Concept Development in the Primary School

Peter Langford

• Publisher: Routledge
• Year: 2016
• Print ISBN: 9781138653245
• eBook ISBN: 9781317226925
• Topic: Psychology
• Subtopic: Cognitive Psychology & Cognition
• Index: Psychology

Originally published in 1987, this book introduces work on the intellectual development of children in the primary school. It contains chapters on the teaching of reading, writing, art, science and mathematics. While critical of many of the once popular ideas of Jean Piaget, the author also emphasises the continuing validity of some aspects of Piaget's thinking.

Chapter 1
Introduction

General Orientation

The aim of this book is to introduce the primary teacher to recent work in the area of cognitive development that is relevant to the interests of the classroom practitioner. The field of cognitive development is one that has changed quite considerably in recent years and it is as well to be aware of the general nature of these changes.

For many years the best known work in the area was that of the Swiss psychologist Jean Piaget (1896-1980). From the publication of his first book The Language and Thought of the Child in 1926 until his death in 1980 Piaget published over forty books and innumerable journal articles on cognitive development in children. His leading idea was that the child's thinking moves through stages of increasingly abstract concepts until it reaches adulthood. He outlined three main stages in development the sensorimotor stage from 0 to about 2 years, during which the child's thinking is closely tied to practical activity; the stage of concrete operations, from about 2-11 years of age, during which children think about what is physically possible, such as adding together objects or altering the world by moving things around, lifting them up, stretching them or otherwise subjecting them to transformation; and finally the stage of formal operations from about 11 years onward, in which the adolescent learns to think about purely abstract entities like geometrical points and lines, to understand mathematical functions and how to control factors in an experimental situation.

Piaget also believed that children's thinking develops primarily as a result of their activity in the world in making things, altering situations and transforming objects. It was partly as a result of this Piagetian emphasis on learning through doing that primary schools in the UK began to adopt 'activity methods' of teaching in the 1930s in which children were encouraged to explore the natural environment in a practical way, to undertake projects and to learn mathematics by using practical apparatus enabling them to count collections of objects and observe relationships between objects. In the 1950s and 1960s this adoption of activity methods became widespread and also migrated into secondary schools, although even in the 1970s surveys showed that many primary schools continued to emphasise paper and pencil activities rather than practical work and projects.¹

Piaget's ideas were never without their critics within psychology and education. In the 1930s many of the criticisms aired in more recent years received publicity.² However Piaget persisted with the main elements of his theory, though continually breaking new ground in his study of specific topics and the details of their treatment. In the 1960s his ideas gained new popularity both in the UK and the USA. In academic psychology the 1950s produced the 'cognitive revolution'. Behaviouristic psychology's emphasis on 'rats and stats' and the formation of habits and its neglect of thinking and higher mental processes began to be challenged. A professional joke of the time was 'First psychology lost its soul, then it lost its mind'. In this new climate Piaget came to be seen as a kind of hero of the cognitive revolution, who had held out against behaviourism and accumulated a vast store of observations on children's thinking in real-life situations. This at a time when American psychologists of the 1930s had sometimes appeared lost in the mazes along with their rats.

In education the 1960s saw two changes that helped Piaget's cause in that field as well. American education became concerned at the apparent technological lead held by the Russians in space research. It was felt that the education system should devote more of its time to developing the thinking, conceptual understanding and problem solving skills needed by the scientist and engineer. At the same time the youth revolution and 'flower power' of the 1960s led many educators to search for a less rigid and formal view of learning than that which had hitherto dominated educational thinking. Again Piaget seemed to have something to offer.

The three best known alternatives to Piaget within educational psychology in the 1960s, and still to some extent, even today, were all Americans. Bruner, Gagn6 and Ausubel all proposed alternative views of how children learn during the 1950s and 1960s. Of these, Burner's views have declined in popularity in recent years, while considerable publicity has been given to both Gagne and Ausubel as promising alternatives to Piaget. For the present I will only comment on the relation between Piaget and Gagne. Ausubel's work will resurface continually throughout the book.

The idea of a hierarchy of skills is crucial to recent discussions of cognitive development. There are two kinds of hierarchy of skills, which we can call expression hierarchies and logical hierarchies. Reading, writing and drawing are examples of expression hierarchies as they involve low-level skills like handwriting, word recognition and skill with a pencil in the service of expressing high level concepts or ideas. Logical hierarchies occur when there is a logical sequence of concepts within a curriculum area, as we find for instance in geometry, where the concept of a straight line logically precedes those of angles or triangles as we need the concept of straight line to define angles and triangles.

