Archaeological evidence for an abacus goes back to 5th century BC Greece, however, there is indirect evidence of their use in Mesopotamia, Egypt and Persia. It is still widely used in Asia. The humble electronic calculator was the first computer to impact teaching and learning. It quickly replaced mechanical slide rules and mechanical calculators in the 1970s. Calculators now include scientific, algebraic, trigonometric and graphing functions.
Education is still stuck in pre-calculator age
Everyone’s miserable about maths: employers, politicians, teachers and especially learners, many who fail and hate the subject with a passion. Indeed, governments have become obsessed with the subject, largely on the hysteria surrounding the PISA rankings.
One issue that is receiving intense attention is ‘calculation’, which is kicking up a storm in maths education. The ubiquity of calculators has led some to question the way we teach maths in schools. They claim that the world has changed from analogue to digital and the teaching of maths needs to respond accordingly.
Some argue that calculators have led to a reduction in numeracy and maths skills. They recommend not using calculators in schools until a certain level of competence in mental arithmetic is reached. Others argue that the traditional focus on ‘calculation’ needs to be replaced by a more sophisticated curriculum of solving problems using maths. Why teach long division, when you are unlikely to ever use it in real life? Calculators can also be used to do the necessary calculation spadework on algebra, trigonometry and graphics.
Maths need exaggerated
Some, like Roger Schank, believe that the need to learn maths is grossly exaggerated as only a tiny proportion of adults will use the maths that is taught, beyond basic arithmetic. His point is that most of what is taught, especially algebra, is of no real practical use and does not help people to think logically. He often asks highly educated audiences to tell him the quadratic formula – few ever answer. Sure, some will need maths in their later career, so says Roger, let them learn it later. Roger has traced this obsession with maths back to early 19th century curriculum choices and claims that this is a historical problem, fuelled by the fact that maths is easy to test, especially ‘calculation’
Too much calculation
Conrad Wolfram decries the focus on ‘calculation’ in school maths. We spend most of our time teaching calculations by hand, which any calculator and computer can do better than any human. Practical, mental arithmetic is fine, but what are these numeracy basics? Automation pushes the user towards using the tools in more sophisticated ways. Maths is not calculation and over the last thirty years calculation has been automated by calculators. Education is still stuck in a pre-calculator age.
Far better to understand what you’re trying to achieve. He recommends that programming is a better way to do maths. It makes maths more practical and academic at the same time. He goes further and argues that the obsession with calculation in maths kills off the initiative, intuition and perseverance that maths needs. In other words we’re turned off maths by maths. Students learn to look for and apply formula, which they then proceed to calculate. Text books are full of primitive, dry, exercises that seem like chores. Many now argue that real life problems should stimulate mathematical enquiry through the use of more word based problems.
Calculators and computers
A calculator is pretty standard as a native application on PCs, Macs and mobile devices. Tills automatically calculate the correct change for customers. Calculators are therefore embedded in newer forms of technology making them more readily available. This is one potential use of mobile devices in schools that teachers should consider.
Maths is forced, by law, upon people who see it as lacking relevance and don’t want to learn it, taught by people who, because they’re good at maths, often don’t know how to teach it. Yet the curriculum is aimed, largely at those very few who will use high-level maths professionally.