SPOTLIGHT ON EARLY CHILDHOODMarketing Research and Data Analysis
Part-whole experiences Young children are naturally curious about their world and have an interest In how the things in their world fit together or can be taken apart, -which leads to an understanding of parts and Moles. They also develop an interest in how things can be shared between people. Ideas such as these underpin the later development of fraction concepts. There will be many opportunities to explore these Ideas and develop the appropriate language with young children. both in their daily Ide and in pre-primary settings. There are three types of part-Mole experience that young children ail encounter. 1. Naming parts. They learn that many of the objects ri everyday 111e consist of different parts: toys, sets of pencils. packs of cards, cars, plants. animals and even they on bodes. Parts can be named and in some crcurnstances taken apart and put back together (e.g. a pack of cards), although in other situations the parts cannot be taken apart and put back together (e.g. an animal’s or a child’s own body}. 2. Parts of wholes. They learn that whole things can be divided into parts: trot is cut up, a loaf of bread is sliced. juice is poised into several glasses, a piece of paper is cut into pieces and the playdoucji is dvded into several smaller chunks. The size of these pieces can differ. Actmlies such as these provide opportunities to introduce and practise the lanoiage of part-Mole: divided, shared, samakkiferent equallunequal. more or less and, where appropriate, fraction names le.g. half. quarter, third. fifth). 3. Parts of sets. Children learn that groups of things can be &vide& biscuts we shared at mornng tea. the pencis are distributed fairty and cards are dealt for a game of snap. Again, there are opporturities for comparing amounts and usng the relevant language — divided, shared. equal; unequal. more or less and freeborn names. Initially, young children who are oven one biscuit when another person receives two biscuits onll be quck to say that this is an unfair distnbution. However, if their biscuit is broken Into two pests. they and be satisfied that it is now a fair distributon_ When asked Ashy this is a fair drathbution they coil say that they each have ‘two bscurts’. According to Piaget and Inhelder 0969), young chidren who think Ike this we stIl in the preoperational stage and have not learnt to conserve quantity. As a result of further cognitive development these children Anil team to conserve quantity and be able to understand that the amount of biscuit they have has not changed simply because their biscuit is broken into two pieces and that this is stil an unfair distribution.
Models of the part-whole meaning Attributes such as region. length. set and area arc useful in modelling the part-whole meaning of a fraction. The region is the most commonly used model for this and the most easily handled by children. You can also model the quotient interpretation using any of these attributes. but here again the region model is most often used because it is the simplest. Other attributes. such as capacity. volume and time. can also model the meaning of fractions. Region In the region model. which is a special version of the area model_ the region is the whole the unit). and the parts are congruent (same size and shape). The region may be any shape. such as a circle. rectangle. square or triangle. You should use a variety of shapes when presenting the region model so that the children do not think that a fraction is always a particular shape — for instance. ‘part of a pie’ lid the region is a circle). A rectangle is the easiest region for children to draw. and as figure 112 indicates. it is also the easiest region to partition. (Try partitioning each of the shapes shown into three equal parts to see which is easiest.) The circle has the advantage of being easy to sec as a whole. but this does not outweigh the advantages of the rectangle. which we use extensively throughout this chapter_ Length Any unit of length can he partitioned into fractional parts of equal length_ Children can begin by folding (partitioning) a long, thin strip of paper into halves. quarters and so on. Later. you can use length partitioning to represent fractions as points on a number line. For example. as shown in figure 12.3. you could partition lengths into thirds to help children realise that the number is 4 + 4.