Section 7 – Testing
Of course we need reliable ways of determining whether children can read and spell. If we start using the experience approach to literacy, at Reception level, most children will be independent, across the literacy spectrum, by the age of seven. So it makes sense to administer formal tests at that age, primarily to identify the youngsters who may have fallen through the net.
We must recognize, though, that it isn’t possible to evaluate progress in all the literacy areas in the same way.
Understanding print, for example, is so immediate, and so transparent, that it’s difficult to catch ourselves doing it, let alone anybody else. The good news is that it’s quite possible to measure children’s experience in this area indirectly, instead of using a formal ‘test’.
School based records [Compile these as you go along – no need to wait until Year 2/Primary 3. Print off copies of the record sheets whenever you wish.]
Reading for Meaning
What we really want to know is whether children are confident readers, if they have fallen in love with books, if they spend a fair amount of time reading, and who their favourite authors are.
A ‘Reading for Meaning Record’ is the best way of doing this. It can be filled in by teachers, parents, grandparents, classroom assistants, or even older children – the more the merrier.
A child needs to have experienced a particular book in some or all of these ways: following the print for part of the time while listening to it being read; just listening for part of the time; reading back small amounts (see Section 3); reading silently.
Record the dates he started and completed the book. He reads out the title and the author (with help if necessary) for you to write in, then tells you the story of the book, in brief, but with sufficient detail for you to know he has experienced it.
Give him a certain number of points (based roughly on the length of the book, about 4 points for a book of average length), which will count towards a ‘Reading for Meaning’ certificate when he has earned, say, 20 points.
The section on ‘Evaluation’ is the most exciting, as the child (not you) is the one doing the evaluating! He awards the book a certain number of stars (up to five), based on how much he enjoyed it. (In practice this will range between three and five stars, as he should have abandoned any book worth less than that in the early stages.) Most children take this very seriously, looking back to see how many stars they awarded to earlier books, before deciding on their opinion of the current one.
These record sheets show you, at a glance, whether the children are at home with books, and who their favourite authors are: all you need to know in this area. If a youngster has only a few entries on his record sheet, with not many stars, you need to work harder to find the books particularly irresistible to him – or he may need books in bigger print, or coloured overlays to smooth his passage into reading. See Section 6, on Dyslexia.
The Phonic Checklist
The phonic checklist charts a child’s journey from total independence on someone else to sound out written words for him, to total independence, where he can manage the whole thing by himself. Again, involve as many other people as possible in monitoring his progress, and cheering him on. Award a certificate when he has completed Step 5.
The Handwriting Checklist
This can be compiled alongside the phonic checklist, in the same sort of way. The handwriting programme establishes an excellent foundation for accurate spelling. Award a certificate on completion.
Reading Aloud
Once we recognize that understanding print, and reading aloud, are two different processes, it becomes easier to see that we need to record children’s progress in both areas.
Don’t expect your pupils to be able to read aloud, by themselves, until they have completed the phonic programme. When that is accomplished, though, they need as much practice as possible in independent reading aloud.
Because the words in the programme form a complete phonic ‘reading scheme’, you can now use any reading material for reading aloud practice – phonic reading schemes, look-and-say reading schemes, or ‘real books’. (The Dr Seuss books, for example, are apparently unstructured, but phonically based to a great extent, which is why they are an excellent choice for beginning readers.)
You will need to note down the reading levels of the ‘reading aloud’ books available to your pupils. I suggest that the simplest books could be Level One; those at reading age 6, Level Two; age 7, Level Three; age 8, Level Four; and age 9+, Level Five. Any reading scheme books can then be included in this system. Don’t start at the very beginning of a reading scheme, though, but select a title at the child’s interest level, and carry on from there, moving as quickly as possible so he doesn’t get bored. (It’s the amount of practice that matters.)
