Realistic mathematics problems in the secondary classroom

Abstract

The Dutch theory of realistic mathematics education (RME) calls for mathematics to be presented as a human activity. Learners can be guided to reinvent mathematics themselves through exposure to problems which are experientially real to them. This dissertation provides a review of the main ideas leading and pertaining to the RME theory. It also reports the planning and the implementation of a developmental research cycle conducted according to this theory. Two realistic problems adapted to secondary classrooms, 'The Bus Stop Queue' and 'Bags of Sugar', were developed and tried out in teaching experiments with a boys' Area Secondary Form 1 class and a girls' Junior Lyceum Form 3 class. The analysis and ensuing discussion involved an evaluation of the tasks in terms of the extent to which they were experienced as realistic and of their potential to extend the thinking of the participating students and of learners in other classrooms. The developed problems proved to be realistic in that the experiential reality of their contexts helped the students to engage in mathematising. 'Bags of Sugar' was tried out with both classes; it proved to be suitable for pupils whose mathematical experience and learning style differed considerably. Both tasks provided a picture of the students' mathematical understanding and growth, upon which further instruction was designed. The teaching experiments proved feasible and effective to promote a meaningful encounter with mathematics in the secondary classroom.