This paper responds to the current debate on a “progressive” knowledge-based approach to the curriculum (Lambert and Biddulph, 2015) by addressing the question of what students have an entitlement to learn in the mathematics classroom. In doing so it draws on the outcomes of a recent empirical study on developing mathematical thinking and in particular discusses the nature of epistemic quality (Hudson, 2017; Hudson, 2016 and Hudson et al., 2015) further in relation to the concept of powerful knowledge (Young, 2013). In considering the role of the curriculum theory in relation to “access to knowledge”, Young (2013, p103) argues that it is the neglect of this role that is at the heart of ‘the crisis’ referred to in the title of his paper. He argues the need to address epistemological issues concerning questions of the truth, and reliability of different forms of knowledge and how such issues have both philosophical and sociological dimensions. He also draws attention (ibid., p115) to the work of Morrow (2008) on epistemic access in arguing that our task as curriculum theorists and teachers is to develop curriculum principles that maximise the chances that all pupils will have access to the best knowledge we have in any field of study they engage in. This paper develops the distinction between knowing that and knowing how by drawing on the ideas Winch (2010) related to epistemic ascent as cited in Muller (2016). In particular it draws on two different kinds of know how – inferential know how and procedural know how. It is argued that mathematical thinking is central to such procedural know how involving processes of reasoning and in particular of processes of creative reasoning. Furthermore, it is proposed that such creativity needs to be recognised as an orientation or disposition toward mathematical activity at the outset of planning to teach and that this can be fostered broadly in school. However sufficient time needs to be given to the development of such creativity, central to which is learning from errors and mistakes and last but not least taking the time to think mathematically. In conclusion, the paper considers the role of teachers as curriculum makers in these processes in which “curriculum making is in effect curriculum thinking in practical action” (Lambert and Biddulph, 2015, p217) at the classroom level where curriculum and pedagogy effectively merge.

1. Hudson, B. (2017) Epistemic Quality for Inclusive and Equitable Mathematics Education for All, WERA 2017 Focal Meeting/Hong Kong Education Research Association International Conference, The Education University of Hong Kong, 30 November – 2 December 2017. 2. Hudson, B. (2016) Boredom, alienation and anxiety in the maths classroom? Here's why, The Conversation, http://theconversation.com/boredom-alienation-and-anxiety-in-the-maths-classroom-heres-why-69570 3. Hudson, B., Henderson, S. and Hudson, A., (2015) Developing Mathematical Thinking in the Primary Classroom: Liberating Teachers and Students as Learners of Mathematics, Journal of Curriculum Studies, Vol. 47, Issue 3, 374-398. http://dx.doi.org/10.1080/00220272.2014.979233 4. Lambert, D and Biddulph, M. (2015) The dialogic space offered by curriculum-making in the process of learning to teach, and the creation of a progressive knowledge-led curriculum, Asia-Pacific Journal of Teacher Education, 43, 3, 210-224. 5. Morrow, W. (2008) Bounds of Democracy; Epistemological Access in Higher Education. Pretoria, HSRC Press. 6. Muller, J. (2016) Knowledge and the Curriculum in the Sociology of Knowledge. In D. Wyse, L. Hayward and J. Pandya (Eds.) SAGE Handbook of Curriculum, Pedagogy and Assessment, Sage Publications, 92-106. 7. Winch, C. (2010) Curriculum design and epistemic ascent, Journal of Philosophy of Education, 47(1), 128-46. 8. Young, M. (2013) Overcoming the crisis in curriculum theory: a knowledge-based approach, Journal of Curriculum Studies, 45, 2, 101-118.