Encouraging the transfer of ‘school’ mathematics to the ‘real world’ through the integration of process and content, context and culture

Abstract

This paper reports upon a research project which considered the transfer of students' mathematical understanding across different task contexts. The research involved two groups of students from contrasting learning environments. The first environment was characterised by the complete integration of mathematical process and content using open ended activities. The second environment represented a ‘typical’ English classroom with a content based scheme being predominantly used. The research demonstrated that the procedure and performance of students in response to addition and fraction tasks varied considerably when the context of the tasks changed. This variation suggested that students' perceptions of the contexts were individually constructed and contexts did not have a uniform effect upon the difficulty of tasks. The research also suggested that students who had learned in an environment characterised by the integration of process and content were more able to transfer their learning across contexts. Students who had learned mathematical process independently of content were more likely to vary their procedure and performance in response to the contexts of the tasks. This was considered in relation to the problems of ‘school’ — ‘real world’ transfer and the effectiveness of different learning environments.