The design of a mathematics course. A theoretical reflection

Streefland, Leen

doi:10.1007/bf01274105

Cited by 32 publications

(8 citation statements)

References 6 publications

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“…This after image may foster reflection, which in turn may lead to the insight that the model can be used for other problem situations. The model has become a 'pre-image ('voorbeeld' in Dutch) that is used for reasoning about other situations (which he in later publications expands with supporting abstracting and level raising (Streefland, 1992(Streefland, , 1993.…”

Section: Emergent Modellingmentioning

confidence: 99%

A Socio-Constructivist Elaboration of Realistic Mathematics Education

Gravemeijer

2020

ICME-13 Monographs

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This chapter describes a socio-constructivist elaboration of Realistic Mathematics Education (RME) that emerged from my collaboration with Paul Cobb and Erna Yackel. It is argued that RME and socio-constructivism are compatible and complement each other. Socio-constructivism points to the critical role of the classroom culture, while RME offers a theory on supporting students in (re-)constructing mathematics. Furthermore, the role of symbols and models is discussed, which was considered problematic in constructivist circles, while being central in RME. The emergent modelling design heuristic is presented as a solution to this puzzle. Together, guided reinvention, didactical phenomenology, and emergent modelling, are combined to delineate RME as an instructional design theory. This is complemented by a discussion of pedagogical content tools as counter parts of the emergent modelling and guided reinvention design heuristics at the level of classroom instruction. Finally, research on student learning and enactment of RME in Dutch classrooms is discussed.

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Section: Emergent Modellingmentioning

confidence: 99%

A Socio-Constructivist Elaboration of Realistic Mathematics Education

Gravemeijer

2020

ICME-13 Monographs

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“…In this study, the teacher did not realize the importance of facilitating students to go through various levels of understanding, namely: from solving real problems with informal strategies and finding patterns and forming insights about how concepts and strategies are interrelated. This process inspires students to use useful models or symbols to bridge the gap between informal and more formal mathematics [24][25][26]. Mathematical formula or procedure which is the ultimate goal of learning and known as formal knowledge should be achieved by students gradually [9].…”

Section: The Fifth Characteristic: Intertwinementmentioning

confidence: 99%

Teachers’ understanding about the characteristics of realistic mathematics education

et al. 2020

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The application of Realistic mathematics education (RME) in schools has not satisfied. The efforts of educators to help teachers implement RME are an ongoing process, including by providing examples of learning process through the video lessons. This study aims to investigate teacher understanding of the characteristics of RME through watching video lessons. Three elementary school teachers in Aceh, Indonesia, were involved in this research. Data was collected through questionnaires and semi-structured interviews. Data were analyzed descriptively. The results showed that the teacher did not understand three of the five characteristics of RME. Teachers' understanding of real problems is only limited to the use of concrete objects. The teacher could not identify activities on the video about using models or symbols to scaffold students from concrete to more formal knowledge. The teacher also did not realize that the relationship between mathematical concepts can help students understand mathematics well. The implication of this study is that researchers need to guide the teacher design the learning trajectory before watching learning from other teachers. After watching the whole video lessons, the teacher also needs to be moved to identify important events related to the characteristics of RME in the learning in the video.

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“…Again, the work of Streefland (1985Streefland ( , 1993 and his notion of progression from 'model of' to 'model for' was crucial here. Although as teachers we came to re-define how we saw progression, we struggled to articulate this within the U.K. curriculum.…”

Section: Didactic Practice In England and In Rme: Pressure To Move Tomentioning

confidence: 99%

Intervening with Realistic Mathematics Education in England and the Cayman Islands—The Challenge of Clashing Educational Ideologies

Dickinson

Eade

Gough

et al. 2019

International Reflections on the Netherlands Didactics of Mathematics

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In this chapter, we discuss the issue of implementing Realistic Mathematics Education (RME) in the English education system over a number of years and education sectors. We also consider the experience of one of us in the Cayman Islands, a British overseas territory with an education system that is influenced by British tradition, but is distant from many of its politically driven accountability pressures and measures. We illustrate first the challenges of developing an RME approach which is operable within the English system, highlighting the issues of student expectation, dominant didactic practices and assessment, all of which influenced what we were able to do. Second, we describe the outcomes of interventions in England at early secondary school level (age 12-14, Key Stage 3) and at General Certificate of Secondary Education (GCSE) level (normally age 15-16, Key Stage 4, but also available in post-16 education). Finally, Frank Eade describes his experience of building on our early work to develop an RME approach in the Cayman Islands. We conclude with a discussion of the lessons learned from these challenges. We argue that despite the problems we encountered there are reasons to remain optimistic about the potential of an RME approach in the English system.English mathematics education traditions have had a well-documented impact on classroom cultures and on student experiences and expectations, all of which present challenges for the implementation and impact of an RME approach. In particular, student performance in public examinations is used in systems of school measurement and accountability, often leading to 'transmissionist' classroom cultures that empha-

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The design of a mathematics course. A theoretical reflection

Cited by 32 publications

References 6 publications

A Socio-Constructivist Elaboration of Realistic Mathematics Education

A Socio-Constructivist Elaboration of Realistic Mathematics Education

Teachers’ understanding about the characteristics of realistic mathematics education

Intervening with Realistic Mathematics Education in England and the Cayman Islands—The Challenge of Clashing Educational Ideologies

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