If you wish to use ‘real books’ straightaway, you may need to grade them in terms of their ‘readaloudability’ levels. One way of doing this is based on sentence length, and the number of words with more than two syllables. Choose a representative 100 word passage, divide 100 by the number of complete sentences in the passage, disregarding any part sentence, and add the number of polysyllabic words in the same passage. (Don’t count the same word twice, don’t count proper nouns.) Multiply by 0.3, and add 5 to give you a ‘reading-aloud’ level in years. The formula can be expressed concisely as follows:
0.3 x (100 + P) + 5
S
Of course this will give you only a rough approximation, but that is all you need: some indication of the ease with which a particular book can be read aloud by the young reader.
It is important that this reading aloud progression should be made apparent to children, which is why you grade the books numerically, instead of using a colour coding system (designed to conceal the relative levels of difficulty rather than otherwise). The children are going to be active agents in all this. They need to know what they are aiming for, and the different stages along the way. Then, within that context, they are perfectly free to choose a ‘reading loud’ book from any level at any time. If a particular book proves too much of a struggle, they know where to find a simpler one, and can go on moving backwards and forwards in this manner until they have had sufficient reading aloud practice to earn a certificate.
Give a child points for the amount of accurate reading aloud completed – to begin with, 4 points for a whole book. As he moves on to longer books, you can allocate these points fairly by deciding that, say, 2000 words qualifies as a ‘whole book’, and write at the front of each book the number of whole pages containing 2000 words. (This isn’t as tedious as it sounds – I can now count and calculate quite rapidly – you need to work it out only on the basis of one page.) The number of pages read (adding part pages together) is then recorded in the ‘Pages Read’ column of the reading aloud record sheet.
Award a certificate when a certain number of points has been achieved: 30 or 40 points is probably about right. Further certificates can be earned for reading aloud at higher levels.
These record sheets enable you to see at a glance how much accurate reading aloud a child has accomplished, and the approximate reading level he has reached. At the same time, he is the one in charge, and he decides which books he is going to read when. (Of course, you can encourage him to try ‘harder’ books whenever you feel he is ready.)
Formal tests
You need to use formal, ‘unaided’ tests at some point, if only to provide objective evidence about the effectiveness of your programme. Secondly, as already stated, formal tests identify the children who may still be struggling (for whatever reason).
The good news is that only two tests are sufficient: to establish reading age and spelling age.
Reading Age – Imagined context
What do we mean by ‘reading age’? Good question – and one on which the experts have disagreed passionately over the years. Part of the problem is that we need a test which measures ability in both areas of reading – reading for meaning, and reading aloud.
How do we determine the meanings of new words? Well, because we developed language to represent physical reality, we always learn the meanings of words by reference to a physical context of some kind. Nouns are learned in relation to objects, verbs in relation to actions, sentences in relation to physical events – ‘Dad is climbing the ladder’. Even so-called ‘abstract’ nouns, like justice, truth, love, anger, are first learned by reference to people being fair, or saying what is the case, etc.
This physical reality can be actual – or (as the child’s experience of language develops) imagined. Suppose he encounters the sentence ‘The sailors were carrying rundlets of rum on their shoulders from the stores to the ship.’ The words summon up a mental picture of men walking towards a ship, carrying something on their shoulders. This something contains a liquid, so has to be water-tight, and can be carried on a man’s shoulders: it’s probably a small barrel (correct). The imagined, physical context enables the reader (or listener) to deduce the meaning of the unfamiliar word ‘rundlets’. (See Frank Smith’s book Reading, Cambridge University Press, 1978, p. 95. Smith has scores of interesting things to say in his book, but unfortunately misses the point in several key areas.)
Similarly, because familiar spoken words are embedded in the context of a physical reality, they make this rich context instantly available to their written equivalents, whenever a reader matches one with the other.
We don’t, then, need a test to establish how a youngster is working out the meanings of new words, as we all do that in the ways I’ve just described.
No, the test simply needs to reveal the level of context already available to a reader: a good old fashioned word recognition test is ideal for the purpose, precisely because the words are presented out of context. In addition, a significant proportion are phonically irregular, so if a child gets them right, this shows he must have learned their meanings from his previous reading – exactly what we want to know.
