several respects (level of mathematical content, characteristics of the problems set and the way they are worked on in lessons). In particular, there seems to be room for improvement in the specific context of the didactics of mathematics (e.g., the level of cognitive and mathematical challenge).

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“…Wittmann pleaded for considering mathematics education as not a mere addition of different areas like mathematics, pedagogy, psychology or others, but as a scientific discipline on its own, with its own specific problems and aims (e.g. Wittmann 1974;Wittmann 1995). Through many years and up to the present day, Wittmann has always worked on defining this specific characterisation of mathematics education as a 'design science' with explicit reference to the Nobel Laureate Herbert A. Simon (cf.…”

Section: Mathematics Education As a Design Sciencementioning

confidence: 99%

On the Importance of Subject Matter in Mathematics Education: A Conversation with Erich Christian Wittmann

Akinwunmi

Höveler

Schnell

2014

EURASIA J MATH SCI T

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Particularly in the second half of the 20th century, historical approaches became Erich Christian Wittmann is one of the primary founders of mathematics education research as an autonomous field of work and research in Germany. The interview reflects on his role in promoting mathematics education as a design science and its consequences as well as his view on current developments within the discipline and his activities.

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Grundfragen des Mathematikunterrichts

Cited by 67 publications

References 0 publications

Integrated learning: ways of fostering the applicability of teachersâ€™ pedagogical and psychological knowledge

Integrated learning: ways of fostering the applicability of teachersâ€™ pedagogical and psychological knowledge

Expertise in Mathematics Instruction: Advancing Research and Practice from an International Perspective

On the Importance of Subject Matter in Mathematics Education: A Conversation with Erich Christian Wittmann

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