From an explorative study on how professionals engage in mathematical modelling in their work, three main types of activities were identified, i.e. empirical, theoretical and applicational modelling. Based on the outcomes of the study, some issues related to mathematical modelling in education are discussed.

A new national curriculum has recently been implemented in the Swedish upper secondaryschool where one of the goals to be taught is modelling ability. This paperpresents a content analysis of 14 ”new” mathematical textbooks with the aim to investigatehow the notion of mathematical modelling is presented. An analytic scheme isdeveloped to identify mathematical modelling in the textbooks and to analyse modellingtasks and instructions. Results of the analysis show that there exist a variety ofboth explicit and implicit descriptions, which imply for teachers to be attentive tocomplement the textbooks with other material.

Researchers argue that teachers’ conceptions (beliefs) about mathematical modelling have an impact on the low integration of modelling activities into the mathematics classroom. This paper presents a case study of 18 teachers, investigating their conceptions about mathematical modelling and their experiences of working with modelling activities in Swedish upper secondary school. The results, based on an analysis with a grounded theory inspired coding strategy, indicate that the teachers’ conceptions of the notion mathematical modelling relates to designing a mathematical model based on a situation. It is also concluded that the teachers have minor experience of the notion of mathematical modelling in mathematics class, but in physics class modelling is used as a common activity. Overall the teachers in this study seem not to give priority to integrate mathematical modelling into their everyday mathematics teaching. One reason may be related to teachers’ conceptions about mathematics where more than every other teacher expressed that some of the modelling items discussed during the interviews were not considered to be mathematics.

This paper presents a critical review of literature investigating assessment of mathematical modelling. Written tests, projects, hands-on tests, portfolio and contests are modes of modelling assessment identified in this study. The written tests found in the reviewed papers draw on an atomistic view on modelling competencies, whereas projects are described to assess a more holistic modelling competence but obstacles regarding reliability of assessing projects are identified. The outcome of this investigation also indicates that the criteria used in frameworks or modes of assessment seldom are derived from a theoretical analysis, but more often based on ad hoc constructions, experience from assessment situations or empirical studies of students work. Finally, this study suggests that an elaborated view on the meaning of quality of mathematical models is needed in order to assess the quality of students work with mathematical models.

In this paper Sfard's theory of commognition is used to investigate how two students work collaboratively to develop mathematical models in a natural school setting. The students' communication is analysed from both an insider and an outsider perspective to recreate the construction of their developed models in terms of realization trees. The analysis shows how the students draw on different discourses and that the models evolved through activities of recognition and negotiation. In particular, the students formulated their mathematical models using already known mathematical models. However, these latter models were tacit models in that they were not explicitly mentioned or discussed during the developmental process. To facilitate students’ capability to productively engage in mathematical modelling, the result of this study points to the need renegotiate the learning-teaching agreement so that it incorporates activities offering the students opportunities to practice negotiation and recognition.