My Oscar predictions were confidently made this year- out of the 24 catagories I got 16 correct.

Of the big 8 (Picture, Director, Actors & Actresses, Screenplays) I picked 5 correctly.

If we assume 5 nominations per catagory (although Hair & Makeup only has 3 and I’m not going anywhere near the tie in Sound Editing!), then the question of the day is:

Should I be pleased?!

Have I done well?

NAS

Photo from www.empireonline.co.uk

The final Maths lecture- given by the Upper Sixth Further Mathematciians- each in 4 minute mini-lecture bursts!

A Maths Blog by Mrs Crewe-Read, Deputy Head (@KSCDeputyHead) and, of course, formerly Head of Mathematics.

Am I alone in being unimpressed by Sir Tim Gowers and Cambridge University’s bid to restructure A Level maths? The Dept of Education have lost no time in agreeing to adopt his ideas for the maths curriculum, we are told in this week’s TES. ‘It is incredibly exciting that some of the best mathematicians in the world want to fix A Level maths,’ said Mr Gove.

But is A Level maths broken, I ask myself? And if it is, where is the evidence? That Cambridge argue ‘the majority of their students do not have a sufficient mastery of basic maths’ I find astonishing. Competition for places on their maths and science based courses is fierce and students’ mathematical ability is tested by exam or exactingly at interview. Are they saying these students do not have good enough maths? The impression that our Oxbridge alumni give us is that, whilst the pace of work at university is uncompromising, they feel we have prepared them well. And let’s be honest here: the preparation they receive from us is largely, though not entirely, that laid out in the A Level syllabus.

According to reports in The Telegraph, the new A Levels will

a) focus around Key Mathematical Ideas (as opposed to ….what?)

b) have demanding questions to stretch the most able

c) drive up educational standards

To which my response would be that the topics listed as necessary (trigonometry, combinatorics, probability and centres of mass) already feature in the A Level specs, that the place to stretch able mathematicians is in the classroom, not the examination hall (I am not saying here that exams should be easy) and that setting harder examinations does not
make children cleverer. My last point may come as a surprise to Mr Gove, whose justifications for the EBQ (GCSE replacement 2015) seem to be underpinned by exactly this belief.

The Telegraph (see below) does suggest that other universities find that student’s maths is not up to scratch- but is that the maths of students who major in mathematical sciences (and who did so at A level) or is it, for example a concern regarding the abilities of those reading for degrees that do not require maths A level? If it is the former, then I am surprised, because none of our alumni have reported that their maths is insufficient to support further studies and we are lucky enough to have good contact with many such students. That being the case I would suggest that it is not the A Level (either content or examination) that ‘needs fixing’. More that the teaching/learning in some cases and schools lacks breadth, depth and understanding of the complex connections between topics.

So perhaps the most useful of Cambridge’s offers is that they (and other universities) will produce teaching materials to support the A level curriculum. This I am in favour of: for as well as teaching, we must all demonstrate our commitment to learning and through that, keep up to date with the pedagogical advances. Whether or not universities are best placed to help us with that, given reports last year of national dissatisfaction with the quality of teaching and assessment in HE institutions, is the subject of a whole new blog entry entirely.

(http://www.telegraph.co.uk/education/educationnews/9628595/Cambridge-University-academics-to-set-maths-A-levels.html)

MathsJam

If you’re reading this blog & don’t know what MathsJam is, click here:

http://www.mathsjam.com/

The BBC is far from alone in reporting a boom in geek culture (http://www.bbc.co.uk/news/magazine-20325517) & last weekend I spent a day with 100 Mathematicians whose sole aim was to share cool stuff they’d come across. Here are just some of the things spotted & nicked already- look at the @KSC Twitter feed for more!

Can you explain what this means?

Click on this Video clip! chain

Each presentation lasted for a maximum of 5 minutes & the whole event was friendly, funny, open & highly enjoyable- I’ll be going again.