It is typical of the Piagetian approach to think that in expression hierarchies learning is top-down. If the child or adolescent get their high-level general concepts sorted out then lower-level skills will automatically fall into place. The way to get the student to understand broad and general concepts is to encourage discovery of basic principles by exposing the learner to situations and materials that will allow them to discover such principles without much assistance from the teacher.

Piaget's contention in regard to logical hierarchies was that such orderings are an illusion produced by taking a logical rather than a psychological approach to development In his view the various concepts involved in a topic like arithmetic or geometry develop alongside one another rather than in logical sequence, finally achieving logical rigour more or less simultaneously as a new intellectual structure is formed.

Gagné says that for both expression and logical hierarchies the child must begin at the bottom of the hierarchy with low-level skills and work up to more general levels of understanding. The way to do this is to place the child in a highly structured learning programme that teaches the skills to be acquired with a minimum of errors.

To give examples, in the area of writing the Piagetian educator will tend to say that we should concentrate on the topic of the writing, say pigs. Once the child knows all about pigs, their habits, intelligence, usefulness to human beings, food, etc., then ability to write well about pigs will quickly follow. The Gagnean teacher will say that we should first begin with the skill of letter formation, then practise writing words, then sentences and finally look at information about pigs to help us to write stories about them.

In a curriculum area like geometry the Piagetian teacher will delay instruction until the structure of geometrical thinking has matured, which in the case of Euclidean geometry is not held to occur until early adolescence. The Gagnéan teacher will begin teaching simple concepts like straight line and angle much earlier and use these to gradually develop more advanced geometrical instruction.

The main message of more recent work and classroom experience has been as follows. Firstly, for expression hierarchies there is no general prescription as to whether learning should be 'top-down' or 'bottom-up'. What the child needs to learn in order to develop a given cognitive skill will depend mainly upon the levels at which they are weakest. This may differ from child to child and from area to area. In some areas it may be that most children need more help with low-level skills, in others they may need more help with high-level conceptual understanding.

For logical hierarchies we find that it tends to be true, as alleged by Gagne, that a strictly logical understanding of a topic does require an orderly development from basic concepts to those that are defined with them. However it is both possible and desirable to provide intuitive and pictorial insights into a topic as a whole before proceeding with detailed logical development. In geometry, for instance, we might want to begin by showing examples of how relatively advanced Euclidean geometry can be used in such things as calculating the distance of the sun from the earth or the height of an unclimbable mountain before proceeding to detailed definitions and methods of proof.

Another finding is that there is no single prescription as to how best to learn a given cognitive skill. Children may benefit from exploration, discovery, 'hands on' experience or from being told, from a demonstration or a tightly sequenced programme to develop a specific skill. Most children seem to benefit most from a mixture of these methods. Some generalisations about learning are, however, possible. It is usually better to practise an expression skill like reading or writing as a meaningful whole, even though the student may initially be very weak in all aspects of the skill, than to break up the task into component subskills like handwriting or word recognition and practise these in isolation; though a moderate amount of practice with component skills will be accepted by the student once they have realised where these skills fit into the overall skill of reading or writing. It is, however, desirable to sequence the curriculum in accordance with the logical sequence of concepts, particularly in science and mathematics.

It is always important to keep the student interested and mentally involved in the activity in question. It is important to ensure that the activity does actually practise the skills it claims to practise. Teachers should look very carefully at claims that practice in one area benefits skill in an apparently unrelated area. Direct practice of a skill is always better than transfer from another area.

Descriptive Changes in Cognitive Abilities

Piagetian theory was in some respects rather successful in suggesting the kinds of topics appropriate for primary age children. Piaget called the period from roughly 7-11 years of age the 'substage of concrete operations', which is to say that it is a substage of the broader stage of concrete operations extending from about 2-11 years. By this he meant that in the age range 7-11 children successfully understand the world in terms of operations they can actually perform on it. It is important here to avoid a misunderstanding that beginners often have in approaching Piagetian ideas. 'Concrete operations' does not mean simply understanding what does happen in the world. Even 4 and 5 year old children enjoy stories about dwarfs and giants that they have never seen. They have seen things getting larger and smaller and they can imagine what people would be like if they got larger or smaller. Concrete operations means possible extensions of concrete experiences.

In some ways it would be more realistic to think of 'concrete operations' in this sense as the period from 4-9 years. From 4 years children begin to understand things like arithmetic and logic from a concrete point of view. By 9 years there is already evidence that children can in some circumstances break away from physical reality in their mathematical thinking. Thus Langford (1974) asked children to imagine the number 1, to add 1, then another 1, and so on. When asked 'Would we ever have to stop?' a majority of 9 year olds said 'No', showing that unlike younger children they can imagine going on forever, which is physically impossible but is a concept used by mathematicians. Younger children tend to say 'You would have to stop for lunch' or even 'You would die'!

