Although there seems to be a consensus among mathematics educators that judgments of the quality of research should be based on a set of widely accepted criteria applied in a constructive, non-dogmatic way, such criteria are not yet available. Instead, because a common vocabulary has not been used, various sets of criteria for research quality have been proposed, and no one has attempted to uncover those latent issues concerning quality whose realization and a step-by-step utilization would be particularly beneficial for novice researchers. This paper proposes the grouping of criteria for the quality of research in mathematics education into three basic comprehensive standards. The appropriateness of the three standards is established through an analysis of a representative sample of proposed sets of criteria. The standards are examined in terms of suitable indicators and then applied to the realization of a study searching for the dimension of mathematics attitude that mainly influences mathematics achievement. Although the standards may appear to apply only to the evaluation of research reports, their use may also increase the quality of the design and management of research activities for both quantitative and qualitative research studies.