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Oct 16

Another Report about Education

The Cambridge Primary Review today published their recommendations for how the primary curriculum and classroom environment should be arranged. The briefing is an interesting read, the headlines of which can be found on the BBC News website.

As I read the part on SATs I reflected on the way in which the relationship between politics and education continues to work to this day. The review argues that SATs narrow the curriculum focus and put pressure on children unnecessarily. It argues that the concept of standards that underlies the system of SATs is “restricted, restrictive and misleading”. It further argues that assessment of childrens’ learning should be detached from assessment of schools’ accountability.

It is perhaps inevitable that this is how education and politics interact: governments change the way education works with an agenda justified by their electoral mandate, but often with no educational justification to back it up. It can then take a decade or more for evidence to be gathered, arguments to be made and reports to be compiled before the deficiencies of the system can be established to the satisfaction of politicians, and the scheme can be scrapped. Then, another government can come in with their agenda and try again.

I knew that SATs restricted curriculum, failed to assess students reasonably and were a monumental waste of time and money, years ago. I’ve blogged about it before, years ago. Most of the bright, intrested teachers that I’ve met have known similarly. But education is one of the few things that governments with mandates can interfere with almost at will, and the obvious truths for teachers on the ground are difficult to express to people living in the ivory towers of Westminster. It’s about to happen again. I believe that the best we can hope is that they (whoever they are) make a slightly less-bad set of decisions in this next round of reforms.

Sep 23

Mary Midgley

Mary Midgley was born on September 13, 1919 and was the Senior Lecturer in Philosophy at Newcastle University. Despite publishing her first book at the age of 59, she has a fearsome reputation in the Philosophical community. Her work has largely focussed on science; attacking the pretensions of ‘scientism‘, and arguing in favour of scientific pluralism; that we must recognise “that there are many independent forms and sources of knowledge” (Myths We Live By, pp 26-7).

Famously, she and Richard Dawkins have had a thirty-year disagreement. Midgley argues that Dawkins goes beyond the scientific to sell “the worship of competition”; that he projects Thatcherite free-market economic beliefs into his theoris of evolutionary biology; a charge which Dawkins disputes!

In May 2009, my dad Alan McEachran, who has taught Philosophy and Sociology all of his professional life, gave a talk about the work of Mary Midgley to the Erasmus Darwin Society in Lichfield, Staffordshire. The prepared text for this talk follows:

Mary Midgley, by Alan McEachran

This is the second talk that he has given to the Erasmus Darwin Society. His discussion of John Gray is also available from this website.

Sep 18

Book Review: Plato’s Shadow

Neel Burton, Plato’s Shadow – A Primer On Plato

Academic texts try to appeal to specific readerships. Though Plato’s Shadow has merit, this reviewer is left wondering who it was written for. It works best as a reference book of sorts, since it contains easily-read summaries, each of between two and twenty pages, of all Plato’s dialogues. Each précis is faithful to the original text and provides the reader who is unfamiliar with any dialogue a clear account of what is to be found there. The author also devotes the first forty pages to a useful account of the historical context of Athens and its relations with other city-states, and to a discussion of Pre-Socratic Greek thought and the place of Socrates in the dialogues which follow. A final introductory chapter also looks at scholarly views of when Plato’s works were written, in what sequence, and with what connection to each other.

A student encountering Plato on a Philosophy or a Classics course would undoubtedly benefit from having this book to reach for as a preliminary step before reading one of the dialogues for the first time. A general reader would also find this a useful reference book because of the way it treats each dialogue separately – something you don’t usually find in such a short and accessible paperback.

However, to call this “A Primer On Plato”, as the author does, is misleading. Anyone trying to understand Plato’s thought won’t find much help here. Nothing is done to point the reader to where Plato is specifically exploring metaphysical, ethical, epistemological, political, etc. themes. This book cries out for an index; both the student and the general reader are likely to want help in finding where Plato talks about The Sun Metaphor, or Forms, or Diotima. The occasional attempt is made to enhance understanding by the use of an illustration; this makes most sense in the Meno and Republic dialogues, though in the latter it is The Cave which is illustrated rather than The Divided Line, which almost every other book about Plato rightly and helpfully presents as a diagram.

