Concrete operations in practice

In Chapter 2 we described Piaget’s definition of ‘concrete operations’ as the ‘mental operations
involving the world of material things’. Let’s Think through Science! 8 & 9 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
9 provides activities
type of activity that each schema needs. Let’s Think through Science! 8 &
that will help pupils to develop thinking abilities related to all six of these schemata.
Classification
Even elementary work on living and non-living things requires pupils to put them 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 ways of
moving. Colour, shape and ways of moving are all variables. Each variable may have a number
of values. The variable ‘colour’ may have the values blue, green, red, etc. The variable ‘ways of
moving’ may have values walk, fly, swim, 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
9 pupils explore Causality in a variety of contexts, such as the relationship
through Science! 8 &
between the brightness of a light and the elements controlling that brightness (Activity 6.3:
Controlling the Light), and the relationship between animals and habitat (Activity 2.2: How
am I Adapted?).
Seriation
Seriation means putting things in order. In the first Let’s Think! pack (Adey, Robertson and
Venville, 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 eight- and nine-year-olds. In Activity 3.3: I like my Soup Hot, pupils have to order
materials in terms of how good an insulator they are — which is quite difficult. 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 1.3: What makes me
Move?, for example, pupils are encouraged to develop a concrete model showing how bones,
joints and muscles work together to effect movement.
Relationship between variables
‘The bigger the bone, the stronger it is Is that true? In other words, is there a relationship
between the variable ‘size of the bone’ and the variable ‘strength of the bone’? 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 3.2: Hotter or Colder? and
Activity 5.3: Late for School).
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 some eight-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 eight-year-olds to grasp. Activity 4.2: I can’t find the Sugar uses this schema.
These six schemata, or ‘ways of thinking’, underlie all scientific thought and much general
thinking as well.