Concrete operations in practice

Previously we described Piaget’s definition of ‘concrete operations’ as the ‘mental operations involving the world of material things’. Let’s Think through Science! promotes this type of thinking; it is designed specifically to stimulate intellectual growth through concrete operations. Here we will describe in a little more detail some of the different kinds of thinking that comprise concrete operations.

The word schema (plural schemata) is used to describe a general way of thinking that can be applied in many different contexts. If pupils did not develop schemata, they would be condemned to devising a new solution each time they encountered a familiar problem in an unfamiliar situation, whether or not they had solved it before in a different context.

Some examples of concrete schemata are described below, together with examples of the type of activity that each schema needs. Let’s Think through Science! provides activities that will help pupils to develop thinking abilities related to all seven of these schemata.

Classification

Even elementary work on living and non-living things requires them to be put into groups with some characteristics in common: that is, to classify them. Classification problems can be graded in difficulty according to how many variables are involved, how many values each variable has, and how clearly the different groups are defined. A variable is simply a way in which things vary from one another. For example, they may vary in colour, in shape, or in number of legs. Colour, shape, and number of legs are all variables. Each variable may have a number of values. The variable ‘colour’ may have the values blue, green, red, puce, etc. The variable ‘number of legs’ may have values two, four, six, eight, and so on.

Causality

Causality is a special type of relationship between variables. What causes what? We may laugh if we hear a young child say that the wind is caused by the trees waving back and forth, and yet from the perspective of a three- or four-year-old child, this may be a perfectly reasonable conclusion. The confusion of Correlation (things happening together) with Causality (one making the other happen) is a problem that besets even some supposedly ‘intelligent’ adults. A classic example is the belief that ‘larger classes get higher grades’. This may be the case, but does it follow that we should therefore increase class sizes to improve grades? In Let’s Think through Science!, pupils explore Causality in a variety of contexts, such as the relationship of teeth types to diet (Activity 1.2: Animals and Teeth), and shadow to sun (Activity 6.1: Shadow Stick).

Combinatorial thinking

How many different numbers can be made using only the digits 1, 2 and 3? An adult will immediately think of 1, 2, 3, 11, 12, 13, 21, 22 and so on. However, it is difficult for a seven­year-old to think of all the possible combinations of a limited number of variables. Some pupils may be able to write down various combinations at random as they come to mind, but to do so in a systematic way is challenging. Activity 1.3: Sandwiches is an example of an activity that develops this kind of thinking. Pupils need to use Combinatorial thinking to devise as many different sandwiches as possible using limited numbers of fillings, types of bread and ‘extras’ (for example, mustard, salad cream or pickle).

Seriation

‘Seriation’ means putting things in order. In the first Let’s Think! pack (Adey, Robertson and Venville, published by nferNelson, 2001), five- and six-year-old pupils are set the task of putting 10 sticks in order of length. This provides considerable cognitive conflict for five-year-olds, but would be too easy for most seven- and eight-year-olds. In Activity 3.2: Classifying Materials, children have to order materials in terms of how ‘strong’ they are — which is quite difficult, because the meaning of ‘strength’ can be ambiguous. The point is to develop the general ability to order things; Seriation skills can be used in many different contexts.

Concrete modelling

Concrete modelling is the building of simple models that offer an explanation for observations; each element of the model has a specific concrete referent. In Activity 5.3: Exploring Poles, for example, pupils are encouraged to develop a concrete model of magnetism that includes the ideas of ‘poles’ and a ‘field’ (visualised as the effect on a paperclip at a distance from a magnet).

Relationship between variables

‘The bigger the magnet, the stronger it is.’ Is that true? In other words, is there a relationship between the variable ‘size of magnet’ and the variable ‘strength of magnet’? Science is all about exploring relationships between variables; therefore, some of the activities in this programme give pupils an opportunity to do just that; see Activity 3.1: Clothes to Wear and Activity 5.2: Strength of Magnets.

Conservation

The fact that a quantity of water remains the same when you pour it from one container to another is obvious to adults, but not to many seven-year-olds. In order to become aware of ‘conserved’ quantities, one has to develop the schema of Conservation: an understanding that the amount of many materials stays the same, even though their shape or location has been changed.

Understanding that the volume of water remains the same when it is moved to a differently shaped container (when, for example, it is poured from a short fat measuring jug into a tall thin glass) requires the pupil to see that the greater height of the water level is compensated for by the fact that the container is narrower. This requires considerable mental processing. As adults, we have taken this fact for granted for many years, we are therefore surprised at how difficult it is for some seven-year-olds to grasp.

These seven schemata, or ‘ways of thinking’, underlie all scientific thought and much general thinking as well.

License

Let's Think through Science 7-8 and 8-9 Copyright © by Lets Think Community. All Rights Reserved.

Share This Book