This text is a welcome addition to a shelf of reference books, but it shouldn’t be seen as a general introduction to Plato’s thought.

Sep 2

Linguistic Ambiguity and Ignorant Journalists

Even BBC Radio 4 journalists are unable to recognise the distinction between the following sentences:

  • I do not want Megrahi to die in prison;
  • I want Megrahi not to die in prison.

There ought to be a clear distinction between the intention of the speaker in the two cases: the first does not necessarily convey any intention, while the second takes a clear intentional stance.

On BBC Radio 4 this morning, a five minute interview went frustratingly round in circles because neither the Foreign Secretary nor the interviewer could satisfactorily explain this distinction.

We often use the first form of the sentence when we mean the second, and this linguistic ambiguity was siezed upon in a piece of journalistic opportunisim. Bill Rammel was asked a question about whether the UK government ‘wanted Megrahi to die in prison’. He responded that they did not. The question asked about whether an intention existed; he replied that it did not. He was not asked, nor responded to whether there was the converse intention; he was not asked “Does the UK government want Megrahi to be released from prison before he dies?”, but it is now widely reported that he confirmed exactly that.

Increasingly, it seems that journalists exploit these linguistic ambiguities in order to create a story. No wonder politicians (of every persuasion – I am ambivalent with respect to the different parties) are so careful when asked ‘clear yes and no questions’ and sometimes simply repeat a well-rehearsed phrase. When they are misrepresented so wholly as in this case, can you really blame them?

When they occur, these stories are good opportunities to highlight the ambiguity of language and the care with which language needs to be used to sixth-form philosophy students. It is perhaps the most important practical application of learning philosophy that its students can be forewarned against the pitfalls of such exploitative misrepresentation.

Aug 27

Venn Diagrams (And Mythical Creatures!)

This is a delightful way to revise Venn Diagrams with older students: A Venn Diagram of mythical creatures.

mythicalVenn

Visit Flickr for the original at a range of sizes.

Dec 24

1 Comment

“minus” and “negative”

In the past I have commented on the QI forums that the difference between “negative” and “minus” was a good one and worth keeping*. I didn’t mean it to come across as self-congratulatory psuedo-intellectualism, though I’m aware that this is how it might have come across.

Listening to Stephen Fry’s ‘podgram’ on language, it appears that Mr Fry does not agree that pointing out the difference between “less” and “fewer” is worthwhile. To him, sadly, I am a pedant, attempting to impose a sort of lingustic-conservativism on the world.

Frustratingly, I agree with the majority of what Mr Fry discusses in his podgram; which is that language is a rapidly changing thing, and that what is aberrant in one generation will become established in another. Obliquely he suggests that language is ‘evolving’ though I am scared off that word having read John Gray‘s Straw Dogs, and I think rightly so. The problem with calling something ‘evolving’ is that it somehow implies progress, and I do not think that this is the case for language all of the time.

My reason for believing that “minus” and “negative” should be more clearly demarcated in language is really for its utility in mathematics classrooms, and it is there where I believe the demarcation should be expressed and preserved. There are two separate concepts here: one an operation over two numbers to express (as a directed number) the difference between the two numbers; the other to express the direction of a number, ie whether postive or negative. They are difficult ideas, to be teased out. We tease them out poorly, and need to improve. They would be teased out more successfully if their use wasn’t so interchangeable.

If I am right, then the interchangability of “minus 5″ and “negative 5″ should not be considered part of the great evolution of language. Wittgenstein is right to an extent, when he claimed that the limits of my language are the limits of my world, and if I lose the ability to use two words for two separate concepts, I lose the ability to differentiate the concepts.

I do not wish to be a pedant, but I think that linguistic conservativism is the bathwater to a good many conceptual babies whose protection is worthwhile.

Oct 7

Geometry, by eye

A quickie: here’s an interesting game from Canada where users have to find various interesting geometrical properties by eye and are assessed programmatically on their accuracy:

http://woodgears.ca/eyeball/

My score as about 3.03, having frustratingly crepty above an accuracy score of 3 with a shocking 9 in my final problem.

Sep 7

Maths Education and the Metric System

The following conversation in Metric Views catches the attention both for the interesting article and the subsequent comments.

