It feels like we in math education have been thrown into a hurricane. Is what we do in Canada broken? Are we falling perilously behind other countries as a result of the ways that we teach and prepare our students? Contrary to the stories of doom and gloom that we are hearing, our mathematics education system is not broken. Can we improve what we do? Certainly. Should we throw out the whole thing and go totally back to basics? Absolutely not. There are three key things that can improve what we have – balance, balance, and balance.
We need more balance between the back to basics and the discovery-based approaches in teaching math. Students do need to be taught – sometimes through memorization or by rote – the basic building blocks appropriate to their grade level, such as arithmetic, fractions, percentages, basic algebraic skills, and so on. They then need to be given sufficient time to digest and practise these skills, both in school and at home.
Calculators and computers are of course indispensable tools here, but we all need some level of mastery and fluency by hand to lay the groundwork for what follows. Once students have mastered some of the fundamentals, they then need to spend lots of time solving problems and being led through discovery-based learning activities. Basic skills build the foundation for problem solving and discovery; problem solving and discovery build the foundation for tackling complex real-world problems (mathematical and non-mathematical) and for innovation. These abilities are crucial for Canada to be a world-leader in every discipline. Canada produces great hockey players – they all first learn to skate, pass and shoot the puck, then learn more technical drills and systems while continuing to practise skating, passing and shooting. Mathematics is no different.
We need to promote better balance in helping teachers at all levels make both their pedagogical and their mathematics skills even better. Prospective teachers get support through their education programs in learning pedagogy and other important things that allow them to do their jobs. All of us who teach can of course do things to make ourselves even more effective in the classroom. At the same time, all of us who teach mathematics should always strive to further our own mathematical abilities by doing mathematics ourselves and by learning at least a bit more beyond the level at which we teach. Faculties of education should devote more resources to improving the mathematical abilities and confidence of their graduates. We as a society should devote more resources to providing current teachers with time during the school day to improve their subject-specific knowledge and ability. Neither pedagogy without knowledge nor knowledge without pedagogy will work in the classroom – a healthy dose of each is required, and each constantly needs to be refreshed.
We need better balance between the focus on literacy and numeracy in society. People rarely seem embarrassed to tell you that they were never any good at math, but thankfully a small percentage in Canada are illiterate or would admit proudly to not being able to read. Mathematics is at the core of every aspect of life, from technology to health care to finance to architecture and beyond. We should not give up time devoted to literacy in schools and at home, but more time needs to be devoted to mathematics. As parents, we need to do math with our children at home (practice multiplication, talk about percentages, etc.), just as we read with them, even if we ourselves are not entirely comfortable with math. As a country, we need to promote this and provide resources for parents to help their children (which might in turn even help those of us doing the helping).
Lots of people seem to be saying that the system is broken and we need to start from scratch. Education too often feels like a pendulum – we swing from one extreme to the other. It is too hard on the car to keep weaving from the left lane to the right lane and back again. For the sake of students, teachers, parents, and all of us, let's find a way to spend more time in the centre lane.
Scores on provincial, national or international assessments do not tell the whole story. Yes, recently-released PISA scores and provincial testing scores in Ontario paint worrisome pictures, but tests are not the only indicators of what students are learning. Schools from coast to coast to coast are filled with hard-working, caring teachers who want to improve and want their students to improve. Let's stop bashing teachers and start giving them the support that they need to push Canada's mathematics abilities to the next level.
Ian VanderBurgh is the director of the Centre for Education in Mathematics and Computing at the University of Waterloo