This paper focuses on a design experiment methodology in mathematics education which has been developed as a methodology for establishing a close and dynamic relationship between theory and practice, and discusses the comprehensive characteristics of the methodology. The design experiment methodology intends to develop (local) theories in mathematics education through designing, practicing and systematically analyzing daily classroom lessons over a relatively long period, where a researcher is responsible for students' mathematical learning in collaboration with a teacher. However, the methodology has also been questioned as to its scientific quality by the positivist scholars, since it explicitly deals with classroom practices that can be characterized as complex phenomena. Thus, this paper tries to place the design experiment methodology especially from a scientific point of view. The points discussed in this paper are the following.
1. The design experiment is an effective methodology for realizing mathematics education as a design science, and it intends to create a fruitful relationship between theory and practice.
2. The design experiment aims to construct a class of theories about the process of learning and the means that are designed to support that learning through (a) designing and planning the learning environments, (b) experimenting the design and the ongoing analysis, and (c) the retrospective analysis.
3. The design experiment is an interventionist methodology that goes through an iterative design process featuring cycles of invention and revision.
4. The design experiment has its intention of producing a theory which premises a social and cultural nature of the classroom, active roles of teacher and students, and learning ecologies and complexities of the community. Thus, it is opposed to an orientation of theory-testing that the positivist studies adopt.
5. The design experiment has been critically discussed in terms of the traditional scientific criteria like generalizability, reliability, replicability and others.
6. We can indicate four points as our tasks for enhancing the scientific qualities of the design experiment;
・Implementing consciously both processes from scholarly knowledge to teaching, and conversely from craft knowledge to researching and scholarly knowledge,
・Analyzing practical data in a systematic way and unfolding a logic of the analysis,
・Assessing and evaluating the design experiment using the revised scientific criteria, and
・Placing some philosophy which the design experiment is based on.
