Grundvorstellungen mathematischer Inhalte als didaktisches Modell

Hofe, Rudolf vom

doi:10.1007/bf03338785

Cited by 36 publications

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“…Typically, metaphors are arrows going upwards, from a down-to-earth domain to a more abstract one, and representations are arrows going downwards, i.e., the other way around. In this connection, it is pertinent to recall that in the German school of didactics of mathematics, originally mostly concerned with primary mathematics education and going back to Pestalozzi (Herbart 1804;vom Hofe 1995), representation and metaphor were quite present: as Darstellung-representation aiming at explaining something to others-and Vorstellung-a personal way to figure out or fathom something, operationally equivalent to metaphor (Soto-Andrade and Reyes-Santander 2011). So metaphorising was already recognised and appreciated at the beginning of the 19th century in German didactics of mathematics, well before its irruption from cognitive psychology and linguistics into mathematics education (Lakoff and Núñez 2000).…”

Section: Metaphorising In Mathematical Educationmentioning

confidence: 99%

Enactive Metaphorising in the Learning of Mathematics

Soto-Andrade

2018

Invited Lectures From the 13th International Congress on Mathematical Education

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We argue that an approach to the learning of mathematics based on enactive (bodily acted out) metaphorising may significantly help in alleviating the cognitive abuse millions of children worldwide suffer when exposed to mathematics. We present illustrative examples of enactive metaphoric approaches in the context of problem posing and solving in mathematics education, involving geometry and randomness, two critical subjects in school mathematics. Our examples show to what extent the way a mathematical situation is metaphorised and enacted by the learners shapes their emerging ideas and insights and how this may help to bridge the gap between the 'mathematically gifted' and those apparently not so gifted or mathematically inclined. Our experimental background includes a broad spectrum of prospective secondary math teachers, in-service primary teachers and their pupils, first-year university students majoring in social sciences and humanities and university students majoring in mathematics.

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Section: Metaphorising In Mathematical Educationmentioning

confidence: 99%

Enactive Metaphorising in the Learning of Mathematics

Soto-Andrade

2018

Invited Lectures From the 13th International Congress on Mathematical Education

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“…), wobei dabei die Grundvorstellungen "wieder wirksam werden" (OEHL 1962, 103), welche auch schon "bei der Einführung zur Gewinnung der Einsicht führten" (OEHL 1962, 103). Die mathematschen Inhalte und Verfahren lassen sich jedoch zumeist nicht nur mit einer Grundvorstellung beschreiben, sondern vielmehr durch ein Zusammenspiel mehrerer Grundvorstellungen, welche miteinander vernetzt sein sollten (WARTHA 2007b, 33 in Anlehnung an VOM HOFE 1995, BLUM & VOM HOFE 2003VOM HOFE 2003, 6;aber auch OEHL 1970). Weiterhin können nach VOM HOFE (2003,6) zwei Arten von Grundvorstellungen unterschieden werden.…”

Section: Grundvorstellungen Zur üBersetzung Zwischen Darstellungenunclassified

“…Dabei entsteht im besten Fall ein immer leistungsfähigeres System von Grundvorstellungen zu bestimmten mathematischen Inhalten (WARTHA 2007b, 33 in Anlehnung an VOM HOFE 1995;MARX & WESSEL 2010, 40). Dieser Prozess wird dabei in der Literatur aus mindestens zwei, sich gegenseitig bedingenden Perspektiven beschrieben 10 .…”

Section: Zur Ausbildung Und (Weiter-) Entwicklung Von Grundvorstellununclassified

“…u.a. AEBLI 1963;VOM HOFE 1995;GERSTER & SCHULZ 2004, 46 f.;LORENZ 2011). Dabei wird beschrieben, dass ein mathematischer Inhalt bezie-hungsweise Begriff (hier Grundvorstellungen zu diesem Inhalt bzw.…”

Section: Zur Ausbildung Und (Weiter-) Entwicklung Von Grundvorstellungenunclassified

“…In der Grundschulmathematik beispielsweise zu den vier Grundrechenarten: So beschreibt zum Beispiel KUHNKE , 39 u.a. in Anlehnung an SCHMIDT & WEISER 1993 In der Vergangenheit wurde das Grundvorstellungskonzept dabei vorwiegend aus normativtheoretischer Perspektive genutzt (VOM HOFE 1995) …”

Section: Theoretische Perspektiveunclassified

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Grundvorstellungen und Vorgehensweisen bei der Subtraktion

Wessel¹

2015

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Subject-Matter Didactics

Hefendehl-Hebeker

Hofe²,

Büchter

et al. 2019

ICME-13 Monographs

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In the development of didactics of mathematics as a professional field in Germany, subject-related approaches play an important role. Their goal was to develop approaches to represent mathematical concepts and knowledge in a way that corresponded to the cognitive abilities of the students without disturbing the mathematical substance. In the 1980s, views upon the nature of learning as well as objects and methods of research in mathematics education changed and the perspective was widened and opened towards new directions. This shift of view issued new challenges to subject-related considerations that are enhanced by the recent discussions about professional mathematical knowledge for teaching.

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Grundvorstellungen mathematischer Inhalte als didaktisches Modell

Cited by 36 publications

References 1 publication

Enactive Metaphorising in the Learning of Mathematics

Enactive Metaphorising in the Learning of Mathematics

Grundvorstellungen und Vorgehensweisen bei der Subtraktion

Subject-Matter Didactics

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