Given this slight downward revision in the age range, Piaget's idea that children in middle childhood conceive only physically possible operations on the world remains valid. His serious mistakes began when he tried to say a) that there is a sudden overall shift in patterns of thinking at around age 7; b) that these patterns can be described by logically coherent systems called 'grouping structures'. These claims are not widely accepted today.

In addition to this general description of children's thinking from 4-9 we can also add three rather well-established principles that, other things being equal, will determine the difficulty of a concept for a child in this period. Rather than finding the sudden emergence of a whole bundle of concepts what we find instead is the gradual emergence of concepts in a fashion indicated by these principles. The first is that any problem or statement that involves a difficult constituent concept will be difficult.³ Two examples of difficult constituent concepts are 'not', as in 'Ducks are not mammals', and 'includes', as in 'The class of herbivores includes the class of horses'. A statement involving both concepts, such as 'Cats are not herbivores', will be doubly difficult.

The second principle is that the more complex a statement the more difficult it will be to grasp or operate with.⁴ Thus an arithmetical statement like (2 + 3) × (6 + 4) is more complex than 2 × 6. No one has ever satisfactorily defined this kind of complexity, but in an intuitive sense we know it when we see it.

The third principle is that any problem or statement that places a greater load on memory will be more difficult to deal with. The upshot of these three principles acting together is that the development of thinking from 4-9 shows a gradual increase in the complexity and memory-taxing powers of the problems and ideas mastered and in the difficulty of constituent concepts that can be tackled. Even after 9 years, although the first truly 'abstract' ideas appear, many of the more complex and difficult principles governing the logic and mathematics of physically possible situations are still not grasped. The process of learning these goes on right through adolescence. We also find that concrete statements like 2 + 3 = 3 + 2 are understood before rules that apply to such statements, such as the commutative law of addition which says that for any numbers A and B, A + B = B + A.

The finding that cognitive development does not proceed in sudden leaps has implications for the teacher. It means that we need in most cases to use methods that allow a student to find their own level rather than allotting them to a level of work on the basis of some rather general label like 'late concrete operations' or 'early formal operations'. Two ways of achieving this are to use an individualised programme in which the student works through workbooks and activities that are sequenced in order of difficulty and allow each student to find their own level; or by allowing for self-directed learning, as when students choose their own books to read or their own topics to write about

The Problem of Working Memory

We have already seen that one of the difficulties that children must overcome is that imposed by limited memory. All cognitive tasks require the child to hold a certain number of ideas or mental 'items' for a short lime in 'working memory' while they are acted upon. This has caused a number of theorists to think that the main thing holding up the development of children's thinking is the limitation of this working memory. Examples of this can be found in Pascual-Leone (1971), Case (1979) and Halford and Wilson (1980). These three groups of authors have actually suggested that the working memory capacity of children could be used to provide a new kind of definition for stages in intellectual development to replace those of Piaget. Thus children at one stage would have working memory capacity of two items, at the next stage of three items, and so forth.

There are, however, serious limitations to such approaches. To begin with, the general idea that working memory limitations are the chief thing holding up development is not inherently obvious; it is at the outset just as plausible to think that the problem of learning new ways of processing information — new recognition of concepts, new routines and new strategies — is just as great a source of difficulty for the child. Thus we would need some kind of empirical proof that it is actually the case that working memory problems are what holds the child up. While the authors mentioned above do try to provide such evidence, their critics have been less than totally convinced by the evidence offered.⁵ The difficulties are threefold. It is hard to arrange an independent assessment of the working memory capacity of a child as we never really know how long information must be stored in the child's mind during processing. We know that both adults and children can remember a lot more for only half a second than they can for say three seconds. Secondly, it is hard to know just how children chunk information while performing a task. If the child needs to remember the number 12 for instance this might normally be two items; on the other hand it might be the child's age or their birthday, in which case 12 will be chunked as 'my age' or 'my birthday'. As working memory load has to be defined in terms of number of chunks stored, this creates a further difficulty. Thirdly there has been dispute about the actual strategies children use to perform the particular tasks studied when testing the models. It is of course likely that limitations on working memory play a partial role in restricting the abilities that young children can acquire, as suggested in the model of solving arithmetical problems proposed by Brainerd (1983). It seems, however, quite premature to ...

Table of contents

• Cover
• Title
• Copyright
• Original Title
• Original Copyright
• Contents
• Chapter 1: Introduction
• Chapter 2: Reading
• Chapter 3: Writing
• Chapter 4: Art
• Chapter 5: Science
• Chapter 6: Mathematics
• Bibliography
• Index