I've been meaning to post for a long time to give an update on my 4-year-old daughter's reading and my 7-year-old son's mathematics. The result of the delay is that I'm a bit hazier about some of the details that I found fascinating at the time, and some of what I say is more like a reconstruction based on this hazy memory than a 100% accurate reporting of what happened.
I'll talk about my daughter in this post and save my son for another one. For a long time I had been working to get her to the point where she could reliably answer questions of the form "What does P - I - G make?" By the way, I pronounce the letters puh i guh and not pee eye jee, so there is a direct connection between the sounds of the letters and the simple words that they make, though even then there is a highly non-trivial rule for a young child's brain to induce from the data -- that you have to remove those "uh" sounds and then "concatenate" what's left. Anyhow, she had become very reliable at those, and the rule was firm enough in her mind that she could do more complicated examples like "stop" or "glad". So it seemed like a good moment (I think this might have been February or March) to make a start on two other important stages in learning to read: learning the sounds made by letter combinations such as ch, sh, th, ee, oo, etc., and learning to recognise familiar words such as "the", "here", "my", etc.
Before I say what happened, I want to say a bit about where I stand in the debate about the respective merits of what in this country have been called the phonics method of teaching reading and the look-say method. Roughly, the phonics method is to teach children what sounds the letters make, so that they can work out what words say, whereas the look-say method teaches recognition of whole words, from which, I suppose, the child is supposed to pick up regularities and begin to be able to make predictions about further words that come her/his way.
I used to be very firmly in the phonics camp and contemptuous of the look-say method. But my position is a little different now, and if I had to use one word to describe it, it would be "Bayesian", which turns out to include both phonics and look-say aspects, but with a qualification that I'll come to. (By the way, I don't for a moment imagine that these ideas are original to me, even if I did come up with them independently. As usual when I make this remark, which I do frequently, if anyone knows where essentially these ideas can be found in the literature, then I welcome being told about it.)
The basic idea behind a Bayesian approach is that the effort needed to learn a new piece of information (such as how to read a particular word) should be thought of not as the number of bits needed to encode that piece of information in isolation, but the number of bits needed to encode it given what you know already. I don't want to get too mathematical here, so I won't say how this idea of conditional information can be made precise -- suffice it to say that it can. Instead, let me give a couple of examples. Suppose you have "got" the rule that when your doting father asks "What does cuh a tuh make?" you have to remove those "uh"s and run the remaining sounds together. Then when that same doting father asks, "What does buh e duh make?" you will not need any effort of memorization to be able to answer "bed". By contrast, with a purely look-say approach, the fact that the visual stimulus BED is associated with the sound "bed" is a completely different fact from the relationship between CAT and "cat", so memorization is needed.
But I've ignored some subtleties there. For instance, as I've discussed in previous posts, my daughter didn't go from zero to understanding the rule in one gigantic step. Rather, I had to reduce the burden on her by doing things like asking her to read the word "dog" when there was a picture of a dog right next to it, or asking her to read "rat" when she had just read "cat". Note that in both these examples, one could argue that the conditional probability (in advance) that the correct answer is what it in fact is is higher than if the questions were asked without the accompanying clues: if there is a picture of a dog, then it is much more likely that "dog" is the right answer, and if CAT makes "cat" then it is much more likely that RAT makes "rat".
A second subtlety is that English pronunciation is full of regularities that are usually not formulated explicitly as rules. One that I noticed two or three years ago -- and here I should make clear that I am talking about the pronunciation of the particular kind of English that I myself speak, which is far from universal -- is the strange effect of the letter W on the letter A. Roughly speaking, it turns an A into an O. A few examples: "war" rhymes with "or", "wart" rhymes with "fort", "wattle" rhymes with "bottle", "want" rhymes with the first syllable of "ontological", "wally" rhymes with "dolly", "wad" rhymes with "cod", and so on.
But as with many rules of this kind, no sooner have you noticed it than you start to notice a whole lot of exceptions: "wag" rhymes with "bag", "wacky", as in the Wacky Races, rhymes with "tacky", "wall" ... well, that's an interesting one, because another rule seems to take priority, which is that words ending "all" such as "hall", "tall", "ball", all rhyme with each other and with the word "maul", and again I could go on. Part of that going on would be to detect not just exceptions but regularities within those exceptions and exceptions to those regularities, and so on.
What explains the fact that an adult reader of English who reads of a fictional place called Wapplesford, will instinctively pronounce the first syllable to rhyme with "shop" and not with "clap"? We are not told about a rule to this effect. Rather, we become familiar with a number of words and make a guess based on those words. So there is clearly something to the look-say method after all.
