Teacher’s thinking process occurs within three phases: before, during, and after the instruction. The analysis of this process potentially results in an innovative didactical design, and the three phase process can be formulated as an array of steps to produce a new didactical design. The series of activities are formulated as didactical design research (DDR), which basically consists of three stages: (1) analysis of didactical situation before the instruction in the form of hypothetic didactical design, including didactical and pedagogical anticipation (DPA), (2) metapedadidactical analysis, and (3) retrospective analysis, namely, an analysis which connects the results of analysis of hypothetic didactical situation with those of metapedadidactical analysis. These three stages will produce an empirical didactical design which is likely to be further developed through them.

didactical design research (DDR), teaching, mathematics.