Anthony G. (1996) Active learning in a constructivist framework. Educational Studies in Mathematics\>Educational Studies in Mathematics 31(4): 349–369. https://cepa.info/5221

An important tenet of constructivism is that learning is an idiosyncratic, active and evolving process. Active learning, operationalized by cognitive, metacognitive, affective and resource management learning strategies, is necessary for students to effectively cope with the high level of demands placed on the learner in a constructivist learning environment. Case studies of two students detail contrasting passive and active learning behaviours. Examples of their strategic learning behaviours illustrate that having students involved in activities such as discussions, question answering, and seatwork problems does not automatically guarantee successful knowledge construction. The nature of students’ metacognitive knowledge and the quality of their learning strategies are seen to be critical factors in successful learning outcomes.

Barwell R. (2009) Researchers’ descriptions and the construction of mathematical thinking. Educational Studies in Mathematics\>Educational Studies in Mathematics 72(2): 255–269. https://cepa.info/3731

Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing, understanding and learning. In this paper, using ideas from discursive psychology, I examine the discursive construction of mathematical thinking in the research process. I focus, in particular, on the role of researchers’ descriptions. Specifically, I examine discursive features of two well-known research papers on mathematical thinking. These features include the use of contrast structures, categorisation and the construction of facts. Based on this analysis, I argue that researchers’ descriptions of learners’ or researchers’ behaviour and interaction make possible subsequent accounts of mathematical thinking.

Lerman S. (1989) Constructivism, mathematics and mathematics education. Educational Studies in Mathematics\>Educational Studies in Mathematics 20(2): 211–223. https://cepa.info/2975

Learning theories such as behaviourism, Piagetian theories and cognitive psychology, have been dominant influences in education this century. This article discusses and supports the recent claim that Constructivism is an alternative paradigm, that has rich and significant consequences for mathematics education. In the United States there is a growing body of published research that claims to demonstrate the distinct nature of the implications of this view. There are, however, many critics who maintain that this is not the case, and that the research is within the current paradigm of cognitive psychology. The nature and tone of the dispute certainly at times appears to describe a paradigm shift in the Kuhnian model. In an attempt to analyse the meaning of Constructivism as a learning theory, and its implications for mathematics education, the use of the term by the intuitionist philosophers of mathematics is compared and contrasted. In particular, it is proposed that Constructivism in learning theory does not bring with it the same ontological commitment as the Intuitionists’ use of the term, and that it is in fact a relativist thesis. Some of the potential consequences for the teaching of mathematics of a relativist view of mathematical knowledge are discussed here.

Pixie S. & Kieren T. (1992) Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics\>Educational Studies in Mathematics 23: 505–528.

Proulx J. (2013) Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics\>Educational Studies in Mathematics 84(3): 309–328.

In this article, I present and build on the ideas of John Threlfall [(Educational Studies in Mathematics 50:29–47, 2002)] about strategy development in mental mathematics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition, particularly in issues of problem posing, for discussing the nature of the solving processes at play when solving mental mathematics problems. I complement this analysis and conceptualization by offering two examples about issues of emergence of strategies and of problem posing, in order to offer illustrations thereof, as well as to highlight the fruitfulness of this orientation for better understanding the processes at play in mental mathematics contexts.

Stevenson I. (1998) Book review [of “Radical Constructivism” by Ernst von Glasersfeld]. Educational Studies in Mathematics\>Educational Studies in Mathematics 35: 93–104. https://cepa.info/4090

Radical Constructivism is currently a very influential view in mathematics education. This paper examines its philosophical roots through a review of the book Radical Constructivism by Ernst von Glasersfeld. It begins by describing the structure of the book, and then considers a number of philosophical issues raised by the book. The paper concludes with some reflections on the relationship between philosophy and mathematics education which the book provoked