Comment: ‘If teachers don’t understand mathematical reasoning themselves, it is hardly surprising that students may feel discouraged’
Ruairí Quinn’s announcement, at the annual conference this week of the Irish National Teachers’ Organisation, that primary teachers will be required to have honours mathematics may have drawn heckles from an antagonistic crowd, but there is substantial merit to such a policy.
In Ireland there is a common misconception that honours mathematics is a subject with no real-world relevance, yet it would be difficult to be more wrong: maths underpins practically every field of human endeavour. It is unreasonably effective at describing the world around us, from the smallest subatomic particle to the largest galaxy, and is the natural language of science and logic.
Mathematics is vital for a physician calculating a dose, or a pilot changing course, or a carpenter creating a piece. It is equally essential for anyone calculating interest rates, gambling odds or political statistics. Mathematical patterns exist in everything from a beautiful strain of music to the elaborate petal pattern of a flowering rose to the nuclear heart of our raging sun.
Even when mathematics seems esoteric and far removed from reality, it often has unseen application: the great pure mathematician GH Hardy once declared, “No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” He might be amused, then, to discover that his work on number theory is the foundation of the cryptography on which the internet, and by extension the global economy, are based. Similarly, the geometric theorems we use in everything from construction to cartography were once thought puzzles for the mathematicians of Greek antiquity.
It is important to realise that mathematical ability is chiefly a matter of nurture, not nature – there exists a pedagogical myth that only some people have an intuitive talent for mathematics. This is untrue. We are inherently capable, and one does not have to be “gifted” to have a firm grasp of mathematics. Toddlers intuitively grasp the basics of counting, and by the age of six most children can do mental arithmetic. With proper instruction, and time, children are able to solve even challenging problems.
Mathematics is of vital importance, and the educator’s knowledge base has a powerful effect on how the subject is imparted: research indicates that a teacher’s lack of subject knowledge in mathematics impairs his or her ability to teach material effectively. Conversely, research also shows that teachers with certification in mathematics tend to be more passionate and committed to teaching maths.
This is hardly surprising. It’s not enough to know how to do a particular calculation; one must know why such an approach is used. With mathematics, the correct answer is often immaterial: what really matter are the method and the reasoning underneath it. So teaching mathematics in terms of a simple right-or-wrong binary is deeply unhelpful and counterproductive.
If teachers don’t understand the reasoning themselves, it is hardly surprising that students may feel discouraged. If the logic isn’t made transparent at every step, then mathematics ceases to be illuminating and beautiful, and becomes daunting and arcane, for both teacher and student.
Sadly, this might be the norm in Ireland. The OECD last year found that Irish adults place below average in literacy and numeracy, two life skills with serious implications outside of education. Although literacy is steadily improving, low numeracy persists.
There is still a self-perpetuating apprehension about mathematics, and an attitude of contempt that must be overcome. The comment by Sheila Nunan, the general secretary of the INTO, that “it was the boys who did the honours maths led the country to ruination” borders on the profoundly anti-intellectual, and such sentiments are counterproductive to improving our national numeracy problem.
It is hard to overstate the importance of mathematics today, and the myriad doors that a functional knowledge of mathematics unlocks – doors that remain steadfastly bolted without these essential tools.
The evidence strongly suggests that teachers better trained in mathematics and comfortable in its usage would be of huge benefit to young students, and for this reason Ruairí Quinn’s move should be welcomed. Teachers should be given training and support to help them better their skills and understanding.
It is a damning testament to our skewed priorities that until now we have insisted primary teachers have honours Irish but showed little concern about their mathematical confidence. That we place more value on a minority language than on the language of the universe reeks of misplaced nationalism. Similarly, that we devote 30 per cent of primary teaching time to Irish and religion while our basic literacy and numeracy struggle should raise alarm bells.
DAVID ROBERT GRIMES
The author is a science writer and physicist at Oxford University. He blogs at