John Bald/language and literacy

Sir, what's pi? An attempt at an explanation.

In a maths class in Educating Essex,  a girl asked this question, and didn't get an answer. In one sense, no-one knows. π, or pi, is the circumference of a circle divided by its diameter. It is a constant figure, but one that cannot be precisely described in terms of a number. People have calculated it to an almost infinite number of decimal places, and will no doubt continue to do so.

A history of π , from David Wilson of Rutgers University Maths department is here, including the speculation that it was first discovered by ancient Babylonians using lengths of rope. This could usefully be repeated using a hula hoop, taping string carefully round the outside, and comparing its length with a string stretched across the diameter. The outside string will probably be a little over three times as long as the string stretched across the diameter.

The next stage in the demonstration is to draw a line on a piece of squared paper, of a reasonable length. We don't need to measure it, and we can call it r.  We can then draw a square with r as its base, and we know that the area of the square is r².   Draw another square beside it, using the side of the first square as one of its sides, and the area of the two squares is 2r. Do the same below, so that we have four squares the same size, a little like a block of four postage stamps, and we have four squares with the same central point, and so 4 lots of the original area - 4r².

Set a pair of compasses, carefully, to the same length as r, and draw a circle on the mid point of the squares. The circle will touch the edge of the square once at each side, and cut off the corners. It's easy to see that the area cut off from the corner is the same each time, so multiplying r² by four is going to give an area that is too big. How much are we cutting off? We know that it's the same amount each time - not only can we see it, but the compass is set to the same length all the way round the circle (or it wouldn't be a circle). We also know that it's less then 4. 

We might repeat our experiment with the hula hoop to putting string round other large-ish discs and coins, and find that the longer string is always a little over three times the length of the shorter one. Again, this corresponds to what we can see in the circle - the area is always that much smaller than the area of the squares. But how long is a piece of string, and how accurate are we in measuring it? π provides the answer. We might not know what the ratio is exactly, but we know that it is the same for any circle. Multiplying r², the are of one of our squares, by π, or, for the figure used for GCSE foundation, 3.14, will give us the same reduction from the area of the squares to that of the circle.

This explanation has been helpful to students taking GCSE (and some parents), who remembered the formula, but did not know how to apply it, for example calculating (πr)² and not seeing how this produced an error. There may be clearer explanations available, and I'd be pleased to hear of them.

 

 

Another casualty of guessing game and multicue theories of reading, and a solution.

For the last two weeks, I've been teaching a perfectly intelligent young man who had reached the age of 17 without being able to read at all. All the way through school, he had been told to guess rather than taught how to use the information contained in letters. He had then, of course, been assessed as dyslexic, an assessment that indicates a failure in the schools he attended - the last of them consistently rated outstanding by Ofsted - rather than any disability on his part.

I say that because, as usual, a clear explanation of how English spelling operates had him beginning to read complex and simple words by the end of our first session. Working on the materials for his FE course brought predictable problems from residual guessing - eg reading assignment as assessment - but that had gone by the end of the second session. This particular error in education has North American origins - Frank Smith and Kenneth Goodman - and I thought we'd got rid of it. Apparently, there is still work to do.

I'll post more fully on this case, which was referred to me by my MP, as the work progresses. For the moment, I'm particularly interested in any comments from colleagues in North America and other parts of the English-speaking world in which guessing game and multicue theories of reading persist. They are a cardinal error, but are not to be replaced by the other error of pretending to children that phonics is the only game in town. Phonics are the basis of learning to read, but without explanation of how and why they vary, they cause problems with individual children that are nearly as bad - try to sound out the word "the" one letter at a time, and you'll see what I mean.

PS. For friends who have not seen the explanation of "th", it was introduced by William the Conqueror's scribes as a Latin alphabetic alternative to the Anglo-Saxon þ, that denoted this sound.

Ofqual report on native speakers and A level languages. Some initial thoughts.

The report is one of the most complex I've seen, for a range of reasons. First, it is difficult to identify exactly who is a native speaker. Next, there is a statistical method of "informing" A level grade boundaries on the basis of average GCSE grades, which does not take account of the particular problem of progress from GCSE in the language. The current GCSE syllabus has been discredited for its lack of attention to grammar, and the widespread cheating in controlled assessment. Next, we have the problem with self-declaration as a native speaker, and the fact that only a quarter of schools contacted provided a reply. Experience tells me that schools would not reply to a questionnaire if they felt it might be to their disadvantage, so I don't trust the statistical base. It would have been better to rely on the DfE's own figures - available for around 60% of the entry - than to go for self-reporting, that took a lot of time and money, and resulted in a 25% response.

In German, 17% of entrants are identified as native speakers, and are taking around half of the A* grades. This is serious enough to put potential Oxbridge candidates off taking German A level, and Cambridge is finding it hard to meet its recruitment target for state schools.  A table later in the report estimates that a native French speaker is five times more likely to achieve an A* than an English speaker. These estimations, though are only part of the information we need. Pupils are getting lower A level results in languages than in other subjects. Why? Some people say grading is severe, but that is a matter of statistics rather than the candidates' actual knowledge of the language. We are suffering from the knock-on effect of the weaknesses of GCSE, which often mean that proper language study begins in Y12.  The current reforms to GCSE are an essential step towards restoring language teaching at A level.

The following paragraphs from the report (p4) show  that the issue goes beyond German

Model 1 shows that after accounting for prior attainment, gender and school type, the association between whether students are native speakers or not and overall performance is statistically significant and quite large, ranging from nearly 44 UMS marks for Spanish, to nearly 56 UMS marks for German. This suggests that whether students are native speakers or not has a significant effect on performance, with native speakers outperforming their non-native speaker counterparts. The effect of gender and school type are also statistically significant, with girls and independent school students outperforming boys and state school students. However, these effects are much smaller.

