Curriculum is important. Not because of our rankings in PISA (Program for International Student Assessment), but because curriculum shapes what students can do and the how competitive they are, both in tests but more importantly in the workforce.

When it comes to the revised Australian Curriculum for mathematics, the debate centres on the importance of teaching mathematical skills over inquiry learning.

While most educators agree the mathematics curriculum needs to include both skills and inquiry learning, the outstanding question is, ‘how much time should be dedicated to inquiry at the expense of learning key skills?’ I believe a student has truly learnt mathematics when they can successfully undertake mathematical inquiry. While it is possible to reduce mathematics lessons to the memorisation of formulae and performing algorithms, this basic skills approach would result in a very limited mathematics education.

We must prioritise a curriculum that develops skilled mathematical thinkers that are able to recognise patterns and build paths to solutions. This approach must be developed from an early age so students don’t mechanically follow instructions but instead use critical thinking to reach solutions.

In order to do this, the engagement of students, employment of highly skilled teachers, building a foundation in basic skills, and providing opportunities to demonstrate the relevance in mathematics in everyday life, all deserve considerable attention.

Fostering confidence in students is the start of this work. Students at an early age can identify as being poor mathematicians, often reinforced by school practices and parental reactions. Certainly, some students have a greater aptitude and interest in mathematics, but the vast majority can become competent at school level mathematics given time, good teaching, and the faith of those around them.

Having a solid foundation in the basics in the early years is essential when students attempt more advanced mathematics in the middle years of secondary school. Students who have not mastered their tables, fractions, and order of operations – and retain that facility – are going to find mathematics at this level difficult. I would argue too that the ability of a student to undertake a mathematical inquiry is a basic skill.

At the upper levels of secondary schooling, learning mathematics often has little application in everyday life or tangible connection to other parts of the student’s life. At this level, there is little opportunity for students to apply their mathematical skills to interdisciplinary inquiry.

Expert teachers are essential, but hard to find. Teaching the memorisation of tables and techniques is relatively straightforward while teaching mathematical inquiry requires teachers with expertise who can model the practice, discern effective mathematical thinking, and provide guidance. Finding teachers who are themselves proficient mathematical thinkers, who can provide the right scaffolding to help students develop and nurture their own mathematical thinking is a significant problem in many schools.

Despite the resistance to changes to the curriculum, mathematics tends to be taught in a very traditional way. It remains relatively quarantined from other changes in pedagogical practice. Simply going ‘back to basics’ or alternatively allowing students to attempt mathematical inquiries without the necessary skills would be disastrous. Students need a rich education that helps them develop into competent mathematical thinkers who can use their talents to interpret the world around them and to improve it. Whether the latest curriculum can support that education is debateable, but the curriculum itself won’t ensure the education needed is delivered.