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:
My score as about 3.03, having frustratingly crepty above an accuracy score of 3 with a shocking 9 in my final problem.
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.
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.
I hope you gain as much enjoyment, and as much fervour from its reading as I did.
The new Bowland Maths Website is the website of a new project which seeks to ground maths in an explorative, problem solving environment.
Bowland Mathematics seeks to develop meta-cognitive skills and promote an analytical, quantitative attitude towards problem solving. These goals are worthy, and important life skills, but they are difficult to measure cleanly. With curricula that separate the strands of mathematics in a way that encourages their their teaching to be separated also, and with testing that aims at accountability over intelligence, school mathematics has become ever more piecemeal and disconnected with reality. Bowland is an important project that seeks to reclaim some of the lost ground.
I urge, in the strongest possible terms, that anyone involved in mathematics education take this initiative seriously. I have no vested interest in the scheme, but simply I believe that it is crucial that initiatives such as this succeed and are built upon.
John Mason, Professor of Mathematics Education at the Open University, was the closing speaker at this year’s MA-ATM combined mathematics education conference.
The central theme of the talk was the importance of reflecting upon experiences in order to unify them. We don’t often seem to learn from experience alone Prof. Mason exhorted; we learn incrementally, unifying experiences with one another, gradually gaining awareness of a greater whole.
Unifying experiences does not happen by chance; or rather, it should not. As teachers we must act as faciliators of this reflective process. One way to achieve this is to offer students familiar patterns of problems which are then developed and extended, and the richness drawn out of them through reflection.
The associated prensentation to the talk, with examples of such activities can be downloaded from Prof. Mason’s website, or by clicking on the link below:
Powerpoint: Closing Plenary at the MA-ATM Conference
Of course, this presentation does not do justice to an impassioned talk from such an experienced educator!
There was a great deal of truth in Prof. Mason’s talk. One of the main things that I will take away from the talk was my reflection during the talk that as a teacher I found myself too often concentrating on the activity in quantity, searching to find new activities and new ways of approaching a topic. I would find them on the internet, or in books, or by asking others. By contrast, the activities considered in Prof. Mason’s talk could be found only by taking the mathematics seriously and doing the mathematics for yourself. He searched for activities in quality, searching for ways of reusing the familiar but provoking new thought within that structure. From this, students are in a position to draw upon previous experiences, become familiar with areas of mathematics, and begin to unify their experiences. That is a lesson worth (re)learning!