and several properties, by which we recognise their differences and similarities. When the learners are given the names of the shapes, they do not associate them with familiar objects. The square is a square because it looks like a square. The learners recognise the words ‘circle’, ‘square’, etc., by sight and not by individual letters. In the next stage the learners recognise, identify


and describe the component parts and properties of the shapes, e.g. a square has four equal sides and is symmetrical. The learners also need to develop language to go with the new specifi c concepts. They still do not have a logical order for the properties and do not see a relationship between them. The next stage is the informal deduction stage


where the properties of the shapes are logically ordered. Learners are able to see that one property precedes or follows from another and can therefore make a deduction in this regard. They can use what they know to explain the relationships between shapes, e.g. they can explain why all squares are also rectangles – they have four sides and are symmetrical. Children learn through play. Design activities


which will assist the learners to learn what is necessary for further development. Give the learners different shapes for free play (look at tangrams and other mosaic shapes in plastic and cardboard, and in different colours and sizes). Encourage learners to say what they are doing, talk about the pictures they are making with the shapes and to share their play with each other. In this way, they become familiar with size, different shapes and colours. They see how the shapes fi t together and they become aware of the properties and relationships of 2D shapes. It is diffi cult for learners to conceptualise a


3-dimensional mathematical world when most of the mathematical experiences learners have are 2-dimensional representations. It is important that learners handle the physical or actual objects, rather than only look at pictures. Playing with actual objects allows the learners to explore properties such as fl at surfaces do not roll, but curved surfaces do.


Measurement


The Foundation Phase learners cover time, length, mass and capacity. In all aspects of measurement, the learner should progress from concrete operations involving informal measuring, to formal measurements, and fi nally to abstract operations involving comparisons, conversions and calculations. Learners need to work practically with different concrete objects and shapes, and through such activities, learn about the properties of length, capacity, mass, area and time. Time is represented by the use of clocks, calendars


and watches. Each time piece measures a unique unit of time duration where there are no gaps or overlapping. When doing activities on time, one needs to keep in mind that there is a difference


between telling time and the concept of time. Telling time on a clock face is not necessarily a concept of time. This is why it is so important that the learners become aware of the passage of time by knowing the days of the week and months of the year. Use calendars to work out the months and days before a birthday, weekend, religious event or public festival. The learners need to experience the duration and the passage of time. Learners must understand that events occur in a sequenced order – for example, wake up, breakfast, school, lunch and supper. Learners can use the analogue clock in the classroom to tell the progress of time. Begin with simple time progressions at school – for example, the time break starts and the time it ends; the time school starts, and the time school fi nishes. Encourage learners to use the time vocabulary. Length can denote the height or width or general


size of an object. These properties can most often be visually measured. Learners should explore their environment with measuring length and size in mind. It is important to provide plenty of opportunity to practically compare, order, sequence, arrange and match different objects and materials within class time. Before using formal measuring instruments, learners should be encouraged to develop the skills of estimating and predicting. The concept of capacity and volume is introduced


informally when learners use informal and non- standard measures – for example, how many spoons fi ll a cup, and how many mugs fi ll a jug. This is essentially a series of practical activities and every learner should be an active participant. Learners should estimate how many fi rst, then measure and fi nally compare. In this way, learners are able to order the containers from those which hold the most to those that hold the least. The learners then record and describe their fi ndings by writing them down or through drawing.


Data Handling


This Content Area covers collecting, organising, displaying, analysing and interpreting data. The focus is on sorting objects and data in different ways. The specifi ed criteria for organising the data is either initiated by the learners or the teacher, based on the attributes of the objects or data. Learners are expected to analyse and construct pictographs, and simple bar graphs of the data, as well as interpret and make inferences from given basic graphs. Use data or objects that are applicable to the


learners’ everyday lives; so as to easily engage the learners. This encourages all learners to actively engage and remain equally involved throughout the lesson. Always move from the known and concrete, to the unknown and abstract. Ensure that learners interact and physically sort objects before moving on to more abstract data collection and organisation. Cover different topics and types of data.


Guidelines to teaching in the Foundation Phase 11


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