PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Can/should students learn mathematics theory-building?
Page: 1043
Mathematicians commonly distinguish two modes of work in the discipline: Problem solving, and theory building (Gowers, 2000). Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide opportunities to learn mathematics theory-building practices. It begins by providing a definition of these theory-building practices on the basis of which to formulate principles for instructional designs. The paper argues that theory-building practices serve not only the synthesizing role that they play in disciplinary mathematics, but they also have the potential to enrich learners’ reasoning powers and to enhance their problem solving skills. These instructional designs offer a new approach to supporting student work on generalization and abstraction. They have been piloted with preservice and practicing secondary teachers.