Graphic pictures of maths in action
For many children school becomes a daily routine of attending classes, following instructions and doing their homework which they dutifully settle into without ever grasping what it's all about. And the rapid growth of knowledge in many subjects makes it more and more difficult for them to see the wood for the trees.
In one subject in particular the vegetation is so dense that pupils can stumble around for years without even seeing the trees. The subject is mathematics and what its students often desperately need is a tool to cut through the undergrowth.
Such devices - graphics calculators - do exist, but their use was banned in exams and discouraged in classes because they were thought to confer an unfair advantage on their owners. That regulation has recently been relaxed and in skilled hands these instruments can reveal the hidden shapes in the mathematical forest.
With an untutored user, technology simply breeds confusion. That is why when East Renfrewshire decided to buy 1,000 hand-held graphics calculators for its secondary schools, the authority also arranged for all its maths teachers to be trained to exploit their capabilities in the classroom.
"The calculators will be used for Higher Still at first," says Peter MacEachen, quality development officer for East Renfrewshire, "but after the teachers have completed this course, I'm planning to get a wee group of them together to write materials for Standard grade. The sooner we bring the use of these machines further down the school, the better.
"We've even got two of our primary teachers here today," he says, referring to the first session of a two-day course presented by Jim Wilson, principal teacher of mathematics at Williamwood High school in Clarkston.
"The teaching calculator, connected to the viewscreen," Mr Wilson explains, "gives you, as you can see, an outstanding electronic blackboard." Sure enough, while he guides the teachers through the lessons, the text and images they should be getting on their calculator screens appear, writ large, on an overhead projector screen.
The calculators are impressively well-endowed with options. Some of the teachers are using them for the first time, so the images do not always match. "Don't worry," Mr Wilson reassures them. "The mistakes you're aking are the ones everyone makes. So after this course you'll be able to sort out your students quickly without getting bogged down in why their calculators aren't working."
The support materials have been prepared by Learning and Teaching Scotland and cover 18 Higher Still maths topics, ranging from quadratic functions to the geometry of the calculus.
While the tutor talks and the teachers work, snake-like polynomials wiggle up and down the screens, their roots and turning points clearly visible. Sine and cosine curves, some choppy, others smoother, undulate from left to right. Straight lines intersect. Functions are transformed. Statistics are displayed.
The lessons tease out and reinforce the intimate relationships in the mathematical world between numbers, concepts and images, and the connections each of these makes to the physical world. Instead of struggling to understand written mathematical definitions, the calculator users can see them in action. Even for experienced maths teachers the lessons are satisfying.
The course has been set up and the tutor trained by an international, non profit-making organisation known as T3 - Teachers Teaching with Technology - which was founded in the United States by two maths professors with the objective of getting advanced calculators into maths and science classrooms. T3 Scotland is run by Ian Forbes, a maths education lecturer at Edinburgh University.
"The SCCC's Advanced Calculators and Mathematics Education paper (1998) on the use of advanced calculators in the classroom has recently been endorsed by Sam Galbraith, the Children and Education Minister, who is keen to see progress made," says Mr Forbes. "So we've had a national conference to discuss how best to implement its recommendations and provide advice to the Scottish Executive. It's likely that every maths teacher in Scotland is going to get a minimum of two days training in hand-held technology over the coming year."
The calculator East Renfrewshire has chosen is the Texas Instruments TI-83, but other companies produce machines with similar capabilities, and Learning and Teaching Scotland has prepared - in addition to the TI materials - sets of Higher Still lessons for Sharp and Casio graphics calculators.
Ian Forbes, T3, tel 0131 651 6034.For information on Texas Instruments technology or to arrange a demonstration, contact Guy Harris, tel 01604 663003