The classroom is the work-place of both teachers and children, and a well managed work-place increases job satisfaction and enhances the learning process. Planning facilitates co-operation and the best use of resources and space. This is particularly relevant when mathematics is being integrated with other subjects. Integration with geography may require the use of maps or globes. Science equipment may be required for work on capacity. Integrating mathematics with other areas of the curriculum enables children to use mathematics in a meaningful way.
The mathematics area
Ideally the mathematics area should be a free-standing worktop where children experiment and display their results. In addition it is necessary to have wall space for displaying charts, flashcards and the results of the children's work. The worktop space could be a cupboard or shelving which can then be used to store equipment not in use. Mathematical displays and apparatus should be changed to suit the strand being worked on if they are to be seen to be effective and genuine aids.
Effective use of equipment
Children who are actively involved in a structured task will be more likely to exhibit positive classroom behaviour, and the teacher will be free to work with another child or group of children. It is important that the children share responsibility for the appropriate use and storage of the apparatus, as this will develop their independence. Charts showing labelled equipment and the terminology in use should be visible to those working in the area. These give the child the freedom and independence to work on tasks uninterrupted. If possible there could be a recording area nearby, or children could use clipboards for on-the-spot recording. Colour-coded or number-coded pockets of worksheets could also be provided so that the children can work independently.
Mathematics in the senior classes
Mathematical exploration in the senior classes should continue the use of manipulatives. It is envisaged that there will be an even greater emphasis on problem-solving and the use of examples from real-life situations, for example using information from newspapers or local shops. Calculators may be used for handling larger numbers but children should be encouraged to make decisions about when they need to use them and to be confident in their use. This is where their developing estimation skills will be important.
Where computers are available they will be of great assistance in cross-curricular projects for data representation and interpretation and as a basis for drawing conclusions based on data collected.
Work on simple percentages and their relationship to fractions and decimals can be related to examples of their practical use in the environment and in advertising. Numbers should be kept small and simple to encourage consolidation of concepts.
Work on shape and space should, where possible, involve handling and manipulating shapes.
The content of the mathematics curriculum is sequential and dependent on knowledge gained at each level. This needs careful planning, as children acquire the requisite skills in different ways and at their own individual pace. In planning a sequence of lessons on a topic the teacher must first assess the readiness levels of the children. This can be done by giving a pre-test or when doing revision. The information gained can be used to group the children where necessary. Periods of direct wholeclass instruction can follow, with the children contributing to blackboard or overhead projector work at their own level. Emphasis should be placed on the quality of the contributions, for example how they arrived at a conclusion, how some children found a different method, summarising what has been done, or identifying strategies that might be useful in approaching a task.
Games can be very useful in mathematics. Card and dice games can reinforce number recognition and help in the development of strategies. They also encourage co-operation and turn-taking. These activities should be structured by the teacher, and he/she can discuss with the children why they chose to play the game a certain way. Older children can design their own board games. They will be quick to notice what happens when they put in too many penalties, for example too many snakes in a snakes and ladders type game. The game ceases to be fun if there is little chance of winning.
Children often fail at mathematics because they have missed out on an earlier learning experience, for example one-to-one correspondence, seriation or conservation. Language or reading deficiencies can inhibit the child in approaching written problems. This can often be overcome by presenting tasks concretely, pictorially, diagrammatically or with pictures to support the words. Poor sense of direction, time and spatial relationships can also interfere with the learning of mathematics, and memory deficits mean that the child cannot easily recall number facts.
In planning sequences of instruction the teacher must consider these factors and encourage the development of alternative strategies. The establishment of personal benchmarks in measuring can be of great help, for example the width of my little finger is about one centimetre, if I stretch out my arm it is about a metre from the tip of my finger to my neck. Labelled reference points in the classroom can also assist the child in estimating heights and widths, for example the bookshelf is one-and-a-half metres high and I am nearly as tall as it, four carpet tiles make a square metre.
All children gain from using strategies for number facts. They can learn the 'easy' number facts first ( 1, 2, 5, 10) and use these to build up the others using doubles, near-doubles and patterns of odd and even. These strategies are of particular help to children with memory problems.
It is also important to consider the child who may be particularly good at mathematics. He/she can be given more difficult or taxing problems to solve rather than prematurely pushing him/her forward. Problems with two or three steps or open-ended problems are more difficult and provide a challenge. Once a concept is well understood it is better to use it in problem-solving activities than to overuse rote computational exercises. Sequences of graded work-cards allow children to work at their own pace and to undertake extension activities.
A balanced mathematics programmewill cover concepts, skills and problemsolving and should consider the child's strengths and weaknesses. Computer technology and calculators can be used effectively both in remediation work and in extension activities for the more able child.
Assessing children's work in mathematics
Assessment is an integral part of the teaching and learning process. Teachers use assessment techniques every day. They make decisions about what to teach and how to teach it based on their observation of the children and the feedback they receive from work the children are doing. Reporting to parents is usually based on both the results of tests and the teacher's assessment of the child's approach to the subject.