Mathematical Modelling as a Stimulus for Curriculum and Instructional Reform in Secondary School Mathematics

Curriculum documents often advocate making connections to the real world through the use of mathematical applications and modelling as a means of motivating and engaging students, as well as illustrating the usefulness of mathematics to describe and analyse real-world situations. Although applications and modelling are often coupled together, they differ in the degree of task structure involved and whether the mathematical model has already been learned or must be built by the student. Applications and modelling have received differing attention in school curricula, with modelling viewed as being more challenging and complex than applications. Modelling is challenging for both students and teachers because one does not know in advance what mathematical tools and models are available, what assumptions need to be made, and what outcomes can be expected. This chapter presents two case studies of implementing mathematical modelling within the secondary school curriculum in Ireland. The case studies analyse two different strategies for promoting modelling as a stimulus for curriculum and instructional reform. One approach involves curriculum developers in formulating challenging curricular aims and objectives, while the other supports mathematics teachers in translating curricular goals into classroom plans and interactions with students. This analysis is intended to identify and consider ways of addressing what we refer to as meta-challenges, that is, challenges to offering mathematical challenges for all students.