Facilitating the Development of Modelling Competencies Through the Secondary School Years
One method of engaging secondary students in mathematics classes is through taking a real world modelling approach to the teaching of mathematics, beginning in the middle years (Years 8/9) and developing students’ modelling abilities into the senior secondary years. Of interest in this process is how teachers craft lessons and manage task sequences over time, during one year level and over several years and year levels of schooling, in order to facilitate students’ progress. Further, how can a group of like-minded teachers set up pathways through the middle to the senior years of secondary schooling so the conduit remains open and flowing in the same direction?
This paper documents a case study in an Australian secondary school where such an approach is being established. In particular, the tasks, task sequences, technological tools, and pedagogy employed by one teacher are being investigated. The purpose is to provide an approach through which Year 9 students experience a sense of success that is pivotal to their continued engagement with the modelling process. Both the teacher moves and the students’ moves in this process are being examined. Bearing in mind that the teacher’s aim is that his students have well developed modelling skills within a classroom context by Year 11, students’ transitions between the phases of the modelling process—going from a general statement to the mathematical problem; from the mathematical problem to the formulation of an approach; from formulation to solution; and from the solution of the mathematical problem to interpretation, are of particular interest. Hence, what students do or fail to do in each of these phases is being documented. As Haines and Crouch (2004) point out, transitions especially those “between the real world and the mathematical world are demonstrably difficult for students” (p. 106). Likewise, how these transitions between modelling phases are facilitated, and how this impacts on the modelling approach are being explored. The presentation will focus on selected aspects of this challenging program.
Haines, C., & Crouch, R. (2004). Ability and competence frameworks in mathematical modelling and applications. In H-W. Henn & W. Blum (Eds.), ICMI Study 14: Applications and modelling in mathematics education (Pre-Conference Volume, pp. 103-108). Dortmund, Germany: University of Dortmund.
Galbraith, P.G., Stillman, G.A., Brown, J.P., & Edwards, I. (2005). Facilitating the development of modelling competencies through the secondary school years. Paper presented at the 12th International Conference on Mathematical Modelling and Applications, London.