Developing Mathematics Education in a Systemic Process

Wittmann, Erich Ch.

doi:10.1007/978-94-010-9046-9_5

Cited by 12 publications

(22 citation statements)

References 10 publications

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“…Pepin et al (2013) note that there have been a number of proposals to define 'design research' in mathematics education (e.g. Wittmann 1995Wittmann , 2001) and point to the work of the Freudenthal Institute in the Netherlands (e.g. Gravemeijer 1993;Gravemeijer and Cobb 2006); work in the USA (e.g.…”

Section: Task 'Design' In Mathematics Educationmentioning

confidence: 99%

Research on mathematics teachers as partners in task design

Jones

Pepin

2016

J Math Teacher Educ

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Mathematical tasks and tools, including tasks in the form of digital tools, are key resources in mathematics teaching and in mathematics teacher education. Even so, the 'design' of mathematical tasks is perceived in different ways: sometimes seen as something distinct from the teaching and learning process, and sometimes as integral to it. Whilst task design has often been carried out by designers or mathematicians (perhaps as textbook authors), the focus for this review article is research that has involved mathematics teachers as partners in the design of tasks. The article provides a state-of-the-art review of relevant literature and is presented under three headings that consider, in turn, the role of mathematical 'tasks'; the nature of 'task design'; and the notion of 'partnerships for task design' in mathematics education. Subsequently, we present current research that is providing new insights into tasks, task design, and task design partnership. Based on this, we argue that 'task design' needs to pay particular attention to what to design, which tools are necessary or beneficial, and under what conditions; digital tools and task resources offer particular affordances that traditional resources cannot provide; and not only do teachers benefit from being partners in task design (in terms of their professional learning) but without their involvement some aspects of task design would most likely be neglected.

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Section: Task 'Design' In Mathematics Educationmentioning

confidence: 99%

Research on mathematics teachers as partners in task design

Jones

Pepin

2016

J Math Teacher Educ

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“…The constitutive characteristics of natural differentiation are embedded in theoretical concepts of math education which are widespread (not only) in German schools and teacher education, namely discovery learning (Bruner 1961;Winter 2016), productive practicing (Winter 1984;Wittmann 1992), and substantial learning environments (Wittmann 1984(Wittmann , 2001a(Wittmann , 2004.…”

Section: Natural Differentiation-a Redefined Answermentioning

confidence: 99%

Invited Lectures from the 13th International Congress on Mathematical Education

et al. 2018

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“…Constructivist and socio-constructivist theories open ways of viewing "knowing" (Ernest, 1994;Von Glasersfeld, 1995) and learning in a social environment (e.g., Wittmann, 2001). For mathematics education, investigative learning and productive practicing are seen as the main elements of these paradigms (e.g., Wittmann, 2001).…”

Section: Substantial and Rich Learning Environments-multiple Opportunmentioning

confidence: 99%

“…For mathematics education, investigative learning and productive practicing are seen as the main elements of these paradigms (e.g., Wittmann, 2001). Productive practicing is to be understood in contrast to bare reproduction of knowledge.…”

Section: Substantial and Rich Learning Environments-multiple Opportunmentioning

confidence: 99%

“…Research shows that learning environments that allow natural differentiation (ND) can reduce these risks (cf. Wittmann, 2001;Scherer & Krauthausen, 2010). Natural differentiation means that the learning environment provided is substantial and complex and offers multiple ways of learning and multiple strategies for solving a given problem.…”

Section: Substantial and Rich Learning Environments-multiple Opportunmentioning

confidence: 99%

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Assistance of Students with Mathematical Learning Difficulties—How Can Research Support Practice?—A Summary

Scherer

Beswick

DeBlois

et al. 2017

Proceedings of the 13th International Congress on Mathematical Education

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When looking at teaching and learning processes in mathematics education students with mathematical learning difficulties or disabilities are of great interest. To approach the question of how research can support practice, an important step is to clarify the group or groups of students that we are talking about. The following contribution firstly concentrates on the problem of labelling the group of students having mathematical difficulties as there does not exist a single definition. This problem might be put down to the different roots of mathematics education on the one hand and special education on the other hand. Research results with respect to concepts and models for instruction are multifaceted and related to specific content and mathematical topics as well as underlying views of mathematics. Taking into account inclusive education, a closer orientation to mathematical education can be identified and the potential of selected teaching and learning concepts can be illustrated. Beyond this, the role of the teacher and the corresponding teacher education programs are discussed.

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Developing Mathematics Education in a Systemic Process

Cited by 12 publications

References 10 publications

Research on mathematics teachers as partners in task design

Research on mathematics teachers as partners in task design

Invited Lectures from the 13th International Congress on Mathematical Education

Assistance of Students with Mathematical Learning Difficulties—How Can Research Support Practice?—A Summary

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