Then, since he has to read the words aloud, the test establishes his ‘reading aloud level’ at the same time. Perfect.
The Burt Word Recognition Test is ideal for the purpose, and is available on line for you to download.
Spelling Age
The easiest way of determining a child’s spelling age is by dictating a list of isolated words, at increasing levels of difficulty. You say each word, use it in a sentence to make its meaning clear, then repeat it. The NFER single word spelling test (Nelson), or the Schonell spelling test, are equally good.
Children who have had ample practice in using the Key to Sound Spelling (Section 6, Dyslexia, and the problem of spelling) will probably reach a satisfactory standard. But be on the look out for youngsters with low scores, maybe from other schools, particularly if there is a marked discrepancy between their reading age and their spelling age – dyslexia is the most likely cause.
Diagnosing dyslexia
Once we recognize that the best ways of teaching dyslexics are the best ways of teaching all children, it’s obvious that we don’t need to identify the dyslexic pupils in the early years of primary education, before setting up a literacy programme which will meet their needs.
You may need to test older children, however, so as to work with the ones who have fallen through the net (for whatever reason). For example, when I was teaching literacy strugglers at secondary level, I screened the incoming Year 7s with the following diagnostic dictation, taken from Margaret Peters’ Diagnostic and Remedial Spelling Manual (Macmillan Education). Spelling is the most difficult of the literacy processes for dyslexics, because they cannot visualize written words accurately. But children with reading difficulties almost always have spelling problems as well – you have therefore identified most of the literacy strugglers with this one test. It contains exactly 100 words (so working out percentages when scoring is easy), and contains a wide variety of spelling patterns:
Late one night my friend woke me, saying, “Would you enjoy a trial-run
in my new helicopter?”
I had scarcely scrambled into my track-suit before we were away. The
lights of the city glowed beneath, the stars above. I was beginning to
wonder about our destination when I caught sight of the spinning knife
edge and the surface of what must have been a type of flying saucer
whistling round us. We dodged skilfully to avoid an accident. To our relief,
the space-craft regained height, and we sank down to earth and the
comfortable bed I had never actually left.
I reassured the students, before they wrote out the passage, that spelling problems often go hand-in-hand with high intelligence and unusual gifts, and not to worry if they made several spelling mistakes; and I provided the punctuation as they went along, so they were having the experience of punctuating correctly.
The pupils’ version of this passage then became the basis for a programme enabling them to tackle their spelling difficulties. They learned to touch type, and use the Key to Sound Spelling (Section 6, Dyslexia, and the problem of spelling), to sort out their own spelling mistakes. (See Section 9, Adult literacy; working with prisoners - Part C, Writing, typing and spelling.)
A specific diagnosis of dyslexia, by an educational psychologist, could be useful towards the end of a youngster’s school career: he or she may benefit from special consideration in exams – e.g. extra time, a reader, or even a scribe. Plus, colleges and universities often make provision for dyslexic students who have been identified at school.
Screening whole classes with coloured overlays
You can screen whole classes of children at once for Scotopic Sensitivity (Irlen) Syndrome. (See Section 6, on Dyslexia, for an explanation of the condition, and why coloured overlays and glasses make such a difference.)
All you need is a selection of theatrical gels, available quite cheaply from most stage lighting stores (e.g. Stage Electrics, in Marsh Barton, Exeter). The following colours seem to cover most children’s needs: Rosco 10, Medium Yellow; Rosco 33, Pink; Rosco 55, Lilac; Rosco 63, Pale blue; Rosco 96, Lime; Rosco 388, Gaslight Green; Lee 024, Scarlet; Lee 101, Yellow; Lee 116, Medium blue green; Lee 213, White flame green. The gels come in large sheets which can be cut up into page sized overlays, 20 cm by 12 cm – 12 overlays from a Rosco sheet, and 24 from a Lee sheet.
