Ideas about improving outcomes for Indigenous students in numeracy cover a lot of the same territory as longstanding discussions about improving the quality and impact of mathematics teaching. The use of the term 'numeracy', with its strong implications of practicality, makes this even more emphatic.

The idea of 'working mathematically' has been defined and institutionalised at some levels of education. From this direction come such familiar concepts as

• working in context;
• collecting and organising data;
• seeing and describing patterns;
• creating theories;
• using strategies and skills to prove or disprove theories;
• applying these to actual social and physical issues; and
• communicating results.

But another, older idea of what it means to 'work mathematically' at school has proved resistant to change — ritualised behaviour, barely contextualised sums, right and wrong answers, all bedded comfortably into the idea that maths, 'real maths', is hard, boring and accessible only to some.

The key messages

These materials offer several perspectives to work on.

• As always, improvement in numeracy outcomes will occur if effort is made, using what we already know about good practice.
• Explore and monitor the ways in which students are constructing mathematical ideas and thinking and talking about them.
• Explore ideas of 'working mathematically', teaching what you want known and basing assessment on the same material.