Strands and schemata
In looking at the way that children’s thinking develops over the years at school, it is useful to look at strands of thinking which may be encountered first in Reception or Year 1 and then are re-visited again and again with increasing complexity and sophistication throughout the school years. An example might be ‘putting things in order’, or seriation: in Reception, just arranging ten sticks in order of their length might be quite challenging; later children become able to order things according to two characteristics (for example, colour and size), and by Year 6 they can think usefully about the order of events in a story. Likewise work with numbers develops from early conceptions of a number as abstracted from a particular number of objects through to the complexities of negative numbers, fractions and decimals.
Each of these ‘strands’ represents a rather general type of thinking which we can apply to all sorts of different contexts — think of all the different ways in which we use seriation or number operations. In our Let’s Think! approach to teaching thinking, it is these general ways of thinking that we focus on. Thus the ‘subject matter’ of thinking lessons is not any particular content in, say, the National Curriculum, but rather the underlying general thinking processes on which all of the content is based. In the mathematical Let’s Think! materials we refer to these general thinking processes as strands, but in the other Let’s Think! programmes we use the terms ‘schemata’ (singular: schema) or ‘reasoning patterns’. Below are some more examples of these strands/schemata. Getting a handle on these will help us to see how we can work with children to help them develop their thinking.
Seriation, Narrative Seriation
Putting things in order, by length, size, or some other characteristic. In storytelling, the ability to sequence and re-sequence actions and events to create a narrative and to be able to manipulate different component parts of that narrative, such as time and place, relative to each other — eventually to give multiple meanings and layers of complexity.
Classification
Arranging things in groups with all similar things in the same group. This can develop from simply ‘put them in piles according to colour’ to two- and three-way and hierarchical classification systems, where criteria of class inclusion/exclusion become complex. It also includes linguistic classifications such as noun, verb, sentence and paragraph.
Cause and Effect
Relationships and events in history and literature as well as in science are often about ‘what (or who) caused what?’. While young children often ascribe very simple and irrational causes to effects (the girl was naughty so she lost her sweets), older children can appreciate that events often have multiple interacting causes and that behaviours can have multiple effects. We use cause-effect reasoning to express ideas and communicate meaning through poetry, prose, performance and improvisation in drama, through composition and performance in music, and through creating a piece of art.
Frames of Reference
In a new situation we select a structure called a ‘frame’ from memory. Attached to the frame are several kinds of information. Some information is about how to judge the situation, some is about what happens next and some is about what to do next if these expectations are not met. We can make logical deductions and explore reciprocal meaning; that is, we can reason ‘if this is that, then that is also this’. We can use this reasoning ability to enter into a world of make believe, to create fiction and to fantasise.
Deductive Reasoning
This is linked to the development of narrative seriation and causal thinking. It is basing a conclusion on previously known facts (the premises). If the premises are true, the conclusion must be true. Sherlock Holmes is famous for his deductive powers. Children’s deductive reasoning is better if they are taught to identify and challenge their own and others’ hidden assumptions.
Spatial Perception
Do you have to turn the map upside down when navigating for a friend? The ability to rotate an object mentally is generally quite useful and it is one of those ways of thinking which develops with age and with experience. ‘If I look at this picture of a church, there is a tree on the right-hand side. Where would the tree appear to be if I looked from the other side?’
Measurement
Once number is conserved, it becomes possible to see the correspondence of a ruler’s scale with the size of objects and then to consider fractions. The same principle can be applied to time scales from getting a sense of how long the school day is to a feeling for the remoteness of historical events.
Conservation
Realising that the total number of objects or amount of material, its weight and its volume remain the same as the materials are moved or change shape or are divided up into smaller pieces takes some time to develop, but without this it is very difficult to establish any quantitative relationships between variables.
Number Systems
Learning to deal with numbers in all sorts of ways, such as using rods of different lengths to visualise numbers, putting them together to represent addition, or using 2 x 2 arrays to explore multiplication and commutativity (5 x 3 = 3 x
Critical Reflection
The ability to make critical judgements, after reflection and to incorporate other people’s ideas into their considered judgements. Critical reflection involves being able to shift perspective and giving a full explanation of how a judgement is reached.
Symbolic Representation
The use of visual and auditory symbols to create perspective and imagery and to communicate abstract concepts. Realising that writing is a symbol system and using symbols in increasingly sophisticated ways to communicate thoughts.
Although the reasoning patterns have been described here as if they are each separate entities, they become increasingly integrated as the brain develops. Cognitive growth in one area of reasoning will create the need for the other areas to develop and this becomes a continuous process of feedback.