Use copies of the scoring chart (see below) to help children decide if the coloured gels make a difference when used as overlays for reading; and if so, which ones are the most helpful. Pass round ‘testers’, and ask each pupil to give the gels a score from 1-10, depending on how much difference they make. Offer dictionaries with fairly small print to test the gels, so the child isn’t trying to read the page, just responding to the look of the print. The overlays should be placed across half a page, then the two halves can be compared. You can intensify a colour by using one sheet on top of another, or combine different colours in the same way.
In class, it helps to have a supply of assorted gels for the children to borrow when reading. Also, photocopy worksheets in a variety of colours, and allow pupils to write on coloured paper, or in coloured pens, if this makes a difference. Ask your students if they find it easier to read writing on whiteboards in certain colours, and to remind you if you forget! When this approach is adopted, as a matter of course, for all children, nobody should feel singled out, or that they are struggling to read text in colours that they cannot see.
If overlays prove helpful, it is likely that coloured glasses will be even more so. Irlen Syndrome does not show up on conventional eye tests, and must be detected by qualified practitioners. However, some local authorities are now providing this service – check and find out. But it may well be quicker and cheaper in the long run to obtain genuine Irlen overlays and/or glasses.
Email: irleninstitute@irlen.com for information.
Intelligence testing
Should we test for intelligence, and if so, why?
IQ (intelligence quotient) testing has moved in and out of favour over the last century; a recent series of programmes, broadcast on BBC Radio 4 in the spring of 2014, re-examined the whole question (Intelligence: Born Smart, Born Equal, Born Different, presented by Adam Rutherford).
The underlying assumption seems to be that children differ in their native levels of intelligence. If we can determine those innate abilities at an early stage, we can design forms of education which will place the cleverest youngsters on a fast track to good GCSEs and A levels, leading on to university, and a well paid job at the end of it.
The 1944 Education Act – testing at 11+
The Education Act of 1944 tried to achieve exactly that. It set up technical colleges, grammar schools, and secondary moderns. Grammar schools provided the fast track to university (based on a test at 11+), while secondary moderns were essentially ‘sink’ schools, which had to cope, somehow, with most of the 11+ rejects. In the final radio programme, Born Different, Steve Jones described the effect of this selection on his own working class family. He had passed the 11+, attended grammar school and university in turn, and prospered throughout his later life. But his brother had failed the test, went to a secondary modern school, ended up as a bricklayer (which he hated), and died before reaching middle age.
As Steve Jones pointed out, you often hear people say, “Bring back the grammar schools.” But you never hear anyone asking for the return of the secondary moderns.
This is the inherent drawback to such a project. You cannot have selective grammar schools without their corollary, the sink schools populated by youngsters whose only reason for being there is that they have been branded as failures, rejects of the system, good for nothing but the ‘lowest’ of manual jobs. We have to ask, is that a price worth paying?
Proving that something doesn’t exist
It seems to me that the basic assumption behind IQ testing is, anyway, deeply flawed. For a start, while it is quite possible to prove the presence of intelligence, you can never prove its absence – you can never prove, conclusively, that something does not exist. If a child performs badly on an intelligence test, there are myriads of other possible reasons for his poor showing, besides an innate lack of capability.
One instance is the item on an early test asking children to identify the link between various objects – for example ‘cup’ could be paired with ‘wall’, ‘chair’, or ‘table’, as well as ‘saucer’. Some working class children, who had never used a saucer in their lives, decided to link ‘cup’ with ‘table’, since that was where they put a cup between gulps. Very clever thinking – but of course they were marked ‘wrong’ by the middle class designers and markers of the test.
A culture free intelligence test
The interesting thing is, however, that we are in possession of a culture free ‘intelligence test’ which most children sail through, with the greatest of ease, long before they have even started nursery school.
That ‘intelligence test’ is spoken language.
The roots of language
As we saw in Section 2, How do we learn to understand speech?, just the activity of assigning names to different objects is a very clever thing to do. In fact, it represents a deeply mathematical way of thinking.