Upper Sixth Further Mathematicians will do their own (now annual!) version of these lightning talks just before Christmas, with the aim being not to teach something, but share something interesting they’ve found.

Its never been a better time to be a geek!

http://www.bbc.co.uk/news/education-20259382

Maths ≠ Arithmetic.

Just as English≠ Spelling.

They’re both important structures which, if you master them, bode well for the development of more sophisticated skills needed to excel in the subject at a later stage.

In Primary school, much of the Maths learned is based on arithmetic.

Calculators do arithmetic and so pupils can be fooled into thinking of the calculator as a “magical answer provider”. This feeling can last throughout an educational career: ask a pupil what is 1÷0 and the most frequent reply will be “Math Error”. Ask them to find the square of -3 and an alarming number will use their calculator to gain the wrong answer of -9  as, if you don’t use brackets properly, the calculator will find -(3²) instead of (-3)².

If we want pupils to be comfortable in a Mathematical situation where they have only their own wits to rely upon, then an absence of calculator at an early age seems like a good way to start- we introduce them in year 8 (Shells).

When technology is everywhere (many pupils will have calculator apps to hand before the age of 11) the suggestion that, by not teaching calculator use, pupils will “flounder” in secondary education is odd, as the skills needed to operate a calculator to a basic level are not too taxing & the problems encountered in primary school won’t require many steps to push beyond fundamental use.

A more interesting debate concerns the use of advanced calculators in A Level: why teach the manipulation of Stats tables when many calculators can evaluate probabilities in the same way that made log & trig tables obsolete? Do graphical calcs help or hinder pupils to have an intrinsic understanding for the shape of a curve?

Also of note today is the announcement that A-Level January modules are over.

http://www.bbc.co.uk/news/education-20266533

At Kings’ this makes no difference to our single Maths A-Level courses, but has a significant effect on Further Maths. Most of our FM pupils sit 13 or 14 exams over 2 years (a minimum of 12 are needed) but, at 90 minutes each, the removal of January modules makes for a mammoth summer exam burden for these pupils, especially if they study 5 A2s.

Whilst moving away from repeated resits and modularisation is welcome, the current system was built to make use of January modules. For Further Maths (whose numbers need boosting nationwide) such an intimidating exam requirement may put many off.

The redesign of A levels cannot come too soon for Further Maths.

Recently in the news has been the government’s grant to MEI to develop material for Sixth Form (http://www.bbc.co.uk/news/education-20153731) based on suggestions made by Prof Tim Gowers (http://www.spectator.co.uk/features/8744071/should-alice-marry-bob/). What does not seem to be being reported clearly is that Gowers’ programme (as it says in yesterday’s Sunday Times) are apparently for a new qualification; an alternative to AS to perhaps correspond to Maths Studies in the IB diploma. Gowers’ proposals seem to be for those who have dropped Maths due to disenfranchisement, maybe at the subject’s lack of applicability, but the many news reports are not clear about the impact of this on whatever follows the current version of AS Maths.

“Sir-what use is this in real life?”

If I’m honest, there are few, if any, questions that can come from a pupil that make me shudder more than this one. I am always tempted to answer “None- this is all a colossal international conspiracy constructed purely to specifically waste your time. Actually none of these symbols make the least bit of sense and honestly, I’m making it all up as I go.”

The question, however, is always a valid one and I suspect my impatience for its rare appearance stems from the possibility that it might be my fault- maybe I’ve not already made the application of the Maths already clear or I’ve not gained enough of their trust that I was ultimately heading there.

There is a well established negative perception of Maths in the media as the theoretical wafflings of elbow-patched intellectuals. Journalists, educationalists and politicians can be seen talking of the need to move to the fore the skills pupils need in Today’s Society, in place of allowing Maths teachers to self-indulgently prattle on about theory, proof & derivation.

