ABSTRACTS
(Full texts are available to subscribers only)

Theories of mathematics education: European perspectives, commentaries and viable research directions
Bharath Sriraman (USA); Lyn D. English (Australia) 

In this article 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 complement the discussion at the PME research forum in Melbourne.
 Full text (PDF)

Reflections on theories of learning
Paul Ernest (UK) 

 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, even if they sit more comfortably with one of them.
Full text (PDF)

Theories of mathematics education – Is plurality a problem?
Steve Lerman (UK)

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 Sriraman and English (2005): ‘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 and I draw on the sociological theories of Basil Bernstein to relate the developments to the nature of intellectual communities and their productions. In particular, I suggest that the multiplicity and divergence are not surprising nor are they necessarily damaging to the field. I end by discussing concerns about accountability in relation to research in education.
Full text (PDF)

A brief historical comparison of tendencies in mathematics didactics/education in Germany and the United States
Günter Törner (Germany); Bharath Sriraman (USA)

In this extended paper from the PME research forum in Melbourne, 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 focus of mathematics education over the last 100 years and in this process unravel common focal points in the parallel development of the field in these two countries.  In doing so we also reflect and hypothesize on why certain trends seem to re-occur, sometimes invariantly across time and location.
Full text (PDF)

Theory usage and theoretical trends in Europe: A survey and preliminary analysis of CERME4 research reports. 
Bharath Sriraman (USA) ; Gabriele Kaiser (Germany) 

The 29th PME research forum on theories included only one European perspective on mathematics education. In order to convey trends in theoretical tendencies in Europe we compile, survey and analyze a large subset of the research papers at the 2005 European Congress on Mathematics Education (CERME4) in Spain. That is, this paper includes a discussion of trends seen within CERME4 reports on theory usage by European researchers in seven of the fourteen working groups and (a) Outlines similarities and differences in theory usage and (b) takes a futuristic stance based on the analysis of trends within research reports on common questions and ways in which researchers from different traditions could understand each other. Such an enterprise would further Hans-Georg Steiner’s vision of bridging theoretical traditions which are independently formulated in different regions of the world.
Full text (PDF)

Diversity in theories of mathematics education: How can we deal with it?   
Angelika Bikner-Ahsbahs (Germany); Susanne Prediger (Germany) 

This article discusses the central question of how to deal with the diversity and the richness of existing theories in mathematics education research by drawing on experiences from the working group on theories at CERME4. To do this, we propose ways of structure building and discussing theories and we contrast the proposal for integrating theories with the idea of networking theories.
Full text (PDF)

Mathematics education research, its nature, and its purpose: A discussion of Lester’s paper
Guershon Harel (USA) 

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 - or the emergence of these forces; (b) recapitulates Lester’s outline and model for theory-based research in mathematics education, and interprets Lester’s paper as a call to the MER community to respond to the current political forces that (inappropriately) shape our field, and (c) addresses the role of mathematical context in MER, a topic absent from the paper’s narrative. 
Full text (PDF)

Various theoretical frameworks in concept construction and how to move forward as a field: A commentary to Pegg and Tall
Bettina Dahl (USA) 

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 the problem of having many different theories and fashions, how knowledge grows and accumulates, and if there is a unifying theory to be found. The paper concludes that the development of meta-theories, such as in the work of Pegg and Tall, is necessary rather than uncritical complementarism.
Full text (PDF)

Commentary on Moreno-Armella and Sriraman: The articulation of symbol and mediation in mathematics education
Gerald Goldin (USA)

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 itself as constituting “symbolic technology.”
Full text (PDF)

Commentary on Lesh and Sriraman: Mathematics education as design science
Claus Michelsen (Denmark)

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.
Full text (PDF)