When I declare that I teach mathematics I anticipate with near certainty the typical responses: "How do you do that? I hated maths at school" ... "I got stuck once we started algebra" ... "I passed School C but after that maths was a mystery."
I first taught a Year 9 maths class in 1969; it coincided with the wave of "New Maths". An almost immediate consequence of this curriculum shift was that many parents wrongly assumed they were ill-equipped to help their children with basic maths skills because some of the language changed. Familiarity was lost. Another consequence was that quite erudite concepts were introduced to a younger age group before numerical skills and thoughts had become firmly embedded. Teenage students were being challenged to conceptualise without being able to count or calculate.
Entrepreneurial "educators" took advantage of the quickly developing chasms - they promoted calculators. During the 1970s many schools bought these in bulk, unquestioningly, and sold them on to their captive market, students, at a profit.
The "educators" became rich, some wealthy enough to leave teaching in a classroom, and students were being conned into thinking that this programmed machine could replace mathematical thought and reasoning.
One analogy might be to compare the role of the person who cuts the grass for a farmer as if that person made the hay - the planning for the growth of the grass, the right conditions for harvesting, the use of a baler - myriad different factors make up the final activity. The grass cutter doesn't make the hay; calculators don't and can't do maths.
Of course, there is a role for a calculator - to enable the maths thinker to get to an answer effectively and efficiently after the maths thought has been done.
For students in schools the most important skill related to this is estimation. Forty-four years after I first taught that burgeoning class of students, pupils today are almost scared of an estimate, and profoundly ignorant of its worth. Many find out they cannot top up their mobile phone only after they have tried to pay with an eftpos card and discovered they don't have money. A running estimate as one spends is a lifetime skill that would help not only teenage students but many adults as well - real mathematics.
Another numerical skill that many of the population lack is the use of percentages. For many, not only students, this topic is a minefield. Recently I shopped on a 30 per cent reduction day at my local Farmers. When paying I remarked how few customers would have much idea about their savings. The store assistant agreed. It isn't my job to advise those in the advertising field of the futility of those campaigns - give up on percentage marketing, your audience doesn't know what it means. I note that fast food outlets have learned - they just advertise the lower prices that might apply. Subway doesn't have 20 per cent day - it promotes $8 subs.
The best outcomes that I can promote for students are the ability to use mathematics with some confidence, enjoy the learning, and perhaps as an adult be able to say "I enjoyed maths at school".
Peter W. Watt is a mathematics teacher at St Peter's College.By Peter W. Watt