In order to appreciate this comparison between speech and mathematics, let’s imagine a child who has learned to understand the word ‘chair’, so clearly that if you show her a small doll’s chair, with a rounded back and blue legs, and say to her “What is it?” she will immediately reply, “It’s a chair.”
How does she know? Perhaps she has never seen such a small chair before, or one with that sort of back and legs of that particular colour. But she identifies it without hesitation. So what mental procedures underlie her confident assertion?
To begin with, she has to take note of the word ‘chair’, it has to register. Her mum comes home, and with a sigh and a cup of tea sinks into an arm chair. Her dad leaves his glasses on the rocking chair and the dog sits on them. When it is time for her to have her meals with everybody else, she graduates from her high chair to a proper dining chair.
The interesting thing about all these chairs is that they are really quite different from each other. A plump and squashy arm chair bears little resemblance to a lean and portable dining chair. And yet each of the objects is labelled with a pattern of sounds that is in every case the same.
The child finds this intriguing. Why is the pattern of sounds always the same? And she starts to notice the similar features of these different objects, so as to identify the common ‘factors’ of ‘chairness’. All ‘chairs’, she observes, have a seat designed for only one sitter, they have some sort of a base which rests on the floor, and they have a back for leaning against. If one of the factors is missing, a back for instance, then whatever-it-is might still be sat upon, but is not a ‘chair’ and has to be given another name instead.
How old is this child? She may be less than one – she is almost certainly less than two.
Yet without instruction of any kind, she has engaged in a process which is at once highly abstract and passionately creative. Never mind that each separate chair is particular and tangible. The child’s concept of ‘chairness’ is abstracted from her awareness of all the different chairs in her experience. It is not a thing at all. It is an idea in her head, and she has created it herself.
This has happened in strict accordance with the laws of logic and mathematics. An object cannot be a ‘chair’ unless it has all the essential features; so these essential features, taken together, constitute the ‘highest common factor’ of chairness. The idea takes shape as a child hears the word alongside the many different objects which can bear that word as a name. And she is not performing this feat for just one set of objects. The highest common factors for every group of items in her experience continually crystallize out; and as she forms the concepts, she labels them, she flings a border around each one so as to keep it whole, a border which is one of the most powerful intellectual tools imaginable, a simple pattern of sounds which she uses as a name.
Babies are not merely identifying the highest common factors of sets of objects, however. While she has been abstracting the factors essential to chairness, our miniature Einstein has also been noticing the uncommon factors which are present in some chairs and not in others. Chairs can be different colours; some can have arms; some have four legs, others just one in the middle, and some have legs ending in rockers. They can be made of wood or plastic or metal and be covered with material; they can be soft and comfortable or hard and forbidding. All these factors, too, are combined with her recognition of the essential ones, and form her total conception of ‘chairs-in general’. So her use of the word ‘chair’ is not only an acknowledgement that the object named embodies the ‘highest common factors’ of chairness. The word also summons up for her the characteristics of all the chairs she has come across, and is therefore the ‘lowest common multiple’ of these characteristics.
We could express this in terms of a classic Venn diagram. Let’s suppose that a baby has encountered three different chairs in her life so far: A) a wooden high chair, painted blue; B) a stained wooden dining chair with a cushion on it, and C) a blue upholstered arm chair. Each chair can be regarded as a ‘set’ containing all the characteristics of that particular chair, and this may be represented diagrammatically as follows:
The factors which are common to all three chairs are the seat, the back and the base, so these factors form the intersection of the three sets, and help the baby to construct her central concept of chairness. In addition, she has learned that some chairs are blue, can be made of wood, have tall legs, trays or cushions, and be upholstered, with arms in one or two cases. These factors, taken together with the intersection of the sets, form the union of the sets, and constitute the ‘lowest common multiple’ of chairs in general, as she has experienced them so far. When she encounters further chairs, for example a metal chair on a swivel base, the intersection of the sets will stay the same, but the lowest common multiple will expand to take account of the new characteristics.
