http://vimeo.com/1908224?hd=1

As the comments underneath the video allude to, there is some utility here to attempt to consider the size of magnification that occurs during a portion of the video, and how to express magnifications of such a magnitude.

Flags By Colours

It would be a fun and worthwhile activity to use this site to exercise KS3 students’ abilities to mentally construct and destruct pie charts in a game of ‘guess the flag’

Cell Size And Scale

From a scientific perspective it is interesting to reflect upon the relative sizes of elements, from a Coffee Bean to a Carbon Atom (through various things such as a human Ovum, Sperm, various viruses, compounds and so on).

From a mathematical perspective it is also interesting for the way in which the relative scales are measured in the top-left. Exploring the different notations for small sizes would be a useful exercise in place-value for all levels of Key Stage 3 and 4.

Visit Flickr for the original at a range of sizes.

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.

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.

Most of the puzzles deal with the concepts of power and force, both in terms of their generation and their effect. The aim is to make a little (metal) ball reach a particular goal. It can be done by using wind power to blow the ball, magnetism to attract it, or ‘rollers’ to move the ball along. Some or all of these effects require power, and the different mechanisms for generating and transferring power are really interesting and innovative.

This game is a wonderful way to introduce physics.

One of Firaxis’ contributors Kurt Squire proposes Civilisation as a good model for learning about World History. There is an interesting tension here. On the one hand, a game like Civilisation engages students in such a way that they build a sophisticated model of the game in order to succeed at it. That is good educationally to the extent to which the game models genuine historical processes. It is not clear that the ‘history’ that Civilisation presents is particularly convincing.

While Kurt Squire argues that Civilisation “represents world history not as a story of colonial domination or western expansion, but as an emergent process arising from overlapping, interrelated factors”, it does still give an essentially American – or at least New World – view of history. Land is virgin territory until moved into by the great civilisations; pre-colonial Afrians, native Americans, native Australian Aborigones do not have a story. Intellectual and technological progress happens linearly; the Middle ages and the loss of Roman and Greek learning cannot happen. There is no potential for a European type of historio-political scenario; states are the size of continents.

On the other hand, if one ignores the problems with the historical model, it does offer a ‘big picture view’ of history. Could such a grand model of historical processes be so readily expressed without the means of technology? Certainly the answer is yes, though it would take an extremely talented teacher, and those are notoriously thin on the ground.

The pipedream is for someone to create a game with production values on a par with Civilisation, but which takes as its starting point an historical model that aims at accuracy. This of course, is rather like desiring an historically accurate documentary that looks and sounds like a Hollywood movie, but there will surely be moves towards higher production values in educational software in the future.

Today’s Independent runs this headline on page 27, heading an article by their Education Editor Richard Garner on Dr Paul Kelley’s new book Making Minds.

The Independent quotes Dr Kelly on the SATs sat by every student at 7, 11 and 14: "Testing every child has, overall, a negative on the learning outcomes and attitudes of children. Repeated practice tests reinforced the low self-image of the lower-achieving students. The feedback from teachers often hurts children’s feelings rather than helping them understand their weaknesses. Children often responded by reducing their efforts towards further learning and focussing on performance in tests."

It is encouraging to hear Dr Kelly say this, which seemed apparent to me and to many of my colleagues as soon as we started training to teach. It is important that he says it too. The more high profile criticisms of the current testing regime, the more the government will have to listen.

The current testing regime comes from an array of misguided notions about the appropriate means of assessing schools, teachers and students. It is easy to think that those who argue against the current regime are against testing per se. Not so; the criticism of the testing regime for younger students does not imply a criticism of the idea of testing at 16 and 18.

Richard Garner disputes Dr Kelly’s argument that ‘rising achievement’ can be explained by examinations having been made easier. Garner argues that the rise in perceived achievement is explained by teachers becoming ever more adept at coaching for exams. I’m inclined to think that a little of each is more or less right. I discuss a similar idea in my post Playing Politics with Education.

Dr Kelly has a host of other things to discuss in Making Minds too, from the hours that schools open to the ages at which language acquisition is most acute. It is encouraging that research into neurological science is starting to have an impact on educational thinking. I will post more on these ideas once I’ve got my copy!