This chapter builds on the idea of epistemic quality, as discussed in Hudson (2018, 2019) , which arose from the outcomes of the Developing Mathematical Thinking in the Primary Classroom (DMTPC) project (Hudson et al. 2015) . It does so by relating epistemic quality to a continuum that reflects a trajectory of epistemic ascent (Winch 2013) in the development of expertise from the novice towards that of an expert in the subject. The significance of epistemic quality stems from the need to maximize the chances that all pupils will have epistemic access (Morrow 2008; Young 2013: 115) to high-quality education in school mathematics. This is regarded as a way of making quality education visible and as a precondition for addressing the challenges of UN Sustainable Development Goal 4 to ensure inclusive and equitable quality education for all (UN 2015) . The idea of epistemic quality is in turn...