Iben Maj Christiansen

When Negotiation of Meaning is also Negotiation of Task

Much recent research in mathematics education has been concerned with the negotiation of meaning between students or between students and teacher. But meaning is always meaning in particular context. Therefore, the negotiation of meaning presupposes a taken-to-be-shared understanding of the situation. In familiar situations, this is relatively unproblematic, but it becomes less so in instances where more than one interpretation of the task at hand is possible. This is perhaps the core of the apparent problems many students seem to have when working with applied mathematics. When more students are working together in such situation, a negotiation of the perspective from which the content should be adderessed must be undertaken.I analyse an example which illustrates not only how students discuss how to pursue the task, but also how they do this with reference to the mathematics classroom as the setting for the activity. The example will illustrate how negotiation of meaning and task may be linked in ways infelicitous to the learning of modelling and critical reflections. Thus, students may be caught in a double-bind of psychological support and subject matter control.

Project work in university mathematics education: A Danish experience : Aalborg University

This article discusses project work in university mathematics education. The practice perspective is obtained as students and teachers from Aalborg University share their experiences. A theoretical framework is introduced. It includes the following key-terms: Problem-centered studies, interdisciplinarity, participant-directed studies, and the exemplarity principle. The contrasting of this theoretical conception of project work with the practice shows that the original notion of project work has been modified as a consequence of its encounter with practice. The modification can be perceived as both a success and a failure. To discuss this, different perspectives on project work in mathematics are suggested.

Cross-curricular activities within one subject?

The structural organization, of the Danish Gymnasium greatly hinders cross-curricular activities. However, it is possible to integrate other subjects in the mathematics curriculum, not the least due to the existence of the so-called “aspects” I will discuss a particular course on modeling ozone depletion which was framed by the “model aspect”. The organization and outcome of the course are linked to three types of competencies mathematical. technological and reflective. I will focus on the reflective competency, in particular the criticla evaluation of mathematical models and their use. One conclusion is that modeling furthers all three competencies, and thus should be given more emphasis in mathematics instruction. However, if the reflective competency is to be furthered, the topic must be seen in a broader societal context, and this would be better supported by cross-curricular activities.

Critical Evaluation of Models in Relation to the Modelling Process

This paper is a discussion paper, the main aim of which is to raise what I consider to be central questions and issues for further consideration. The paper takes as its starting point that in order to further democratic competencies, there is a need to promote critical evaluation of models and their use in society. I will argue that if someone should have a basis for engaging in reflecting critically on models, their validity, and their use, then s/he must be somewhat familiar with elements of the preceding modelling process. My hypothesis is that there is a correspondence between with which of the sub-processes a person engages and which types of reflections she can unfold. I attempt to illustrate this by a particular way of graphing the modelling process.

TSG 9: Mathematical Modeling and Links between Mathematics and Other Subjects

The content theme of TSG9 has played a prominent role at all ICMEs? However in reviewing developments in the field we can note shifts in emphasis within the educational debate about this topic. Some of the main trends in the eighties were summarized and discussed in Blum and Niss(1991).