Imagine a country where most post-primary students perform well in mathematics and get good results in their maths exams. Assuming that the exams are of a good quality, the graduates of such a system will generally be clear, logical thinkers and creative problem solvers.
More importantly, the graduates of such a system who go on to become teachers will mostly have strong knowledge of maths – not necessarily the specialised kind of mathematical knowledge that teachers specifically need, but knowledge that will form the basis of such maths. Furthermore, the graduates who become teachers in the system will have spent up to 13 years experiencing and observing mathematics teaching that leads to good results; and because many teachers teach as they were taught, the examples of maths teaching on which they model their teaching will be good. The prospective teachers of maths who go on to enter college with a strong foundation of maths will consequently expect, and be able to participate in, a course that challenges and extends their existing mathematical knowledge. On qualification as teachers, they will be well-equipped to practise mathematical thinking, reasoning and explaining with new generations of young students.
On the other hand, if prospective teachers leave school with disappointing maths results, or if they learn maths in a class where other students get disappointing maths results, their images of success in maths are more restricted. They will have fewer models of good maths teaching to inspire their own teaching and to raise their expectations of how maths teaching can contribute to confident and competent maths graduates. In today’s Leaving Cert results just under 10% of students taking ordinary level maths received a failing grade. Read more here and here.
The difficulties we face in maths achievement in Ireland cannot be fixed by changing teaching alone. Curriculum reform (like that under way at post-primary level with Project Maths), textbook reform, parents’ expectations, society’s expectations all matter. But because those who become teachers are graduates of a system that has difficulties with maths achievement, the challenge of becoming a good maths teacher is enormous. Teachers have to think and act outside the system that has defined their educational experience for as long as they can remember. Their 13 years of learning maths may have taught them much about a way of teaching and learning maths that fails many students. It’s much easier to work with the existing system than to work against it, even if the system needs an overhaul. This point is explained well in The Teaching Gap, a book by Stigler and Hiebert.
We need to look to and learn from other systems to understand how they get more students to succeed at maths. This means looking at teaching, learning, resource use, cultural expectations, and the timetabling of maths and other subjects. This needs to happen while being aware of the constraints, as well as the resources that we have for maths education in our own system. Looking at alternative systems needs to be done by both practitioners and policymakers. Policymakers must make the observation of alternatives more accessible to practitioners.