Teaching approaches
Teachers will notice that the changes in this curriculum cover both content and methodology. New topics have been introduced and other topics have been omitted, repositioned or given a new emphasis in the curriculum. It is hoped that these new emphases will lead to an enhancement of the child's mathematical education and to a heightened pleasure and interest in the subject.
Guided discussion and discussion skills
This curriculum places great emphasis on child-child and childteacher discussion. In this way the child clarifies his/her thinking and gains selfconfidence and self-esteem. Discussion, rather than just questioning, should be the basis of the interactions between teacher and child. This strategy encourages the development of skills and is also the arena for developing mathematical language. Children must be trained in discussion skills before they can effectively use them in a group. Skills such as turn-taking, responding positively to the opinion of others and having the confidence to put forward an opinion of their own are essential skills that transfer both throughout the curriculum and into real life. Children must be secure in the knowledge that others will listen to their opinion and treat it with respect.
Using a hands-on approach
A hands-on approach is essential if children are to understand mathematical concepts. This approach is important right through to sixth class and will require access to a considerable amount of equipment. Working with equipment can be done individually, in pairs or in groups, and the allocation of the equipment can be organised on a class or school basis.
Mathematical language
When children use mathematical language it is important that they use it accurately. Understanding mathematical language leads to the correct interpretation of mathematical symbols and accurate reading of algorithms or word problems. This helps the child to choose the correct operation for the task. Discussing and interpreting symbols in the environment is a good starting-point for introducing mathematical symbols as well as being a learning exercise in itself. Signs often have words on them, while symbols are usually pictorial representations of a statement, for example the no smoking sign, road signs, poison and cleaning instructions on clothes. These are internationally recognised symbols and indicate to the child that these symbols carry a meaning with them, as do mathematical symbols.
It is helpful when teaching to have a common approach to the terms used and the proper use of symbol names. Introducing mathematical symbols and numerals is the last step in the learning process. In teaching place value it is better to use units than ones, as it can be confusing for the child to describe 21 as 'two tens and one one'. Work on place value could include collecting the house numbers of the children in the class and classifying them as being numbers with one digit, two digits or three digits. The same care and attention should be given to the formation of numbers as is given to the formation of letters. Children should practise forming and writing numerals in sand, feeling the numeral on sand-paper or carpet, and tracing it. They should be given clues and guidance on where to start. This exercise can be reinforced by means of charts. The teacher can observe children who have difficulties with, for example frequent reversal of numbers, poor spatial awareness or poor manual control.
It is a particularly good idea when teaching and assessing the child's concept of place value to present the algorithm horizontally. The pupil then has to find the value of each digit before writing the algorithm vertically. It is important that children read algorithms from left to right. This is similar to leftright orientation exercises in reading and writing.
When children see 259 - 156 they should be encouraged to 'read' it as 259 minus, subtract or take away 156. This makes it clear to the child that the smaller number is the subtrahend. Children often misinterpret division statements, for example 410 ÷ 7 could be read by the child as 410 into 7. It should be read as 410 divided by or shared between 7.
