Experiments with diagrams—a semiotic approach

Abstract

A challenging task when doing research in mathematics education is the comprehensible description of activities shown by students and their construction of new knowledge as well when doing mathematics. Charles S. Peirce's semiotics seems to be a well promising tool for fulfilling this task. Since several years, Peirce's semiotics is well known and extensively discussed in the scientific community of mathematics education. Among the numerous research reports several papers dealing with Peirce's semiotics concentrate on the meaning of diagrams as a tool for gaiming new knowledge. The aim of the following paper, where a case study will be presented, is to offer the usefulness of such a view on diagrams. In this study two students, which have to solve a problem from elementary geometry, are introduced. The question presented to them asked for a mathematical description of the movement of a rigid body. To answer this question they started experimenting with this rigid body and afterwards invented and used diagrams in manifold ways. Video-based data show these diagrams to be the source of new mathematical knowledge for these students. Therefore, this paper offers Ch. S. Peirce's semiotics as a successful theoretic frame for describing and interpreting the learning activities of students and their use of diagrams to solve a given mathematical task.