of that collection. Learners also come to realise through counting that the fi nal number remains constant – regardless of the order of counting the objects, or how the objects have been rearranged. Thus, the learners grasp through counting, the relationship between the ordinal aspect (the position in a sequence) and cardinal value (size). Generally, learners only begin to recognise


number patterns once they have familiarised themselves with those patterns after regular practice, by repeatedly counting them. Counting requires repeated repetition of a series


of number names or number symbols in an identical order (stable order principle). Every number name and number symbol must be


matched to only one object (one-to-one principle). The diffi culty comes in when learners struggle


to remember all the number names, connecting symbols and co-ordinating these with the objects being counted. Learners need to be given daily opportunities to practise the recall, reading and writing of the number names, symbols and their discrete values. It will mean practice in the counting of real objects, and by using number lines, number blocks and number cards as support while counting. The various activities and strategies used will


remain the same as the learners develop a strong understanding of the absolute magnitude of each number. The learners are encouraged to move from counting all to counting on, and towards counting on – away from concrete counters – and on to recalled number facts. The counting on is an important step in learners’ development of increased fl exibility in handling numbers abstractly.


Content Areas


Numbers, Operations and Relationships This area focuses on developing number sense, which includes the meaning of different numbers, the relationship between different numbers, the relative size of different numbers, the representation of numbers in various ways and the effect of operating with numbers. In the Foundation Phase, the focus is on whole


numbers up to 1 000 and common fractions. Number concept is developed through working with physical and concrete objects. These objects are used to count, share, group, and combine quantities, skip count, solve problems in context, and build up and break down numbers. Number concept development teaches learners


about the properties of numbers and assists them in developing strategies to help them do calculations. Problem solving in context creates the


opportunity for learners to communicate their own thinking. Problem solving can be done either orally or in writing, through pictures and eventually number symbols and sentences. Learners develop an understanding of the basic


10 Guidelines to teaching in the Foundation Phase


operations of addition, subtraction, multiplication and division.


The concept of fractions is developed through problem solving of physical quantities, or by drawing. These problems should involve sharing with whole number remainders or fractions of the whole. Sharing problems should include both fi nding


parts of a whole and parts of a collection of objects. In Grade 1 learners are not expected to read or write fraction symbols, but should have a basic understanding of the concept.


Patterns, Functions and Relationships


In the Foundation Phase, this area focuses on the description of patterns and relationships. It involves identifying and analysing the regularities and changes in patterns. Learners work with number patterns, such as skip counting, and geometric patterns, including pictures and shapes. Learners start with using concrete and physical


objects to create patterns. They progress to pictures and drawings, and fi nally to symbolic forms. Learners need to be able to recognise, copy, extend, describe and create their own patterns. Copying patterns helps learners to see the logic


behind the patterns. Extending patterns helps learners check that they


have correctly understood and interpreted the logic of the patterns. Describing the patterns helps learners to verbalise


their thinking and enhance their Mathematics vocabulary. Being able to understand the logic behind


patterns, helps form the basis for developing Algebraic thinking. Number patterns support number concept


development and operational sense, while geometric patterns help learners apply their knowledge of space and shape. Number patterns should be incorporated into counting activities every day.


Shape and Space


This Content Area focuses on 2D shapes, 3D objects, positions and directions. Learners explore the properties of objects and shapes by sorting, classifying, describing and naming them. Learners need to draw shapes and build objects. Learners need to be able to recognise, and describe shapes and objects in their natural environment. Learners also need to be able to describe the position of objects and themselves within the environment, and follow and give directions within the classroom situation.


Teaching space and shape When children are very young, they rely heavily on the visual, and they will look at shapes in a non-verbal way. Shapes are determined by their appearance. Children will generally look at them as a whole and not as something made up of parts


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