Daniel Tammet has an extraordinary relationship with numbers. Born with Asperger’s Syndrome, Daniel has an extremely kinaesthetic relationship with number, and has a host of other impressive mental abilities, such as his extreme aptitude for learning languages rapidly. His book Born on a Blue Day is a wonderful memoir of his life to this point, and well worth a look both because it is a great read, and because it offers an interesting insight into Asperger’s Syndrome.

Mathematically however, it is even more interesting. Daniel suffered at school because his mind was creating associations between numbers and other concepts, and between the numbers themselves in creative and unexpected ways. He and his parents had the courage - or perhaps just the necessity - to persist in working in and with those associations. They have served him well; his numerical mental dexterity is far beyond what almost anyone else could muster.

Schools are inevitably ‘one size fits all’ institutions to some extent. Schools are mass-education institutions; it is not possible to ‘personalise learning’ precisely for individual students. That is not to say that the Personalised Learning initiatives from the government are bad things, far from it; merely that because often a teacher is dealing with about 30 students, it is not possible to tailor learning exactly to the needs of every student.

In mathematics classrooms, the tendency to make uniform what is not becomes more apparent. In maths teaching there is a tendency towards drill and rote. It can be seen clearly in textbooks, and it is confirmed by asking any reasonable cross-section of society to recount their experiences of maths at school.

It would be absurd to argue that allowing students more freedom to explore the associations between numbers and to create their own understandings of them will most students become as adept at maths as Daniel. Nevertheless the root of his understanding of number comes across as creatively based rather than based in algorithms and routines. To me, Daniel’s story is compelling evidence in support of the theory that creativity and imagination are central to the development of young mathematicians.

As a foot-note, after reading Daniel’s book I began to reflect on the ways in which I perceive numbers. This directly led me to expand my own concept of the structure of numbers by creating the Primitives concept.

Scientific-Computing.Com’s recent blog articles "Beyond the Prisoner’s Dilemma" and "Global warming and the Prisoner’s Dilemma" are interesting examples of using the logical structures of game theory as starting points for logical thought at younger levels.

The blog conversation starts with the big environmental issue of global warming and this friendly video where the protagonist explains the application of minimax to the global warming debate. He argues, in a nutshell, that given uncertain future consequences of humanity’s impact on the planet, and given also a choice of decisions about how to act against those potential consequences, it makes the most logical sense to exclude the catastrophic choice of doing nothing to prevent global warming by acting as if global warming were a certainty.

I like how the minimax principle here facilitates students’ understanding by offering a powerful structure for considering different possibilities. Because minimax is so clearly structured and relatively easy to grasp, it is the sort of idea, like the Venn Diagram, which ought to be a constantly recurring feature of students’ education. In Mathematics, it bears close resemblance to the Carroll diagram, which is a similarly undervalued structure for understanding issues.

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!