Shake hands with maths
Mathematics is full of hard words. Sometimes mathematicians seem to go out of their way to create long, complicated "mathematical" terms for perfectly straightforward ideas. Take the word hexagon, for example. This is a simple enough concept: a shape with six sides. It is also a simple word - in Greek. Hexagon just means six sides.
Talking in Greek is no more mathematically correct than talking in English - it's really just a historical leftover - so hexagon is no more mathematical than six sides or six-sided shape. But you won't find English terms in the vocabulary checklist for the national numeracy strategy (see references, below). Hexagon, on the other hand, is right there, under 2D shapes for Year 2.
Complicated mathematical terminology can create a barrier for many pupils, particularly for visual and kinaesthetic learners who develop their understanding more effectively by doing things than by saying. Exploring patterns and finding the properties of six-sided shapes can be a delight, but having to learn a lot of disconnected Greek or Latin words may present a significant hurdle.
Pupils who struggle with the formal mathematical terminology may find it helpful to use Sign, the language used by many hearing impaired people. The signs for common maths terms often reflect the original meaning of the Greek words far more effectively than the spoken sounds. For example, take the word congruent. In Greek this just means coming together. The common sign for it involves a movement that conveys this very well. The signer's two hands come together, to show how one shape can fit over the other so that the two match each other perfectly. (See photographs, above) Another word where the meaning conveyed by the sign is close to the original Greek sense of the mathematical term is isosceles. This comes from the Greek iso, meaning same or equal, and skelos, legs. So an isosceles triangle is just a triangle with equal legs.
The signing movement reflects this very well. First the signer shows an ordinary triangle, with two forefingers providing two sides and a base composed of the two thumbs meeting tip-to-tip. Then the two thumbs are tucked away, leaving only two sides. Finally, the two forefingers are held side by side, to convey their equality. (See photographs, above) Describing signs with static photographs is inevitably cumbersome, but any pupil who struggles with mathematical vocabulary is likely to benefit from their regular use when new concepts are introduced. If the class is lucky enough to have a member who is a regular Sign user, then they may be prepared to assist their less fortunate fellows in the mathematics classroom by demonstrating meaningful signs for new terms. Failing that, a CD now on sale, showing short video clips of a wide range of mathematical signs, Signs for Education - Mathematics, is a good investment (see details, below).
However, some signs may actually be considered to be too meaningful by some mathematicians. For example, the 2005 mental mathematics test for pupils at the end of key stage 3 included the question: "The perimeter of a rectangle is 20cm; its length is 7cm. What is the width of the rectangle?"
Signers supporting pupils taking this test were warned, "Take care not to convey meaning of rectangle, perimeter, length, width by choice of sign."
The common sign for perimeter, for example, conveys the original Greek meaning of the word, around (peri) measure (metron), very clearly. The forefinger of the left hand is held up, and then a rough path around the imaginary shape is sketched out in the air with the forefinger of the right hand.
Similarly, rectangle is signed by roughly sketching its outline in the air, while length and width are indicated as the distance between a pair of pointed forefingers.
These signs are clearly meaningful - so, for just that reason, they are banned from the tests. This seems rather bizarre. Surely we should be trying to make the maths as meaningful as possible for the pupils, not creating obstacles with mathematical terms that have to be written or finger spelt.
But at least when children are being taught rather than tested, signs may be used in place of Greek terms such as perimeter, congruent or isosceles.
This makes obvious sense for regular Sign users, but it can also be helpful to those pupils for whom such terms are far more difficult to remember and use.
The writer is a principal research officer at the National Foundation for Educational Research
Teaching Maths to Pupils with Different Learning Styles By Tandi Clausen-May, Paul Chapman Publishing (2005).
National Numeracy Strategy, 1999: Mathematical Vocabulary. DfES publications, www.standards.dfes.gov.uknumeracyl
Signs for Education - Mathematics Microbooks Ltd (2002). www.microbooks.orgl
Mental mathematics scripts for pupils with hearing impairment and pupils who use sign language Qualifications and Curriculum Authority (2005)