At the special conference celebrating the 50th anniversary of the Australian Association of Mathematics Teachers (AAMT), the author was asked to speak about the challenges and opportunities in teaching mathematics as a stimulus for discussion of AAMT's "future directions". With an open invitation to be a little provocative, the author…

The benefits of rich tasks, project-based learning, and other inquiry-based approaches in terms of student understanding and engagement with mathematics are well documented. Such pedagogies are consistent with the development of mathematical proficiencies as described in the "Australian Curriculum: Mathematics" (Australian Curriculum…

There are many recent studies which have explored the notion of high quality or effective mathematics teaching but relatively few have sought the views of students. Student perspectives regarding effective teaching are important for many reasons, and are arguably particularly significant in mathematics given the international trends of declining…

The Teachers First initiative is a grass-roots cluster-model approach for bringing together primary and secondary teachers and school principals: to analyse student performance data; design and practice activities and assessment tools; and promote teaching practices that address students' learning difficulties in mathematics. The balance of both…

The Technological Pedagogical Content Knowledge (TPACK) conceptual framework for teaching mathematics, developed by Mishra and Koehler (2006), emphasises the importance of developing integrated and interdependent understanding of three primary forms of knowledge: technology, pedagogy, and content. The TPACK conceptual framework is based upon the…

It is essential to retain a focus on building students' mathematical reasoning and comprehension rather than merely developing superficial understanding through procedural learning. All too often this approach "takes a back seat" because of examination and assessment pressure, where the importance of "How?" supersedes that of…

Prof. Hanna Neumann gave the Presidential Address at Australian Association of Mathematics Teachers inaugural conference in 1966. The conference was held at Monash University and had the theme of "mathematical unity". In this address, Prof. Neumann described some features of the teaching of mathematics in schools. While she did not know…

When considering the use of games for teaching mathematics, educators should distinguish between an "activity" and a "game". Gough (1999) states that "A 'game' needs to have two or more players, who take turns, each competing to achieve a 'winning' situation of some kind, each able to exercise some choice about how to move…

Despite compulsory mathematics throughout primary and junior secondary schooling, many schools across Australia continue in their struggle to achieve satisfactory numeracy levels. Numeracy is not a distinct subject in school curriculum, and in fact appears as a general capability in the Australian Curriculum, wherein all teachers across all…

The importance of mathematical visual images is indicated by the introductory paragraph in the Statistics and Probability content strand of the Australian Curriculum, which draws attention to the importance of learners developing skills to analyse and draw inferences from data and "represent, summarise and interpret data and undertake…

At a recent workshop in the ACARA [Australian Curriculum, Assessment and Reporting Authority] offices in Sydney, teachers of STEM gathered to reflect on implementations of integrated STEM projects within their schools. The projects discussed illustrated a range of interpretive stances and practical considerations--presented variously as…

A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…

Context based learning (CBL) is a powerful tool that utilises areas of student interest framed in meaningful contexts to foster development of new skills and understanding. For middle school students, engineering activities that relate to real-world problems provide suitable CBL contexts for acquiring conceptual scientific and mathematical…

Teacher professionalism is a social construct which varies across time and place. In relation to the teaching of mathematics in the middle school, professionalism is a concept under siege; with the advent of national testing some teachers predict dire consequences for student learning. In this small research project several teachers depicted their…

The author, an English teacher, presents his views on mathematics teaching. He then discusses themes of learning theories and structure, where advances in the understanding of language and learning may suggest ways of improving mathematics teaching. Suggestions for reformation are included. (MNS)