Students’ individual schematization pathways - empirical reconstructions for the case of part-of-part determination for fractions

Glade, Matthias; Prediger, Susanne

doi:10.1007/s10649-016-9716-5

Cited by 13 publications

(8 citation statements)

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“…The analytic findings contributed to the local instruction theory about progressively schematizing multiplication of fractions (more details in Glade & Prediger, 2017). Rather than conceptualizing progressive schematization only as loss of external representations, the external representations are semiotically contracted by successive compacting of the involved structures and concepts.…”

Section: Identifying Deeper Challenges and Generating Hypotheses By Dmentioning

confidence: 86%

“…In a design research methodology, Glade and Prediger (2017) conducted design experiments with 18 sixth graders in pairs in order to investigate their learning pathways from a graphical part-of-part determination in area models via Fig. 4 Active organizing task structuring the regularizing and preserving process (Prediger et al 2013, p. 52) progressive schematization of their graphical strategies to the discovery of the procedural rule (see Fig.…”

Section: Identifying Deeper Challenges and Generating Hypotheses By Dmentioning

confidence: 99%

“…The subsequent design research endeavors (e.g., on students' progressive schematization processes, Treffers, 1987) provided deeper insights on typical conditions of success for regularizing (Glade & Prediger, 2017;Prediger & Pöhler, 2015). Two hypotheses were formulated on how to regularize from students' ideas to regular mathematics: Hypothesis 1 focused the need for permanent verbalization of meanings and structures and Hypothesis 2 on the elaboration on correct and incorrect solutions relevant for conceptual change.…”

Section: Summary and Limitations Of The Presented Snapshots From The mentioning

confidence: 99%

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Towards a research base for textbooks as teacher support: the case of engaging students in active knowledge organization in the KOSIMA project

Prediger

Barzel

Hußmann

et al. 2021

ZDM Mathematics Education

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Engaging students in processes of mathematizing and active knowledge organization (instead of telling and rehearsing ready-made mathematics) is a key demand for high quality mathematics instruction. Although many mathematically rich context problems have been designed and published in textbooks, their impact on regular mathematics classrooms remains limited, as teachers face challenges in shaping and enacting the important phase of knowledge organization. The 15-year project KOSIMA presented in this paper was aimed at supporting teachers in really enhancing these processes by means of a textbook for Grades 5–10. The paper provides an overview of different studies conducted during the project in order to show how the project developed a research base for the support of teachers. The paper also shows that different research approaches need to be combined to establish an appropriate research base: In iterative design research cycles of topic-specific didactical design research, learning environments were designed and investigated with the aim of understanding the obstacles encountered in implementing the desired processes. In this paper, we focus on an example of one particular obstacle, namely, teachers’ need of support in engaging students in processes of active knowledge organization. This obstacle was overcome by developing new types of tasks for active knowledge organization. The theoretical outcome of the design research resulted in two hypotheses for improving relevant features of the design of these tasks, which were tested in two controlled trials. Finally, a longitudinal field study of 312 students gave first indications that the classes that worked with the textbook had significantly higher learning gains than classes using other textbooks. In sum, we can show that textbooks can support changes in classroom practices when the obstacles that occur for both teachers and students are carefully investigated and treated.

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Section: Identifying Deeper Challenges and Generating Hypotheses By Dmentioning

confidence: 86%

Section: Identifying Deeper Challenges and Generating Hypotheses By Dmentioning

confidence: 99%

Section: Summary and Limitations Of The Presented Snapshots From The mentioning

confidence: 99%

See 1 more Smart Citation

Towards a research base for textbooks as teacher support: the case of engaging students in active knowledge organization in the KOSIMA project

Prediger

Barzel

Hußmann

et al. 2021

ZDM Mathematics Education

Self Cite

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show abstract

“…Although RME hence attaches great value to the theoretical equality of horizontal and vertical mathematisation, there have also been phases in the development of RME where there was a tendency to focus on engaging with questions of horizontal mathematisation (see Van den Heuvel-Panhuizen, 2002). Even today, the research into vertical mathematisation appears to be paid less attention in international mathematical didactics than is the case with horizontal mathematisation (see Glade & Prediger, 2017). Therefore, the focus in this chapter will be on aspects of vertical mathematisation.…”

Section: The Guiding Principle Of Progressive Mathematisationmentioning

confidence: 99%

International Reflections on the Netherlands Didactics of Mathematics

2020

ICME-13 Monographs

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use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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“…The exemplary project explores a well-known design principle: progressive schematization (Treffers 1987), according to which learning trajectories towards procedural rules can be organized as independent discoveries when the learning environment invites the students first to develop models for mathematical concepts and model-based informal strategies; then to explore the strategies and to discover pattern for progressively developing procedural rules. The project (Glade and Prediger 2017) contributed to the theoretical and empirical foundation of the design principle of progressive schematization by empirically investigating students' individual schematization pathways on the micro-level for the specific case of part-of-part determination of fractions (see Fig. 3.14).…”

Section: Illustration Of Research Outcomes For a Typical Project: Expmentioning

confidence: 99%

Design Science and Design Research: The Significance of a Subject-Specific Research Approach

et al. 2019

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Considering mathematics education as a DESIGN SCIENCE has strong roots in Germany. E. Ch. Wittmann in particular contributed to the establishment of this approach. From a DESIGN SCIENCE perspective, substantial learning environments play a crucial role. They comprise mathematical tasks which are connected in an operative way, indicative of a specific epistemological structure. In such substantial learning environments, students are actively immersed in learning mathematics, and the learning environments allow for the pursuit of individual and differentiated learning processes. In this chapter, we first address the scope of Design Science and pay attention to characteristics of the learning environments and how teaching experiments can be conducted. We then focus on key ideas and their role as a design principle. In the next section, we provide a comprehensive example of designing a learning environment. Lastly, we shift our attention to the Design Research approach, which complements designing substantial learning environments by empirically studying the initiated learning processes to gain evidence for both theoretical considerations and design principles.

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Students’ individual schematization pathways - empirical reconstructions for the case of part-of-part determination for fractions

Cited by 13 publications

References 10 publications

Towards a research base for textbooks as teacher support: the case of engaging students in active knowledge organization in the KOSIMA project

Towards a research base for textbooks as teacher support: the case of engaging students in active knowledge organization in the KOSIMA project

International Reflections on the Netherlands Didactics of Mathematics

Design Science and Design Research: The Significance of a Subject-Specific Research Approach

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