Applying mathematics: making multiple-choice questions work

In this research paper we discuss how some multiple-choice questions may be used to improve understanding, to develop and to assess modelling capabilities and as an aid to teaching. 1. Bringing real world contexts into the classroom In this paper we are concerned with applying mathematics in real situations and understanding transitions between the real world and the mathematical world. We use short multiple choice questions to provide context that is readily understandable to the pupil or student and we use their answers, both to the questions themselves and in subsequent interviews and self assessments to try to understand the difficulties they face in making transitions from the real world to the mathematical world and vice versa. Mathematical modelling, in various guises, occurs in all sectors of education, broadly operating under two teaching and learning paradigms (i) a holistic approach in which students learn through experience of complete case studies, projects and investigations (ii) the teaching of modelling by defining in detail the processes and stages through which the modeller passes. Successful modelling and elements of applying mathematics is often described by stages of a cyclic process: real world problem statement; formulating a model; solving mathematics; interpreting outcomes; evaluating a solution; refining the model; real world problem statement...with a seventh reporting stage often occurring after evaluating a solution (Berry and Davies, 1996). It is easy to recognise some or all of these distinct stages in open-ended problems, mathematical tasks and other learning activities in the mathematics classroom. Together, these stages help to provide a rich learning environment through activities where students give meaning to ideas, problems [and] mathematical and non-mathematical concepts (Matos, 1998, p26). Reported research supports this view (Crouch and Haines, 1998; Cooper et al., 1993; Ikeda and Stephens, 2001)