Previous attempts to address the abstract nature of Maths this have resulted in frivolous practical questions, making exams look utterly ridiculous (Seth is starting a free range farm. The number of ducks on his estate is given by the equation y=x²-4x+6…). This media perspective always greatly annoys me- first of all to assume we can predict the Maths needed for the current generation’s future is optimistic when you look back over the past 30 years, but also it implies we should be teaching only algorithms & tricks. Should we be getting pupils to relentlessly memorise and practise the formula “A=P(1+R/100)^n” that many textbooks put in place for finding the amount in a Bank account under compound interest?

Instead if a pupil is well taught how percentage interest works, they can calculate the same total without ever needing any formula, to say nothing of being able to transfer this understanding to similar but non-identical problems, financial or otherwise.

The issue being raised this time is subtly different. One reported implication is that pupils are dropping Maths because of this perceived break with reality and that we can court pupils back if we show them the subject’s transferability by way of the questions we ask them. I suspect, however, that Prof Gower’s original point is that if we are to keep pupils in the study of Maths beyond GCSE, then we need to find ways of developing their open problem solving skills if the established mathematical approaches have not already worked. The open problems posed for consideration he suggests are lovely ones but I wonder which pupils would welcome this style of question under exam conditions? When I showed this material to my bottom set Fifth form groups, they were interested in the problems, but worried about how they’d be assessed.

When I ask prospective pupils who wish to join us in the Sixth form (as well as their contemporaries at King’s), the question “Why do you like Maths?”, by far the most common answer is a variation of “because I enjoy getting it right”.

It is important to note that the techniques Prof Gowers advocates are terrific and valuable and should definitely appear in our teaching. Indeed last week one member of the Maths dept was sharing how they had introduced Hypothesis Testing by having pupils suggest an optimal algorithm for testing practical data against a theoretical model. In doing this the pupils come up with a query over a proposed alternative which neither he, nor I could immediately answer- scary but exciting for all concerned. Transferring this style of learning into exams, however, is risky and the sort of pupil who likes maths but is not excited by any theoretical element could well be freaked out by the lack of structure offered by these problems.

We need to avoid putting the cart before the horse- open problem solving is a crucial skill which we need to develop but should be trying to do so in the lessons. It should be present in an exam, but not make it up entirely. Exams are where pupils show both how good they are at problem solving and also, crucially, which of the key techniques needed for later in their careers (frequently university) they have retained for future use.

The key issue is the abstract nature of Maths. Always finding a practical angle removes some of the joy of playing with questions where uses and solutions are not immediately apparent and undermines the trust that for some topics, these will be revealed ultimately by the Maths teacher, in whom pupils need to have faith. One pupil (in the same U6 Maths class) was asking this week about wider uses of Calculus other than rates of change. Knowing that the reveal of how we get the volume of a sphere to be 4/3 pi r³ is just a few weeks away I replied that he’d have to be patient- an answer he seemed content with.

How could we introduce complex numbers if we had to lead with applications to “real life” when they don’t even exist in the “real” world? [Alert- Maths heavy sentence imminent] All pupils who learn this inherently weird but most beautiful of topics have to trust that it has uses somewhere along the line, but it is only having studied them up FP2 level that you can show how they can be used to solve second order Differential equations whose Auxiliary equations have imaginary roots. Moments like this (solving a “real life” equation but using formulae that apply to numbers that don’t even physically exist), where seemingly disparate corners of Maths suddenly click into each other, make for the most exciting lessons and are not possible if we’re always putting the practical uses of all new Maths front and centre.

Ultimately if all exam questions are wide, open & problem based, we run the risk of isolating and terrifying those who struggle with that familiar feeling in Maths where you haven’t made it to an answer and are not sure what to do next. There was an amusing, if frustrating, article in the Times last Friday which quoted a study by the University of Chicago that had found “evidence” that equated this fear of Maths to that of physical torture (although, ironically, it quoted a sample size of 14 people who had identified themselves as haters of Maths- i.e. rubbish Maths used to rubbish Maths).