This is just what happens when we are dealing with the factor structure of numbers:
The prime factors which are common to all three numbers are 2 x 3 (= 6): the intersection of the sets. The non-common factors (another 2 and another 3), multiplied with 6, form the union of the sets, and generate the lowest common multiple of the three numbers (36). If another number with the same HCF (e.g. 24) is included in the picture, the lowest common multiple expands to include the non-common factor from 24 (another 2) and becomes 72.
Viewed in this way, it might even seem easier to perform the operations with numbers than with the characteristics of various objects. Not to worry – our baby certainly doesn’t, and is soon a dab hand at noticing all the varied differences in detail which will allow her to classify everything she experiences into sets – and so impress her own personal order onto what seemed at first like chaos.
It looks as if the process underlying language is not so much the ability to manipulate sounds, but to form abstract concepts, and to move sets of ideas around inside your head. The pattern of sounds which is used as a name for a particular group of ideas (e.g. ‘chair’) is really no more than a convenience, a unifying focus enabling a baby to combine the elements in her concept and think of it as a unit. The word is a peg where the concept can be safely stored, and which allows for swift retrieval when that concept needs to be thought about.
More mathematical thinking
So, just in order to understand and use names, a small child is operating on sets, and appreciating the highest common factors and lowest common multiples of those sets.
But she is also employing many more mathematical processes as she takes possession of the world of language. Long before she has uttered a single word herself, she has been engaging in what is probably the most basic mathematical procedure of all – that of tallying.
We used tallying to help us count before numbers were invented. A shepherd boy could ‘count’ his sheep by matching each sheep with a notch carved on a stick. Any unmatched notches at the end of the day meant that amount of missing sheep, and he had to find them before settling down for the night. Only when each notch was paired off with its missing sheep could he relax.
Counting is just one application of this incredibly useful procedure. In essence, tallying consists of associating two items as a pair, and we cannot even begin to think without forming such associations. A baby associates the smell of milk with the taste and feel of it in her mouth, and all these things with a nice full tummy. Soon the sight of her mother’s face is linked with the same experiences. She associates the sound of water running out of a tap with the excitement of having a bath; wearing a jacket and hat with going outdoors; sitting in a high chair with eating; cups with drinking, and spoons with more solid food. The list is endless. Whenever a baby shows expectations of some kind, this has to mean that she has previously formed an association between whatever it is she is expecting, and the event which is prompting that anticipation. She has tallied the two things in her mind, so that now the occurrence of one of those two things automatically implies the other.
The association is always between just two items to begin with, but more associations can then be formed with either one of the initial pair, so the baby is soon building up clusters – or sets – of ideas which are all linked with each other.
Words may be thought of as sets of sounds which can be tallied with each other, and added to or subtracted from other sets of sounds so as to alter their meanings. For instance, a child differentiating between the two words ‘pig’ and ‘pin’ tallies the ‘pŭ’ and ‘ĭ’ sounds from each word with each other. These are ‘common factors’ and ‘cancel out’. The uncommon factors are the ‘gŭ’ sound in ‘pig’ and the ‘n’ sound in ‘pin’ – so these are what distinguish the words from each other, and allow her to assign separate meanings to the two words.
Uncommon factors can be added or subtracted in other ways to indicate a change of meaning. Suppose that a child is learning to understand the word ‘smile’. Her mother picks her up, with a broad smile on her own face, and says encouragingly, “Smile!” The youngster smiles back at Mum, and gradually learns that the set of sounds ‘smile’ not only refers to the happy sort of feeling which moves your lips upwards: it is also a request. When you say ‘smile’ to someone you want them to perform the action.
Mum reads her a bedtime story, and they come across a picture of a rag doll wearing a broad grin. “Look,” says her mother, “dolly is smiling.”
