This paper reports on a study that aims to address the challenges of UN Sustainable Development Goal 4 to ensure inclusive and equitable quality education for all. The study focuses on school mathematics in particular. With regard to ensuring equitable access to quality education, it is argued that there is a need to consider the "epistemic quality" of what students come to know, make sense of and be able to do in school mathematics. Accordingly, the aim is to maximize the chances that all pupils will have "epistemic access" to school mathematics of "high epistemic quality." The study is based on the theoretical framework of Joint Action Theory in Didactics (JATD). Associated research questions focus on the quality of teacher-student(s) joint action and on the epistemic quality of the content. The paper draws on empirical research findings of the "Developing Mathematical Thinking in the Primary Classroom" (DMTPC) project (2010-12) and also on the findings of a parallel study of mathematics teachers' assessment practices in Ghana. One teacher's action research project is used as an exemplar to illustrate how mathematics can become more accessible and inclusive thus leading to an evolution in mathematical thinking and high-quality epistemic access "for all."