Australia has recently experienced a curriculum revolution in early childhood education in general, and mathematics education, in particular. Both the curriculum framework for prior-to-school settings - Early Years Learning Framework for Australia (EYLF) (Department of Education, Employment and Workplace Relations (DEEWR), 2009) and the mathematics curriculum for primary schools - Australian Curriculum – Mathematics (AC-M) (Australian Curriculum, Assessment and Reporting Authority (ACARA), 2011) recognise the scope and importance of the powerful mathematical ideas young children bring with them to primary school. The EYLF (DEEWR, 2009, p. 38) lists these ideas as:

Spatial sense, structure and pattern, number, measurement, data, argumentation, connections and exploring the world mathematically are the powerful mathematical ideas children need to become numerate.

Similar ideas are reflected in the strands and competencies of the AC-M (ACARA, 2011): number and algebra; measurement and geometry; statistics and probability; understanding; fluency; problem solving; and reasoning.

The AC-M strands and competencies and the powerful mathematical ideas from the EYLF have been used by educators from South Australian preschools and schools to develop an instrument - the Reflective Continua - designed to assist such educators to notice children’s mathematics and to plan for further mathematical experiences. The Reflective Continua consist of a set of seven interactive tables – one for each of the strands and competencies in the AC-M. Each Reflective Continuum highlights a progression of development and engagement with the relevant powerful mathematical idea.

Each continuum lists ‘behaviours’ that might be expected to be demonstrated by children at each of the levels, along with hyperlinks to examples of how such behaviours might appear in both preschools and first years of school. Most of these examples are learning stories thatemanate from real children and real educators. Learning stories (Carr, 2001; Carr & Lee, 2012) go beyond work samples in that they are recorded as structured written narratives, often with accompanying photographs that document and communicate the context and complexity of children’s learning. They also include relationships, dispositions, and an interpretation by someone who knows the child well (Carr, 2001). Learning stories acknowledge young children’s learning, educators’ pedagogy, and the context in which the learning takes place. They are often used by educators to plan for future, ongoing learning (Perry, Dockett, & Harley, 2007).

This paper explores how the Reflective Continua were developed by early childhood educators and researchers in partnership and how they are being used to assist educators in both schools and prior-to-school settings to notice, explore and implement child-centred and play-based mathematics experiences for their children that meet the curriculum requirements of both the EYLF and the AC-M. Examples of the Reflective Continua, including relevant learning stories will be presented.

While they were developed in Australia, the Reflective Continua have relevance to a much wider audience through their recognition of the importance of educator reflection and documentation and the contexts, in many countries, of curriculum change as children start school.

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