Collaboration between Mathematicians and Mathematics Educators is crucial in advancing knowledge on the teaching and learning of Mathematics, particularly in advanced Mathematics pedagogy. However, there is a need for the type of collaborations where Mathematicians and Mathematics Educators can find common ground, and the synergy of their…

This paper is drawn from a doctoral thesis (Rosa, 2008) that examines the relations established between the construction of online identities and the teaching and learning of the definite integral concept in an online learning course. The role-playing game (RPG) is played out through chat and calls for the creation of characters (online…

This paper addresses the issue of subjectivity in the context of mathematics education research. It introduces the psychoanalyst and theorist Jacques Lacan whose work on subjectivity combined Freud's psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacan's subjectivity…

This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and…

One of the great strengths of Jim Kaput's research program was his relentless drive towards scaling up his innovative approach to teaching the mathematics of change and variation. The SimCalc mission, "democratizing access to the mathematics of change," was enacted by deliberate efforts to reach an increasing number of teachers and students each…

Reports on a study of possible differences in interaction patterns between a sixth-grade teacher and different groups of students. Results showed consistency in the interactions studied, but important differences occurred in the quality and quantity with students perceived as "best" and "weakest" and boys and girls in…

Discusses the interactions of several students involved in a Dutch research project studying student achievement in elementary school mathematics. Results showed progress by most children, particularly those with low scores on the pretests. (TW)

A model of qualities of mathematical activity was developed within a framework of learning goals. A clinical application of the model is described, in which ninth-grade students were given assignment projects. A hierarchy of effective guidance was established, permitting diagnostic evaluation and progressive development of mathematical activity.…

Varying approaches to mathematics were raised in a Philosophy of Mathematics course. Students were asked which foundational schools they preferred and these preferences were compared with scores on hemispheric tests. The results indicate that preferences may be related to the brain's hemispheres. (MNS)

Features and tools to outline and shape the long-term learning process for ratio are presented, with examples. Ratio-anticipating activity and creating visual models and schemes are stressed, with the basis for a theory of teaching and learning ratio presented. (MNS)

Reports on a study into first grade student's interpretations of the equals sign in different contexts. Argues that varying situations affect students' understanding of such arithmetic concepts, including the social interaction patterns in the classroom during arithmetic instruction. (TW)

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

The aim of this study was to gain a better understanding of the difficulties met by adults with lower levels of education on reading perspective drawings. Subjects were asked to describe verbally two perspective drawings of objects, then choose objects with defined spatial properties. Results indicated that success was an "all or…

This paper is a case study of newspaper mathematics courses developed by SACHED TRUST and published as part of a broader newspaper project in South Africa between 1977 and 1980. Findings are presented, culminating in some recommendations for the future use of the newspaper for motivating adults to study mathematics. (Author/PK)

Some research indicates that students often think that their drawings of three dimensional objects can be done without ambiguity, and that properties of drawings are properties of the objects. This "knowing vs. seeing" conflict was studied in three French sixth grade classes. (PK)