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This paper makes a case for placing knowledge at the centre of the school mathematics curriculum, and for knowledge building and knowledge differentiation as critical for both equity and excellence, emphasising that knowledge is much more than a set of descriptions of content as might typically be found in a curriculum document or textbook. The paper commences by discussing the implications of the traditional epistemological view of knowledge as justified true belief for mathematics education and uses this to build a preliminary description of knowledge building. Ideas from critical realism are then used to show that it is not so much the content of knowledge that matters but the production of knowledge and to build an enhanced conception of knowledge building in school mathematics. A distinction is made between knowledge and knowing that provides a non-relativist yet fallible view of knowledge, recognising its emergent but directed nature through its production and legitimation within established fields. The importance of knowledge building as a democratic right is then discussed, highlighting the importance of specialised knowledge and arguing that knowledge differentiation provides a basis for a conception of school mathematics curriculum that is dynamic and empowering. The paper concludes by discussing a range of potential theoretical and empirical research projects arising from a focus on knowledge and knowledge building in school mathematics.

This paper describes the experiences of two pre-service primary teachers in a teacher education subject focusing on mathematics and learning difficulties. It describes how bibliotherapy was a powerful reflective tool that provided them with the opportunity to respond cognitively and affectively to their own schooling. By analysing readings about school students' learning and issues such as mathematics anxiety, they reflected on and reconstructed their understanding of their own school experiences. In turn, this challenged their assessment of their capacity to learn and teach mathematics. Bibliotherapy was a healing process that generated both enthusiasm for teaching and an enhanced confidence as the pre-service teachers looked to the future. (Contains 1 footnote.)

This article draws on some ideas explored during and after a writing workshop to develop classroom resources for the reSolve: Mathematics by Inquiry (www.resolve.edu.au) project. The project develops classroom and professional learning resources that will promote a spirit of inquiry in school mathematics from Foundation to year ten. The centrepiece of reSolve is the reSolve Protocol, a framework that both underpins the development of the resources and provides a vision for excellence in teaching and learning mathematics generally. The Protocol has three key elements: (1) reSolve mathematics is purposeful; (2) reSolve tasks are challenging yet accessible; and (3) reSolve classrooms have a knowledge-building culture. The activity described in this article, and particularly the way in which it was developed, exemplifies these three elements. It starts with a curious number activity that students are asked to explain. The clear purpose is to show the power of algebra as generalised arithmetic, as it is only by expressing what is happening algebraically that students can explain why the "trick" works. This leads to a task in which students explore other possible relations made with a similar process. The use of spreadsheets and the numerical approach make the activity accessible, while the results themselves, as will be clear later in the article, provide a level of challenge that extends well beyond school-level mathematics.

Algebraic reasoning is foundational to all mathematical thinking. This is no less the case in the early years of school, where the capacity to recognise the structure of mathematical processes enables students to acquire deep conceptual understanding. It is through algebra, therefore, that students are able to explore and express mathematical structure, pattern and relationships. This article presents using resources from the reSolve: Mathematics by Inquiry Project to demonstrate how, through a structured inquiry process Years 3 and 4 students can investigate the structure of number and generalise the results. This focus on structure sets the foundation for algebraic reasoning.

This paper reports on the efficacy of an accelerated teacher education program ("Growing Our Own") focused in remote Indigenous communities in the Northern Territory. The program is a joint initiative of Charles Darwin University and the Northern Territory Catholic Education Office, providing an intensive two-year program designed to educate Indigenous Teacher Assistants to full teacher status. We describe the growth in knowledge and confidence that has occurred through the program using the story of one of the students in the project, Philomena, as an evocative representation of the experiences of the participants in the program. This growth is particularly evident in one lesson that Philomena taught towards the end of the program in which she was able to challenge her previously accepted role as subservient to the non-Indigenous teacher. Our discussion highlights some key issues for improving outcomes for Indigenous children, including the potential mismatch between Western and Aboriginal ways of thinking in mathematics and developing the mathematical capacity of Indigenous teacher assistants in remote settings. We suggest that the mutual respect of the participants at various levels of "Growing Our Own," the situated and purposeful nature of the learning, and the capacity of students to engage in that learning without abandoning their community responsibilities have been pivotal in enhancing educational outcomes in remote communities and in providing opportunities for Indigenous people.