Metric Views: Are our schools entrenching the ‘very British mess’?

The gist is that our schools reflect our current social muddle by teaching both imperial and metric measures and their relative magnitudes in school. In the article it is argued that the time and cost wasted on this is horrifying.

I have no love of imperial measures; I find it frustrating to have to remember how many pounds are in a stone, or ounces in a pound, or yards in a mile, and struggle to do so. I also find it difficult to convert between anything other than kilometers and miles. I know my weight in stone, but not in pounds, and certainly not in kilograms. I know my height in both metres and feet-and-inches. I am not sure that I can estimate volume in any unit with any degree of accuracy. It’s a horrible, muddy, confusing mess; that is undeniable.

I think my misgivings about the article are about the underlying idea that we should stop teaching both measures to achieve a feat of social engineering; by removing from the minds of the youth any conception of imperial measures, we would hasten the demise of imperial measures, which would be a Good Thing.

My difficulty is that feet-and-inches is such a good measure of height. I am 1.83m or 183cm, but neither is as satisfying as being 6′ tall, and neither is immediately conjourable in my mind. I don’t like Americans’ removal of ‘stone’ as a measurement either; 13 (and a bit) stone is much easier to remember than… whatever number of kilograms or pounds I am.

Feet, inches, stones and pounds are good measures because they are useful. They give us a scale rooted in humanity and the measurement of humans, and allow us to compare ourselves with others accurately. I am not convinced that the removal of these measures in classrooms will remove their common use.

I should not be confused with someone in defence of a curriculum which monitors and assesses the knowledge of different weights and measures and their conversion. Conversion is a fairly dry arithmetical topic. However, there might be problems that involve imperial or metric measures (or even their conversion) which may contain some good mathematics. I would not want that potential to be excluded from the curriculum any more than I would want their being taught made compulsory.

Jul 27

1 Comment

John Gray – An Appreciation

My dad taught Philosophy and Sociology all of his professional life, and in his retirement continues to study and think about these subjects. He recently gave a talk about the work of John Gray to the Erasmus Darwin Society in Lichfield, Staffordshire.

John Gray is currently Professor of European Thought at the LSE, and has been an outspoken and controversial academic throughout his career. He has written about a great breadth of topics, but the thread of thought that ties his work together is his rejection of our contemporary belief in the progress of mankind.

The prepared text of my dad’s overview of Gray’s views is an excellent introductory text, with a good bibliography pointing towards further reading. I would strongly recommend this text to students as an overview of his thought.

John Gray, An Appreciation

Jul 10

Lockhart’s Lament

In an ongoing email conversation within the ranks of the ATM on its purpose and voice within the uk educational establishment, one of our numbers recommended we read Lockhart’s Lament, an article posted on the website of the Mathematical Association of America by Keith Devlin.

Lockhart’s Lament is a a heartfelt plea to the beauty of mathematics, the place of mathematicians as artists, not engineers, and society’s complete miscomprehension of what mathematics actually is.

The article opens with a parody: what if society had the attitude towards music that it currently has to mathematics? Lockhart asks us to imagine a world where students learn musical theory without ever grasping what music is. In this world, students don’t hear music or feel it, it is a word used to describe a formal system, emotionless and austere. Perhaps a few get to understand, listen to and feel music when they get to university. If they try to describe their joy and amazement, people look at them blankly and conjour up memories of their tests on harmonic scales when they were at school.

For Lockhart, Mathematics is in turns the art of explanation and the music of reason. However, it is as poorly understood by modern western society as music is in his imaginary music-less world. Lockhart argues that “there is no more reliable way to kill enthusiasm and interest in a subject than to make it a mandatory part of the school curriculum.” Through standardisation and testing which puts the onus on memorisation over understanding and exploration, the subject is fundamentally undermined.

The breadth of Lockhart’s exasperation is great: from society to schools, to teachers, and universities, but most forcefully to the government and the curriculum. This, written in 2002 is ever more true. It is an unsettling prospect that the USA is further down the road of standardising the maths out of maths than we are in the UK. Perhaps, using them to see into our future we can change it. Reading this Lament strengthens my belief that we must try.

Read Lockhart’s Lament Here

I hope you gain as much enjoyment, and as much fervour from its reading as I did.

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