“Grundvorstellungen” as a Category of Subject-Matter Didactics View Full Text


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Article Info

DATE

2016-07

AUTHORS

Rudolf vom Hofe, Werner Blum

ABSTRACT

One of the central issues that has long captivated research efforts in mathematical education concerns the question of what mental representations people have of mathematical content. That is, what meaning do people associate with mathematical content, and what role do these mental representations play in teaching and learning mathematics? To this end, a number of different categories concerning mental representations have been developed, including, e. g. “intuition”, “use meaning” or “concept image”. One approach, stemming from the German Stoffdidaktik (subject-matter didactics) tradition, is constituted by the didactic category of Grundvorstellung(en). In this contribution we begin by investigating the origins and the development of the concept of Grundvorstellung in the German-speaking research literature on mathematics education. Then, we summarize the main ideas of the concept, particularly concerning its normative, descriptive, and constructive use as well as the distinction between primary and secondary Grundvorstellungen. Following this, a number of typical areas of application will be considered. We will then discuss the use of Grundvorstellungen in the construction and classification of items for quantitative assessment, as well as the role of Grundvorstellungen as a descriptive and explanatory category in empirical classroom research. More... »

PAGES

225-254

References to SciGraph publications

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  • 2004. Grundvorstellungen als aufgabenanalytisches und diagnostisches Instrument bei PISA in MATHEMATISCHE KOMPETENZEN VON SCHÜLERINNEN UND SCHÜLERN IN DEUTSCHLAND
  • 2015. Grundvorstellungsumbrüche beim Übergang zur 3D-Geometrie in GEOMETRIE ZWISCHEN GRUNDBEGRIFFEN UND GRUNDVORSTELLUNGEN
  • 2015-09. Inhibitory control in mathematical thinking, learning and problem solving: a survey in ZDM
  • 2015. Geometrische Darstellungen als Vorstellungsgrundlage für algebraische Operationen am Beispiel der negativen Zahlen in GEOMETRIE ZWISCHEN GRUNDBEGRIFFEN UND GRUNDVORSTELLUNGEN
  • 2012. Proportionalität und Prozentrechnung in der Sekundarstufe I, Empirische Untersuchung und didaktische Analysen in NONE
  • 2005-06. With a focus on ‘Grundvorstellungen’ Part 1: a theoretical integration into current concepts in ZDM
  • 1999-03. Intuitive rules: A way to explain and predict students' reasoning in EDUCATIONAL STUDIES IN MATHEMATICS
  • 1991-04. Preformal proving: Examples and reflections in EDUCATIONAL STUDIES IN MATHEMATICS
  • 2009. Didaktik der Bruchrechnung in NONE
  • 2015. Analysis: Leitidee Zuordnung und Veränderung in HANDBUCH DER MATHEMATIKDIDAKTIK
  • 2005-06. With a focus on ‘Grundvorstellungen’ Part 2: ‘Grundvorstellungen’ as a theoretical and empirical criterion in ZDM
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    URI

    http://scigraph.springernature.com/pub.10.1007/s13138-016-0107-3

    DOI

    http://dx.doi.org/10.1007/s13138-016-0107-3

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