Structure of the curriculum
The areas of content in this mathematics curriculum are referred to as strands. The strands form a network of related and interdependent units. These are further developed as strand units. Each strand unit contains the content and some exemplars for that unit. Measures, Shape and space, Data and Algebra form a greater part of the curriculum than Number but number is an integral component of all of the strands. No strand stands alone and this should be reflected in timetabling.
How the content is presented
- content is presented in two-year blocks, for example first class on the left and second class on the right of each page. The treatment of content is common to both classes. This presentation helps the teacher in planning and in revision
- the strand unit is in coloured type to the left of the page
- the content statement is indicated by a bullet
- the content of the exemplars is in italic type. These are limited suggestions for implementing the strand unit. It is envisaged that teachers will develop and extend these suggestions as they work through the programme
- vocabulary relevant to the strand unit is shown in bold type, for example long/longer, short/shorter, positive/negative
- the sequence of presentation of the strands in the content document is: Number, Algebra, Shape and space,
- integration opportunities are indicated in some strand units but these are merely suggestions. It is hoped that teachers will identify other opportunities to integrate
mathematics with the rest of the curriculum.
Early mathematical activities
All children come to school with some mathematical knowledge and language, which they have gained at home and through play. It is through play that young children learn to share ideas and co-operate, to share toys and express ideas. This differs greatly from child to child. Play in the classroom develops these skills by providing structured situations for the child to explore. Early mathematical activities guide this basic knowledge and provide a solid foundation for subsequent mathematical investigations both at school and at home.
It is envisaged that this strand will be covered intensively and will therefore provide a solid basis for subsequent work. The emphasis will be on developing the use of correct mathematical language and confidence in handling the materials.
A ceiling has been placed on number work to allow for more extensive treatment of the mathematics programme as a whole and to allow more time for concept development. Less emphasis is placed on complex computational exercises involving whole numbers and fractions. It is hoped that writing will not be the sole method of recording and that symbols will only be used when appropriate to the child's level of understanding. Recording can also be concrete, oral, pictorial or diagrammatic or can include modelmaking. Calculators have been introduced from fourth to sixth class when it is expected that the children will have achieved mastery of basic number facts.
All number work should be based as much as possible on the children's own experiences and real-life examples used. It is essential that children see mathematics as relevant to their own lives. Projects that use advertising features from newspapers or prices from local shops and supermarkets can be used to link many of the strands. Work on fractions and decimals in general will place more emphasis on understanding the relationships between them. This might best be achieved by the use of manipulatives and paper-folding.
In the addition and subtraction of simple fractions and simple mixed numbers it is suggested that equivalent fractions be used to simplify calculations.
Children will need experience of many examples of equivalent fractions, and this is best done through generating families of fractions, for example
The same process can be followed with thirds, fourths and fifths.
belongs to the set of equivalent fractions
belongs to the set of equivalent fractions
In sixth class, listing multiples rather than constructing factor trees should be used to find common multiples and denominators. Initial examples should be restricted to simple fractions that are in common use. Hundredths and thousandths are best introduced through money and measures and their relationship with decimal fractions.
Algebra, which includes patterns, sequences and statements such as 2 + ? = 5, has always been part of the curriculum but is now formally recognised at all levels. At infant levels it includes copying and extending patterns in colour, shape, size and number. First and second class progress to exploring and using addition facts, and third and fourth class work includes exploration, extension and description of sequences of numbers. At the senior level positive and negative numbers are introduced. Rules and properties of brackets, priority of operations, equations and variables are also covered. It is expected that the numbers used will be kept small so that the children can understand the concepts presented.
Shape and space
This strand explores spatial awareness and its application to real-life situations. Here again the child's experience must be a practical one. The child must know how to choose the correct mathematical tools for the problem and be able to use the correct vocabulary to describe his/her work. Shape and space is particularly suited to integration, as children will enjoy finding shapes and angles in the environment and creating tessellating patterns in art. Since angles and tessellation are so closely related it will be necessary to encourage children to make this connection when covering surfaces and examining paving and tiling. This leads to the discovery that shapes that tessellate form an angle of 360° at the points of contact.
This strand has six strand units. In this strand children are given frequent opportunities to undertake practical activities. These activities are particularly useful in facilitating linkage within the strand units. Fractions, decimals, percentages and operations can be applied in measuring activities.
Children learn how to select the correct measuring instruments and the most appropriate strategy for tackling a particular problem. Problems set in these strands should be mainly practical, with the totals easily verified by measuring. Initially children work with the measuring unit present, i.e. the metre stick, halfmetre measure or centimetre. This provides a visual reference when estimating and assists in the development of the concept of a metre or centimetre.
Children should be taught from an early age to estimate the weight, length or capacity of an object. This can be done by comparison, using a labelled object that weighs one kilogram, for example a bag of sugar. The child can feel the weight of the labelled object and compare it with the test object by hand weighing. The actual weight can be discovered by using a weighing scales.
Children will need to handle and use a wide variety of materials within each strand. They will need to investigate the capacity of tall, narrow containers and short, wide containers. They can then discuss and compare their findings. Activities in weight can include the comparison of the weight of a small, heavy ball of Plasticine with the weight of a large bag of polystyrene.
When learning about capacity they will need to become familiar with the major and minor markings on containers and note the differences between the various methods of marking.
The reasons for using standard measuring instruments should be explored in a practical way with the child; would we all get the same amount if we bought potatoes by the bucketful? Children who have grasped the concept of standard measure will realise that there could be many different sizes and shapes of bucket. Teacher observation of such learning experiences can be valuable in assessing the child's progress.
Graphical representation and interpretation have always been part of the curriculum, but data handling is now a separate strand. Infant classes collect personal information and represent it on a pictogram; older children create and interpret bar charts and pie charts. Interpreting and understanding visual representation is essential, as the child needs to be enabled to interpret data in an increasingly technological world, and it is hoped that, where available, information technology will be used by children in data-handling exercises.
We manipulate data in the formulation of simple bar charts and pictograms at quite an early age. Databases allow us to extend this knowledge to the real world by handling larger amounts of information. However, children must understand how important it is to enter relevant data and ask clear questions if the information we extract from the database is to be of any use. In collecting information on, for example birds, the children will have to decide under which headings they will collect the information: name of bird, habitat, number of eggs per clutch, wing span, main food source. There can be much discussion on what they wish to discover: for example, do all fish-eating birds live near the sea? Do birds with a large wing span lay more eggs? By the time they have collected the information, constructed the headings, entered the data and considered some questions they will already have gained an understanding of how a database works. Using the database to find the answers then becomes a technical activity, merely a tool for the manipulation of a large amount of information.
The concept of chance has great importance in a number of areas. We have all experienced chance when playing board games and participating in sport. It is fundamental to decisions made in such areas as business and weather forecasting. It represents real-life mathematics and promotes thinking and discussion. Many children and adults have poor or inadequate notions of chance and likelihood. Some assume there are 'lucky' numbers, which urn up more often than other numbers in a raffle. This can provide the basis for interesting experiments. These topics are introduced through problems, practical experiments and simulations that help to develop intuitive foundations for future work and are fun for the child. It is intended that the area of chance be explored in a practical manner with the emphasis on accurate use of language.