This paper reports on the design and methodology of an ongoing study in belief re-search. The study addresses the question of the potential and perceived influence of the KappAbel competition on the mathematical attitudes and practices of the partici-pating teachers and students. We shall outline our main methodological considera-tions and also discuss, and to some extent challenge, what we consider dominant ap-proaches to research on teachers'beliefs. We address three interconnected methodo-logical difficulties: (1) the problem of not using conceptual frameworks that are well grounded empirically; (2) the question of overemphasising teachers' views of mathematics for their educational decision making; (3) the problem that no terminol-ogy carries unequivocal meanings and more than an indication of agreement or dis-agreement with the rhetoric of reform is needed to outline teachers' and students' school mathematical priorities.