ABSTRACT
The work of design research involves using experience as part of the process with which these sequences of tasks are designed. This chapter discusses the use of students' experience to refine the design and study how the tasks work, and the use of a designed intervention to explore students' mathematical thinking and learning that are complementary in design research. A mathematical argument for the study of geometry emerged in the second half of the twentieth century and recognized the possible role that geometry could play in replicating the activities of doing mathematics. Unlike the logical argument that sought to separate mathematical logic from mathematical substance on the grounds that logical reasoning could be useful in multiple endeavors, the mathematical argument sought to maintain the unity of methodology and focus as it gave students opportunities to experience mathematical discovery.
