Thursday (am): After dinner last night I headed to the bar. But having spent £16 on two drinks I realised that it wouldn’t be a late night for affordability reasons, so I set about looking for a TV to watch the Brighton game. (Awful game, and not a great use of 90 minutes, to be honest, but I did enjoy meeting Tom, another Brighton fan who was at the conference and who had convinced the hotel to switch channels to show the game.)

What are the chances of that? (Rhetorical, but given the readership of this blog, I imagine that quite a few of you are working this out).

And so to bed. Not a late night, meaning I was up early and (smug-face-warning) hit the hotel gym. For the first session I decided to go to a session on double-sided/two-colour counters.

I’m a big fan of these, particularly for fraction work and number relationships, and have a big collection at home. (My wife is so pleased…)

For the first half an hour we were discussing our favourite manipulatives, and the usual suspects emerged: Cuisenaire (which got a round of applause!), Numicon, the Slavonic Abacus, Tens frames, bead strings, Dienes, etc.

Next came a chance to list all our favourite ideas with counters. I actually really liked this – however much knowledge one person has, nobody will come up with a list as comprehensive as the group. We collated ideas on flipcharts.

A few nice ideas – helping with subitising was one: it is easier to see spot groups when they are in two colours.

Negative numbers and zero pairs were discussed on our tables. (As were baked beans and lentils, but that’s another story.)

The part-whole model was shown, but I have a bit of a bee in my bonnet about this. The example given was 2+3=5. To my mind, this means that there should only be 5 counters in play, but the example shown used 10 counters: 5 in the ‘whole’ box, and 2 and 3 in the ‘part’ boxes.

Scott demonstrated the benefits of using arrays; I liked the use to demonstrated the associative law being derived from arrays where some columns were ‘flipped’ to the other colour.

Directed numbers can be done if we define one colour as ‘1’ and the other colour as ‘-1’.

There was an interesting discussion about the difference between finding the total of 1 and negative 1, and the process of adding 1 and subtracting 1. This is a subtle but actually crucial difference. ‘Minus’ is a dangerously ambiguous word – sometimes verb as in ‘take away’, sometimes adjective as in ‘negative’.

Finally, Scott mentioned a free PDF from Abby Cotton which can be downloaded from here.

A quick coffee break, a chat with the wise and wonderful Dave Hewitt, a tour of the Exhibitors lounge (including an exciting moment of insight to solve the Axiom maths puzzle of the day!) and it was time for the next session.

I opted for two half sessions. Firstly, an informative update from Lynne McClure about what’s happening at a national level. I arrived a few minutes late, due to chatting with Nathan, Dave and Anthony (oops) but when I came in Lynne was talking about the Mathematical Futures working party from the Royal Society. They are working on a number of things, including for example the lack of shape  and space in the EYFS curriculum, the wilderness of KS3, and more meaningful assessment of competences.

She talked about attitudes to maths in society needing to change, and the challenge of advising government departments on policy.

This has led to the birth of the Academy for the Mathematical Sciences. It aims to be a – no THE – single voice to advise government.

Lynne chairs the Education workstream. This is a group of 25 experienced people who will consult with DfE and are drawn from schools and universities.

Research: Lynne mentioned a few projects. Nottingham University are currently running a new ‘Nottingham Observatory’ project, working on large data sets in the hope of informing systems and policies, and running a series of cohort studies which follow single cohorts from EYFS to Y6, and onwards to secondary for the next five years.

This longitudinal approach  will hopefully give them a deeper understanding of why and when those students who don’t attain as well as others start to fall behind expectations. Finally they are coming to the end of an intervention project which aims to give every FS child daily counting opportunities.

Loughborough: Colin Foster mentioned the LUMEN curriculum that they have produced. It is a brand new set of resources for KS3 students (at the moment) and completely free. Check it out here. Colin also mentioned their 5-year project looking into Early Years maths.

Lynne briefly referenced the very useful EEF KS3 guidance.

The Maths Excellence Fund (£9,000,000 of funding) was up next, which aims to keeping students engaged in maths education and onto university.

Lynne talked about the government’s current plans for an English version of the Baccalaureate, including the much-vaunted plan that everyone will do ‘some’ maths and English until they are 18.

Labour’s policy was also shown – it was a bit short on detail but hard to argue with, or as Lynne described it ‘Motherhood and apple pie’ There were a few specific pledges, including; free breakfast for all students, mental health support, a broader and richer curriculum, and an increased emphasis on sports and arts.

Lynne also talked about the specialist maths school network – I was quite surprised that there were only 11 in the whole country. (I actually met the students from the Liverpool maths school two years ago as they all attended my Christmas lecture at the Liverpool University!)

Axiom Maths: formerly MESME, this aims to support good mathematicians from poor socio-economic groups. Students are given an hour a week to think deeply in mathematical ways. Some students describe this as ‘finding their tribe’ – and ‘it’s OK to be geeky!’

I arrived late to my final choice for the morning with Jenni Back. This was the second half of her session on manipulatives.

I feel as though I have known Jenni for a billion years – she’s such an experienced teacher, researcher and author. I have sat in untold meetings over the years with her, and whatever the discussion, you can be sure Jenni will have a thoughtful contribution.

As I arrived Jenni was looking at combining numberlines, digit counters and Dienes blocks for modelling addition and subtraction. Inevitably there was a discussion about the introduction of the written algorithm, and broad agreement that it is introduced too early.

LOTS of discussion ensued around the various ways in which children were introduced to subtraction; there was a broad consensus that the concept of subtraction as ‘apartness’ was harder to grasp, and led to a poor understanding. I did think that while the various visualisations were powerful and important they did not all lead to the ‘formal’ method, and I suspect that herein lies the challenge for teachers who feel the pressure to get them to the algorithm too rapidly.

The discussions were reflective and respectful, particularly when we started to think about visualising divisions in different ways. Time ran out far too soon and it was time for lunch. By the way if anyone hasn’t eaten yet, the Chicken and Hock pie is incredible… here