POWRE: School-Work Connections: Generalizing Mathematics Learning

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A central aim of school instruction is to facilitate the generalization or transfer of knowledge beyond the initial learning context to new circumstances. Recent concerns over the adequacy of school mathematics to prepare students for the workplaces of tomorrow give the transfer of learning new relevancy. However, transfer research has floundered in recent years due to findings that transfer is difficult to engineer in the laboratory. Furthermore two controversies in the literature indicate theoretical problems with the construct of transfer. The research study proposed here extends the work that the principal investigator has already begun in building a new theoretical approach to transfer, through the following research and educational activities: 1) identifying how a particular mathematical concept (namely, slope) is used in tow work or everyday settings; 2) working with a high school teacher to design a unit instruction that implements suggestions from prior research and from the ethnographies; 3) identifying the types of relations of similarity (or general knowledge) that students construct across school and non-school settings; and 4) developing instructional recommendations that can be incorporated in the mathematics courses that the principal investigator teaches for prospective teachers. Several methods of analysis will be employed. The first study involves ethnographic analysis of the use of mathematical concepts in work or everyday settings. The second study involves the video-taped data of students solving problems in interviews and of students learning about slope concepts in high school classrooms. The analyses are largely qualitative, based on methodological techniques for fine-grained analyses of videotapes and will follow interpretive techniques used in the development of grounded theory.