As an aside, I would like to say that if somebody makes the mistake of thinking that (x+y)^2 = x^2+y^2, then you should not think of that person as stupid. They are using a very important mechanism of thought -- saving mental effort by guessing that unfamiliar situations will be similar to familiar ones -- that happens to give the wrong answer in this case. I'm not sure what the best way is to convey the point that the rule "Mathematical operations tend to distribute over addition" is nearly always false, but it's not an unreasonable thing to think when almost all the instances of f(x+y) you have come across are when f is multiplication by a constant.
The problem with the look-say method if that is all you use is that the process of induction (in the scientific sense) of the rules is very hard. If you learn the words "not", "come", "go", "home", "above", and "move" as single entities, what are you going to make of the role of the letter O? A much better method, in my view, is to learn the phonic alphabet (that is, a, buh, cuh, duh, e, fuh, etc.) and how to use it to make simple three-letter words, and only then to move to recognising whole words. The point then is that after you have done that, you no longer have to learn how to read entire words in isolation from any system, but rather how the way words are pronounced differs from what you might otherwise have expected. And a few more rules make that process easier still. Suppose, for instance, that you have been told that the reason "home" is pronounced the way it is is that the final E (which some people call a magic E) makes the O (as in "hot") say Oh. Now let's look at the list of words given earlier. The word "not" is straightforward. "Home" follows from the magic-E rule. "Go" doesn't follow from any rule the child has been taught, but at least the idea that an O can be pronounced Oh is familiar, and there is an additional rule that is extremely helpful, namely that words you see in books are actually words. Furthermore, the correct pronunciation of a word often resembles the pronunciation you get from blindly following the rules, even if it isn't quite the same: we have something like an error-correcting code here, where we pass from what we see to the word that is closest to it. So it isn't hard to learn to read the word "go". And once that's been done, it is even easier to read "so" and "no" and "ho ho".
In order to get my daughter started on recognising common short words, I dug out some books from a reading scheme that everyone in the UK of a certain age is familiar with: Peter and Jane. (The main drawback with these books is what to a twenty-first-century sensibility comes across as the most incredible sexual stereotyping -- Jane is always helping Mummy put out the tea while Daddy is showing Peter how to put oil in the car and things like that.) These books introduce words one or two at a time, so the first few books in the series have an extremely limited vocabulary, and are therefore full of sentences like "Peter likes the toy and Jane likes the toy." This has a marked effect on the conditional probabilities: for example, if the context is such that a main verb is expected, then that verb has a very good chance of being "likes". So my daughter will often look at a word like "is" and say "likes". And just as with (x+y)^2=x^2+y^2 this is actually an indication that her brain is working in the right way, though remaining patient when she does it for the tenth time is a challenge.
Here are a few other interesting (to me at any rate) things I've noticed.
1. She had no difficulty with the words "some" and "come", guessing them without my having to say "These are strange words and the O is pronounced Uh". That illustrates very well the principles I discussed above: there just aren't very many words that fit the pattern S-vowel-M (maybe also she had picked up that final Es are not usually sounded) or C-vowel-M, especially when the sentence context is taken into account.
2. By contrast, the word "the" is still a real problem. I've told her countless times what it says, but she still hasn't got to the point where she reliably recognises it. That said, she often does recognise it because often it is followed by "dog" and she knows the book well enough to know that the phrase "the dog" occurs frequently. I've also told her frequently what TH makes, but this still hasn't sunk in.
3. It is possible for me to tell her what "the" says, and for her not to know what "the" says one line later (and there are very few words per line in the early books). However, if I make her spell it out, it increases the chances that she will be able to read it.
4. Sometimes she finds "the" fairly easy to read, but still can't read "The". This suggests that a certain degree of (phonetically informed) whole-word recognition is going on.
5. Back when I first started with the Peter and Jane books, she had a problem recognising the letter Y, because in the font they used a lower-case Y was not made of two line segments but was more like a lower-case G with the top removed. She would read it as a G. It was as though her brain was a neural network that was not yet fully trained (which is presumably because that is exactly what it was), so it picked up on the way the tail of the letter curved round underneath a curvy shape above, without realizing that there were two letters that could be described that way that needed to be distinguished from one another.
6. When we started, she was very enthusiastic, and pleased that she had managed to get through an entire book. We got through the first couple of levels in the series and made some headway with the third, but that was quite a bit tougher and in the end we both lost enthusiasm and didn't do much reading for a while. Then when we came back to it, she had improved as if by magic. Of course, during that time she had had plenty of opportunities to spot more patterns, with the help of the knowledge she already had.