This research raised two main methodological problems. The first is that practices and theoretical concerns associated with what may be referred to as "social, cultural, political approach," which integrates a critical perspective in mathematics education, are still at the margins of the realities of mathematics classrooms. That is, they are not widespread in the current mathematics education system and readily available for investigation. Hence, the methodological concern is that of producing a research design and process that brings these theoretical ideas into the realm of practice. This problem is addressed by allowing researchers and practitioners to imagine a hypothetical situation inspired by a theoretical landscape, and to create an arranged situation for research, by intervening in some existing, current actual situation. The second concern is to develop an appropriate methodology in which the research processes and practices are consonant with the educational processes and practices. That is, the theoretical underpinnings and commitments of a critical approach to mathematics education need to be maintained within the research approach. To this end, a critical approach to research in mathematics education is explored through a series of key issues in the third part of this paper, which were identified in undertaking such research. (Contains 31 references.) (Author/KHR)