Anyone who works with Maths at any level (including teachers) knows this feeling well- the dropping of the stomach and discomfort/irritation/panic at realising that you can’t immediately see the full picture and don’t know exactly what to do next. This is also often why the “What is this for?” question appears in classes- in a frustrated bid to defeat the question morally if not intellectually. The chance to help pupils master this sensation is fundamental to the teaching of Maths, whilst also underlining the subject’s importance.

Forget finding the formulae for success in modern life- getting pupils to understand that having and mastering this feeling is not only normal but necessary in the learning of Maths is what we need to prioritise.

When presented with a problem outside of the classroom, there are rarely a set of memorised steps for any of us to safely follow when we walk in the “Real World”.

Following on from the Headmaster’s blog (http://www.kingschester.co.uk/news/1524/131/Maths-in-Japan) on Maths teaching in Japan, Alex Bellos’ page on this is also worth a look, especially the first video clip on this link: (http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/oct/29/mathematics?CMP=twt_gu ).

Rote learning in Maths can be dangerous.

The video clip in the above link  shows pupils who have learned abacus-based techniques so that they can process mental arithmetic at terrifying rates, but to what end? Can that skill be used elsewhere? If rote learning means cramming for short term gain, then there is little use for it in a Maths classroom but conversely it is always desirable for some skills to be drilled so that they ultimately come instinctively to a pupil when tackling deeper problems. This could relate to basic arithmetic and estimation in lower years but also applies to methods of calculus in the sixth form, and at times we as Maths teachers do have to ask pupils to repeatedly practice and learn some key techniques.  When these lessons come around (rarely but regularly) I call them “Karate Kid” lessons, where a sufficient amount of time is spent waxing on & off, but the long term instinctive skills are absorbed. This is the main issue I hear from universities- that a pupil starting a Physics course has forgotten how to integrate by substitution when they arrive and are hamstrung from the start. There are always skills that we need pupils to retain as they move upwards through their levels of holistic Mathematical understanding and the proposed move back to a 2 year A Level course, when all material has to be retained for two 3 hour exams at the end of Upper Sixth would solve much of this problem.

Our problem is that rote learning, however, is how some pupils want to see Maths. When talking discussing with an Upper Sixth set the idea that Maths can be seen as “Hard”, one pupil agreed adding “It definitely isn’t an easy subject like…” and cheekily named a couple of other departments (whose names I won’t repeat!). If we have a national system where knowledge is needed only for exam purposes, is it any wonder that many find Maths such a challenge? The issue is a modularised educational culture that encourages pupils to sit exams but then forget what they have learned. For Maths, where knowledge builds vertically, this is a disaster and it is this issue that universities tell me is the bigger problem with A Level Maths - new pupils having crammed for their A2s have forgotten many techniques and, worse, only had a grasp on the sort of common question the exam board regularly asked. This is what we aim to address in our lessons at Kings’ – to build the knowledge first and then ultimately fit it to the test. Indeed, the other question I dread in the sixth form is “will this be on the exam?”

The attendance and interest in our series of Sixth Form lectures & Maths challenges show that the majority of our Mathematicians are not purely in it for the grade.

The posters are up & the first lecture has already been met with high praise and 50 in attendance!

See here for more…

http://www.kingschester.co.uk/news/1510/96/Former-pupil-Rob-Eastaway-gives-inspiring-lecture-to-Sixth-Formers

Now that the dust has settled on the start of term, we’re all back in the swing of things in the Maths dept.

Our shiny new office seems to be generating a few stares of admiration & we have warmly welcomed Mr Kersten from New Zealand, whose accent appears to be a match for mine in incomprehensibility.

There is much to look forward to this term, with visits from James Grime & an Enigma machine as well as old King’s Scholar Rob Eastaway, our most prominent Mathematician. They will lead the popular VI from Maths lectures, which will begin after Half Term.

For pupils, we’ll be posting more resources on this website in the coming days including material to help you prepare for the first set of tests.

With Maths challenges, team competitions & the event that is The Maths Factor all to come, it priomises to be an exciting year.

NAS