# Pre-service teachers expressions of mathematical critic during educational modelling activities focusing on real world model use

## Project owner

Western Norway University of Applied Sciences,

## Project period

September 2013 - September 2017

## Project summary

Background for PhD project

The use of mathematical modelling in education, henceforth modelling, is a central topic in mathematics education research (Blum, Galbraith, Henn, & Niss, 2007). Typically, mathematical modelling is introduced in educational settings with what can be seen as two intentions characterized as modelling as vehicle for content learning and modelling as the content of learning. The modelling as vehicle focus to classroom activities describes the use of modelling in the classroom where the context of the modelling activity supports the learning of a specific mathematical content. In the modelling as vehicle approach the context of the modelling activity thus provides a support for the learning of a particular mathematical content or procedure. (Julie & Mudaly, 2007)(Blomhøj & Kjeldsen, 2010b) When working with modelling as content, the process of modelling itself is the focus of learning (Julie & Mudaly, 2007)(Blomhøj & Kjeldsen, 2010a). In society mathematical modelling is used as a basis to assist decision processes regarding environmental questions (Barwell, 2013), warfare (Greer, 2008), economical and general political decisions about investments and distribution of means in society (Barbosa, 2006). Understanding the role of models in decision processes and their limitations is thus a vital critical democratic competence. A third perspective to modelling in education that adresses the role of models in society can be labled as a ‘models as critic’ perspective. In this perspective the learning of mathematical concepts and development of modelling competencies serve the purpose of developing critical reflections in students about the use of mathematical models. (Barbosa, 2006; 2009)(Blomhøj & Kjeldsen, 2011).

The concept of critic is used in a critical mathematics sense eg. in the works of Skovsmose(2004). Critic is thus to be understood not only as an act of voicing a misliking if something, but also as an act of invetstigating the faults and merits of something.

Aims of the Phd Project

In the current PhD study the role of mathematics in students critical reflections when disussing topics involving model use is investigated. The study is a qualitative study of a group of preservice teachers participating in a masters level course with a mathematical theme on models. The project investigates when and how students express critical mathematical reflections during seminar activities focusing on modelling. Furthermore the project seeks to idetify connections between the students expressions of critic and the educational situation in which the critic takes place. Two research questions are

- In which activities and during which sequences do students and lecturers make use of critical argumentation?

In particular what is the educational focus to modelling during the sequence where the critical argumentation is observed?

- In what sense if at all does the critical argumentation made by the students build on mathematical, technological or contextual aspects of their work during seminar activities?

Since the project seeks to connect the critical argumentation to the setting in which they occur, students and lecturers linking of activities in their argumentation is also investigated. This gives rise to two other research questions

- What references are possibly made in-between modelling activities with different educational focuses to modelling (“models as critic and content”) by lecturers and students?
- What might such references imply about working with modelling from the three aims of modelling

## Method

The project analyses video and audio recordings of three seminar sessions along with written materials produced by the participants. Lecturers powerpoint presentations and task assignments are also part of the datamaterial.

The project uses a normative pragmatics methodology in combination with theoretical constructs from critical mathematics to analyse the students critical discourse during the seminars modelling activities.