In order to identify the difference in meaning between the two words ‘smile’ and ‘smiling’, the child has to notice that the set of sounds ‘smile’ is common to both words, and carries the same root meaning of bending your mouth around in a happy sort of way. The difference between the two sets is the ‘ing’ ending. Attach that to the set of sounds ‘smile’ and you change the force of the word. From being a request it becomes a description. So ‘smile’ plus ‘ing’ equals a new word, 'smiling’. ‘Smiling’ minus ‘ing’ equals a different word, ‘smile’.
She discovers that you can do this with any number of words: in no time she is adding and subtracting prefixes and suffixes all over the place, so as to modify the meanings of the words she is learning to understand and to say.
As the child moves on increasingly to talking herself, and stringing her own words together to generate spoken sentences, it becomes obvious that still more intelligent procedures are coming into operation. Have a look at some of the things older children are saying – four and five year olds: much more accomplished talkers now, but still barely school age.
For example, when my daughter Gwynneth was four, she declared thoughtfully one day that our breadcrumbs were great big loaves to dollies. My niece Susan, at five, made an equally exciting discovery. “Do you mean,” she said to her mother, “that my Granny is your Mummy?”
What delights both Gwynneth and Susan is an appreciation of similarities – but it is not two objects they have identified as similar. What is the same in both cases is the relationship. Loaves are to people as breadcrumbs are to dolls. Grannies are to mothers as mothers are to children.
This is the mathematical concept of ratio. Again, it is a highly abstract concept, and again small children are forming it over and over without difficulty. Listen to any young child, and you will discover the idea of ratio is quite central to her thinking. It is, in fact, a very important means by which she orders her experience. She soon comes to realize that things have to be fitting. Her own clothes, shoes, gloves, wouldn’t do for Mum. Miniature tea sets are satisfying because they go with the size of the dolls. A throne in a giant’s castle is as much a chair as the smaller version in her own home: it is just scaled up in ratio to the size of its occupant. Some tools (e.g. knives and forks) are appropriate to some activities (eating); whereas buckets and spades are what you need for building sand castles. It is no semantic accident that we call ourselves rational beings, for this appreciation of ratio – what is fitting, what is appropriate, what goes with what, and how – is fundamental to all our thought processes, and our acquisition of language. We would be unable to learn language at all without using this concept, because the relationship between any word and the idea it represents is the same as the relationship between all other words and their meanings. Unless we understand this, we cannot grasp the purpose of the myriads of sound patterns we are busily storing in our minds.
The more we examine these comparisons between language and mathematical thinking, the more apparent it becomes that the acquisition of language is an amazingly clever process. It is fascinating to pursue this line of enquiry by noticing a child’s mistakes. Mistakes are interesting because they are not copied from other people, they are the child’s own invention – and therefore tell us a great deal about how the child’s mind is working.
Gwynneth, again at four, intrigued us all because she persisted in saying “I have tooken,” rather than “I have taken.” If you examine the logical patterns of thought which have culminated in this construction, they are quite staggering.
For a start, she already knew how to form the past tense of words like ‘jump’, ‘skip’, ‘walk’, etc. – just stick a sharp ‘d’ sound on the end. To form the perfect tense, you put a ‘have’ in front of the past tense, making forms like ‘I have jumped’, ‘I have skipped’. (She didn’t explain what she was doing to herself, she merely went ahead and did it.)
Some words, though, like ‘wake’ and ‘break’, change the vowel sound to make the past tense (‘I woke’, ‘I broke’) and then you have to tack on the suffix ‘en’ to get the perfect tense (‘I have woken’, ‘I have broken’).
She must have worked out that this is what has to be done, because she has constructed the form ‘I have tooken’ by analogy with forms like ‘I have woken’ and ‘I have broken’. She hasn’t come up with ‘I have tōken’ (which would be an analogy by rhyme). Instead, she has identified the past tense, ‘took’, and added the suffix ‘en’ to that past tense form, so as to construct what seems to her a completely logical perfect tense. She has abstracted the idea and force inherent in the vowel change and the suffix ‘en’, and she has applied those ideas in a construction which is entirely of her own making.
