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This commentary discusses the framework for mathematics education researchers outlined in Lester's (2005) paper. The author reacts to (a) Lester's concern about the current political forces in the U.S. to define scientific research in education rigidly, and offers a possible reason—apart from political ideology—for the emergence of hese forces; (b) recapitulates lester's outline and model for theory-based...
The 29th PME research forum on theories included only one European perspective on mathematics education. In order to convey trends in theory usage in Europe we compile, survey and analyze a large subset of the research papers from the 4th European Congress on Mathematics Education (CERME4). That is, this paper includes a discussion of trends seen within CERME4 reports1 on theory usage by European...
We briefly comment on different perspectives on (1) the role of mathematics education theories, (2) the issue of plurality and healthy heterogeneity versus consolidation; (3) underlying inquiry systems or the implicit role of philosophy in theories of mathematics education. This paper also outlines developments within the European research scene on theory usage in mathematics education research, which...
This article discusses the central question of how to deal with the diversity and the richness of existing theories in mathematics education research. To do this, we propose ways to structure building and discussing theories and we contrast the demand for integrating theories with the idea of networking theories.
This paper first summarises and discusses Pegg and Tall's (2005) fundamental cycle model of conceptual construction from action to object and its relationship to other theories. Then the paper compares this with another model of different psychological theories of learning mathematics and discusses how these models can either be merged or complement each other. This leads to a general discussion about...
In this paper we outline in macroscopic terms major tendencies in the mathematics education histories of Germany and the United States. In particular, we spell out periodic shifts in foucus of mathematics education over the last 100 years and in this process unravel common focal points in the parallel development of the field. In doing so we reflect and hypothesize on why certain trends seem to re-occur,...
Four philosophies of learning are contrasted, namely ‘simple’ constructivism, radical constructivism, enactivism and social constructivism. Their underlying explanatory metaphors and some of their strengths and weaknesses are contrasted, as well as their implications for teaching and research. However, it is made clear that none of these ‘implications’ is incompatible with any of the learning philosophies,...
In this paper the author critiques and comments on the global ideas presented by Moreno-Armella & Sriraman (2005) on the development of representational systems drawn from the prehistory and history of mathematics, their discussion of tools and technology as mediators of mathematical action and cognition and the claim that we regard present-day computational media as mediators and mathematics...
In this developed contribution to the Research Forum, held at the recent meeting of the International Group for the Psychology of Mathematics Education, the theme being “Theories of Mathematics Education”, I focus on the call by the organisers: ‘the time seems ripe for our community to take stock of the multiple and widely diverging mathematical theories’. I examine empirically the diversity of theories...
In this commentary, the author discusses the strengths and weaknesses to Lesh & Sriraman's (2005) ambitious proposal of re-conceptualizing the field of mathematics education research as that of a design science.
The paper presents and analyses experiences from developing and running an inservice course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10~12. The course objective is to support the teachers to develop, try out in their own classes, evaluate and report a project based problem oriented course in mathematical modelling...
Modelling and application are seen as a highly important topic for maths lessons. But so far the concept «modelling competencies» has not been described in a comprehensive manner: The aim of this paper is to supplement former descriptions of modelling competencies based on empirical data. An empirical study was carried out which aimed at showing the effects of the integration of modelling tasks into...
The paper reports on University seminars of mathematical modelling at school, that were held together by the departments of mathematics and mathematics education and some schools in Hamburg. Prospective teachers together with students in upper secondary level carried out modelling examples either in ordinary lessons or special afternoon groups. They tackled authentic problems proposed by applied mathematicians...
This paper describes the development of mathematical modelling as an element in school mathematics curricula and assessments. After an account of what has been achieved over the last forty years, illustrated by the experiences of two mathematician-modellers who were involved, I discuss the implications for the future—for what remains to be done to enable modelling to make its essential contribution...
In this paper I will discuss and exemplify my perspectives on how to teach mathematical modeling, as well as discuss quite different faces of mathematical modeling. The field of mathematical modeling is so enormous and vastly outspread and just not possible to comprehend in one single paper; or in one single book, or even in one single book shelf. Nevertheless, I have found that the more I can illuminate...
The reconstruction of pupils modelling processes can be found in many empirical studies within the literature on modelling. The empirical differentiations of the phases, which includes putting statements and actions of the pupils in the right phase, has not been reconstructed from a cognitive psychological point of view on a micro level thus far: In this article different modelling cycles are discussed...
In this article we present, illustrate, test and refine a framework developed by Galbraith, Stillman, Brown and Edwards (2006) for identifying student blockages whilst undertaking modelling tasks during transitions in the modelling process. The framework was developed with 14~15 year old students who were engaging in their first experiences of modelling at the secondary level.
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