Model 2 shows that for each language, there is also a significant interaction between mean GCSE score and whether students are native speakers. The interaction term is negative, indicating that as the mean GCSE score of a student increases, the difference in performance between native and non-native speakers decreases. In other words, the role of being a native speaker is larger for students with lower prior attainment. This is summarised in Table 11, which reports the effect of being a native speaker on UMS marks for students with a mean GCSE score of 5 (representing a typical grade C student at GCSE) and a mean GCSE of 7 (representing a typical grade A student at GCSE). 

It is not surprising that non-native English speakers do not do as well at GCSE as English native speakers. This suggests that their relative advantage at A level is even greater than the raw results suggest.

Eliminating Copying in Language Teaching - it works! Letter from a teacher.

Since 1980, I've been campaigning against the practice of copying in schools. Switching the eyes back and forth between the original and the child's copy interferes with the development of understanding, and is anti-educational. I've just had this from a teacher who tried it.

Dear John

 

Some time ago I was in contact with you regarding the possibility of carrying out some research.  The sticking point as I remember for me was your insistence that children should not be copying off the board.  Again if memory serves me well I did not at the time understand how, from a practical point of view in an ordinary classroom with 30 challenging youngsters, it could be achieved.  I just wanted to up date you with the fact that I did not forget what you have written about copying from the board, and my pupils no longer copy from the board apart from the date and title which they are obliged to do in the school I now work in. 

It has been a good decision and freed up time for more productive activities.  I have moved to a school where I am the only teacher of French and so have a certain amount of autonomy as to how I teach French.  It is a high school so the children begin in year 9 and much of my work is building confidence.  Thank you for your blog it really makes me think and change my practice for the better .  I am just about to look at the material on teaching phonics (French).  I already do this but feel I need to so more extensively.

Kind regards

 

S.

 

Interlude: Patrick Hemmerle Performances.

Patrick will be playing in the 2017 Cambridge Summer Music Festival. He is one of the finest players in Europe, well worth listening to, and a steal at these prices.

 

Thursday 20 JULY at 2.00pm in the Old Divinity School, St. John's College, Cambridge.

 

J.S Bach The Well-Tempered Clavier Book 1

 

Wednesday 26 JULY at 2.00pm in Jesus College Chapel, Cambridge.

                                                                                                       

J.S.Bach The Well-Tempered Clavier Book 11

 

Tickets £15 (also concessions) Cambridge Live Tickets 01223 357851  Book for both concerts and save £3

 

  

Patrick's new CD - Piano Modern RecitaL VOL. 1 (Indesens)

                                                  

Novak (1870-1949): Pan: a tone poem in five parts, and is a evocative hymn to nature.  

 

Tchesnokov ((1982- ) : La Neige. These two Etudes also portray the natural world

 

This may be bought from Patrick ([email protected]) or  ([email protected]) and costs £12.  

Action Tutoring

Interesting Guardian piece on Action Tutoring, an organisation that deploys volunteer tutors to help children whose parents could not afford to pay for individual tuition. Action Tutoring operates in London, Brighton, Bristol, Liverpool, Birmingham and Sheffield, and has attracted a wide range of powerful sponsors. Full details here.

Vox Cantab at Holy Trinity, Hildersham. Grace, elegance and deadpan humour.

Congratulations to Vox Cantab on a wonderfully subtle, varied and enjoyable concert at Holy Trinity Church, Hildersham, on Saturday afternoon. The Cambridge choral scholars who make up this small choir now follow a wide range of professions, but continue to sing to an international standard,  for charity, for the pleasure and joy they bring to their listeners, and for their own satisfaction in doing what they know they can do, just about as well as it can be done.  

Director Louisa Denby had chosen a programme based on the theme of journeys. The first half was serious, beginning with the story of Christ’s journey through life and death, and ending with a moving reading by Charlotte Denby of the moment, in Anne Holme’s I am David, where the sheepdog deliberately sacrifices its life to save that of David,  and Brother James’ Air on the 23^rd psalm. The second was occasionally winsome, more often a splendid example of deadpan humour, Andrew Watts doing particularly well with Three Men in a Boat and Mr Micawber’s departure for Australia in David Copperfield. The finale, Over the Rainbow, was a triumph of humour hidden behind a straight face. All of the pieces gave full scope to individual talent, blended to perfection by Louisa Denby.

The concert was part of a busy weekend, with evensong at Barton and performances tomorrow at the Old Royal Naval Chapel, Greenwich, and St Stephen’s, Rochester Row. The choir performs frequently at Fitzwilliam and other venues around Cambridge. Highly recommended.

Assessment in language learning - the key skill, and how to focus on it.

As we learn a new language, we adjust and extend our thinking from the structures we have learned while learning our first language. These involve, in the initial stages, big changes in pronunciation and in our understanding of the use of letters to represent sounds in words. The primary toolkits on this site show how these can be introduced and explained in the first few lessons - and in particular in the very first lesson, where colours illustrate most of the main changes, in a context that is self-evident.

To communicate using the new language, however, we need to know how to put our words together to make a sentence, and to understand sentences that we hear or read. This can be achieved by building up sentences based on personal experience and preferences, and gradually extending these to encompass as much of the scope of the language as a learner wishes, or is able, to know. This sentence construction uses grammar for communication, rather than as an end in itself.

The techniques in the toolkits, if possible supported by the teacher's own resources using Clicker,  enable each child to learn to compose and understand sentences, without the illusions created by copying. The approach is very easy to use, and builds assessment into the teaching, so that there is no extra work for the teacher. Any system of assessment that does not focus on sentence construction is giving a false picture of a child's ability to understand and use the language.  I'm happy to discuss this further.