If quantitative criticalism is thought to be a bridge between positivist epistemologies prevalent in quantitative work and social constructionism often found in critical qualitative work, then this bridge is fraught with challenges and tensions. This chapter examines the methodological issues, questions, and tensions that emerged from a research team project. What constitutes "good" research? To what extent do we take our critical perspective in our analysis? Is quantitative criticalism a coming together of different research paradigms? What training is essential for quantitative criticalist work? These critical methodological questions require some frank discussion as we move forward in developing research designs that incorporate quantitative criticalism and in training new researchers.