John Bald/language and literacy

Basic number work - facts or fingers?

First, a reference

Gray G and Tall D, Journal for Mathematical Education 2, 1994, pp116-140

This article studied the way above- and below-average children (their teachers’ estimates) tackled simple arithmetical tasks. Their first series consisted of adding single digit numbers whose sum came to below and above 10,  then adding a single digit number to a teen number, when the sum was below 20 (eg 15 + 3).  A second series had similar tasks for subtraction.

The authors identified the following main strategies for completing the tasks

• counting from scratch
• counting on (or back in subtraction) from one number to another
•  answering the question from known facts (eg knowing without working it out that 9+7=16)
• using “derived facts” – eg in subtracting 9 from 16, first subtracting 6 from 16, and then 3 from 10).

They found that the above average group moved swiftly from counting to answering questions from known facts, and then derived facts, as in the example above.  The below average group were slower to learn facts, and were still using fingers and thumbs on the more difficult of these tasks at 11+ and 12+.  These children almost never used “derived facts”, and their reliance on counting left them with no useful strategies for tackling larger problems.

Professor Jo Boaler, in The Elephant in the Classroom, has argued that low-achieving children’s problems with maths are caused by their being placed in low sets, where they are given undemanding work (Making Low Ability Children). However, the study above, which I found from her book, shows that the origin of the problem is much earlier, and so defeats her proposition on cause and effect. The higher-attaining children in the study only began to use derived facts rather than counting after they had virtually complete knowledge of number bonds. The low-achieving children were still counting because they did not have these.

Why, though, were they still counting on their fingers, and why has the national numeracy strategy not eliminated this problem? Children should not go to secondary school counting on their fingers. This is the real scandal, and one the national numeracy strategy has not tackled - as you will see from earlier postings, I still meet ten and eleven year olds who use their fingers, and they are not all from inner city primary schools.

I was also informed by a researcher two weeks ago that the Nuffield project on mathematics had found no difference in children’s knowledge of tables. This is, apparently contained in one of the two unpublished volumes of its research – why they are unpublished seven years after the completion of the project is another interesting question.  Yesterday, though, a primary headteacher, who had been interested in my suggestion that counting in multiples interfered with learning tables, told me that she had tried the idea and that she thought I was right. This needs to be investigated, along with the interesting question of whether it is better to learn tables as we do in England, 1x2 is 2, 2x2 are 4 etc, or as they do in Scotland and Italy – 2X1, 2x2, 2x3 etc, where the numerator comes first.

Ofsted SEN report

The SEN scandal has been with us for years, since it came to be in the interest of New Labour's managerial headteachers to label anyone likely not to achieve the required grades in tests and examinations as having special needs. The Ofsted report analysing the present state of affairs, its roots in ignorance, authoritarianism, laziness and fraud, and ways to sort it out, is  here. It is a superb piece of work, showing that HMI can still deliver the goods despite the damage done by David Bell as chief inspector. It should be the basis for a complete policy review. The NUT's response is predictable and typical of its determination to defend incompetence to the last gasp, though how much either of its spokespeople really know about sen is debatable, to put it mildly.

Another perspective on French education

Guardian, here, has an account of an unhappy experience in a French primary school that needs to be seen alongside some of the rosier views we have seen recently. Children in France behave better than in most UK schools as, in practice, they have little choice. Poor behaviour is not tolerated, and psychological pressure can be intense. The French also have a tendency to blame all failure on the pupil, and to make maths the beginning and end of success. Overall, their system is very good for those who reach the heights of their Grandes Ecoles, and at times very poor for those at the bottom. We have learned some useful lessons from the French system - small whiteboards, for example - but the grass is not always greener.

Michel Thomas and writing - a solution to a problem.

On the front of every box of Michel Thomas Language Course is emblazoned No Writing. As I've said in previous postings, I counted Michel as a friend, albeit not a straightforward one, and left him on our last meeting with a bearhug. Here is part of our last conversation, for a Guardian review of his advanced course, with two of the publisher's staff present:

MT  They don't need to write. If they can say it, they can write it.

JB  (realising that if you contradicted Michel directly, he would just repeat what he had said). Some people need more of a bridge. Here is my bridge (demo of sentence building in French, using Clicker 5 and Acapello)

MT  This is good...this is very good...you are a great teacher.

 

Michel failed in his attempt to introduce his approach into the British school system. This was partly due to the way those in charge of it ignored and belittled him, and partly due to poor choice of schools for his trials. The use of writing in the current adaptation for schoools is inconsistent with the sentence building approach that runs through his teaching. We can't know, of course, what he would have thought of the approach to writing in MT for schools. I do know, however, that it is not consistent with his principles for teaching languages. More importantly, I do know what he thought of my approach, because he told me. Michel's principles co-incided with those I had developed myself in my work with literacy problems - a cause of some friction after our first meeting, as Michel thought that anyone who really understood what he was doing would be likely to pinch it. He only talked to me again after he had secured his deal with the publisher (having been turned down by Microsoft...) and so did not feel at any risk. Clicker 5 and Acapello are available to everyone at a much lower price than MT for schools. They are the solution to the problem of adapting Michel's techniques for writing, and I would welcome correspondence from anyone interested in investigating them.

Political Interlude - AJ Blair's memoirs

Balzac said, Il est toujours dangereux d'écrire,  (Le Curé de Tours). Even AJ Blair cannot avoid the occasional lapse into truth. The following has been picked out by the Telegraph (on the late Princess Diana)

“We were both, in our own way, manipulators” — good at grasping the feelings of others and instinctively playing on them."

A rationale for his cheating, scheming and lying, and an abuse of the word "good".

Telegraph also picks out this quote, in the context of Northern Ireland

Mr Blair admits to “bending and distorting” the truth as prime minister, but says a degree of manipulation and distortion are necessary to govern, and voters accept that. “Politicians are obliged from time to time to conceal the full truth, to bend it and even distort it, where the interests of the bigger strategic goal demand it be done. Without operating with some subtlety at this level, the job would be well-nigh impossible.”

Discussing his approach to the truth, he suggests that, at a deeper level, voters retained trust in him because he was trying to do his best for them.

He says the public discriminate between politicians they do not trust at a superficial level — “ie pretty much all of them” — and those they do not trust at a more profound level.

This is the level at which the public believes that the political leader is trying to do his or her best for them. “This is the level of trust that really matters.”

In Blair's case, there is no such level. His personal endorsement of the MMR vaccine probably did more to shake public confidence in it than anything else - people believed that everything he said was a lie until proved otherwise. This voter does not accept being lied to, much less to having government based on systematic and deliberate, organised lying on every subject all the time, so that the truth, in this artificial atmosphere, ceases to exist. Getting the truth back must be a key aim of politics, and particularly of education.