In this instance, she is thinking algebraically. She may not have the words for ‘verb’, ‘past tense’, ‘perfect tense’ – but she does have the concepts. She has arranged these concepts in her mind in an algebraic formula. ‘X’ is the concept of the past tense. ‘Y’ is the pattern of the pre-word ‘have’ and the suffix ‘en’. ‘Z’ is the concept of the perfect tense. The formula X+Y=Z works when you substitute the past tense of verbs like ‘break’ and ‘wake’, so it’s reasonable to suppose that it will also work if you substitute the comparable form of ‘take’...
Now find any four-year-old, record her mistakes – and analyse the mental processes underlying those mistakes. I guarantee you will revise your assumptions about the level of intelligent thought taking place in that small head, quite matter of factly and unobtrusively.
As an integral part of their ability to use spoken language, children must also be handy at sequencing and organizing, and have excellent memories. Spoken English uses about forty-four different sounds all told, but those forty-four sounds can be arranged in such an infinity of different ways that we can generate hundreds and thousands of words, and still find new sound patterns when new concepts arise and need words to represent them. A spoken word is a particular arrangement of sounds. The only difference between many words is that their constituent sounds are differently arranged, and most children can appreciate this with no trouble. Words like ‘spill’ and ‘lips’, ‘cat’ and ‘tack’, ‘carts’ and ‘stark’, ‘pain’ and ‘nape’, use the same sounds, but are rarely confused because the sounds emerge in a different order. Some words may be muddled when a child is first learning them, but are soon sorted out: they have to be if the child is going to be understood by her family and peers. So the awareness and learning of different sound sequences is, once again, fundamental to our use of language; and we have to have first-rate memories if we are going to be able to store all these different sound patterns.
Similarly, spoken sentences are particular arrangements of words, and the order of those words is vital to the meaning of the sentence. ‘Man bites dog’ conveys a different meaning altogether from ‘dog bites man’; saying ‘my toy fire engine was under the chair’ is not the same as saying ‘the chair was under the toy fire engine’. Children soon become very good at organizing their words so as to convey the right meaning, which shows us that they are very good at organizing their thoughts in a logical way, and making sure that the order of their words reflects that logical organization.
What I have tried to show is that these sophisticated mental processes – tallying, adding and subtracting, forming abstractions, operating on sets, identifying the highest common factors and lowest common multiples of groups of ideas, appreciating ratio, thinking algebraically, sequencing and organizing sounds and words, as well as the ability to learn and remember – are not ‘optional extras’: they are essential to language. We cannot use language, to any extent, without employing all these processes. Because we need them to acquire language in the first place, they cannot be taught (since language would be required to teach them), so they must be innate, already in place at birth, waiting only for the relevant experiences which will bring them into play.
(If we ‘tested’ children at the age of ten, say, and discovered they could engage in most of these procedures, wouldn’t we be justified in expecting great things of them throughout their lives?)
Exercising intelligence
Unfortunately – or perhaps fortunately – we are not aware of how clever a child needs to be in order to understand and use spoken language. So without even thinking about it, most of us succeed in providing the massive experience of language which is what children need in order to flourish in its use. As a result, they are continually exercising their native intellectual powers across more and more territory.
Written language gives us access to an even wider world. It breaks down the barriers of both space and time, so we can see with the eyes of people who lived long ago, and far away. It is a world which belongs to all our children by right, if only we can give them the massive experience of understanding it, matching it with spoken language, and forming it themselves.
Intelligence, it seems to me, is innate, but it has to be exercised in order to develop. Instead of trying desperately to measure it, before putting educational programmes in place, let’s just assume it’s there, and focus instead on giving all children the greatest possible scope for using it.
Then, if they want to go to university when they leave school, they can. If they want to apply their native intelligence and creativity in more practical ways, they can. If they want to be bricklayers, encourage them to be the best bricklayers they can possibly be – and read Shakespeare in the evening. Society needs many different skills, why do we have to applaud some and sneer at others?
What matters is the human spirit, and its infinite possibilities.