Report on Finland’s Education System

I think there are a few things that they miss out from the report, like a very homogenous population, a smaller wealth gap between rich and poor, and a very low density of population. Still, it does paint the picture of an idyllic scenario of an educational system free from interference from politics. I with a party in the UK would put that in their manifesto!

This article is a little heavy on the politics for an average maths classroom, but is perhaps useful for A-level students, and is definitely useful for any teachers teaching the IB, as it has excellent cross-over with theory of knowledge. Worth a look

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.

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.

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.

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.

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.

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!

In this month’s Mathematics Teacher magazine is an article about prime factorisation by me. It discusses an idea for teaching and learning about prime factorisation that minimises ‘telling’ and maximises students mathematical exploration.

Dave Hewitt, a lecturer in Mathematics Education from the University of Birmingham (and my PGCE mentor a few years ago), has written a series of articles about separating the arbitrary (or contingent) and the necessary and mathematics, and teaching by ‘telling’ only those things which are arbitrary. The idea is that students need to engage and discover for themselves the necessary connections and patterns in mathematics, but the arbitrary are not discoverable in the same way, and so need to be told to people.

This position has influenced my thinking about mathematics education, particularly with respect to algorithms. My conjecture is that using an algorithm involves no mathematical thought; at best, it is an exercise in arithmetic. However, where an algorithm exists there is likely to be a kernel of really interesting mathematics, and creating an algorithm to perform a particular function involves a great deal of mathematical thought. The goal of the investigation was to capture the interesting maths in an interesting way, that the students can engage with, and which they can learn from.

The accompanying software can be found in the primitives section of this website.

The SSAT argue that the government has “consistently exaggerated the technical rigour of national assessments and the GCSE“. They argue that by changing the curriculum and therefore changing the content that is being tested, it becomes extremely problematic to maintain and compare standards.

The SSAT also argue that there are testing cause a degree of stress and that the level of continued stress that students are exposed to has become unreasonable and counter-productive. In place of the SATs they suggest using sample testing of randomly selected pupils to monitor performance.

The response from the DCSF is staggering: “… we are not looking at sample testing of randomly selected pupils … It is hard to see how any sample of children could be truly representative of one school … the idea that children are over tested is not a view that the government accepts … we don’t believe that in this day and age parents can be expected to have hidden from them the real achievements of their children at school.”

If the governmental body responsible for our curriculum do not understand sample testing, then I am deeply concerned with the science curriculum; if do not understand how sample testing can give representative data, then they do not understand science. Science is based wholly upon the statistical analysis of sample data. Given a sample and the overall population size, we can very accurately calculate how representative that sample is. Simply, this argument is nonsense.

The original premise for introducing SATs was as a means of measuring schools performance. The DCSF statement concedes that they have now become GCSEs for younger students – performance assessments for the students and their parents to measure themselves with.

Despite this the government does not accept that children are over tested. I am absolutely and utterly convinced that the government is wrong about this. Sadly, there is no easy way of measuring what level of stress is acceptable to expose children to. However, I would have thought that until tests GCSEs, the natural inclinations of all parents and teachers would be to minimise unnecessary stress. This is not the government’s inclination.