I just read the recent ACME consultation paper on the question of the Use of Maths A-Level and think that a 2-pathway approach would be appropriate, which ensures that  Maths – like English – continue to be compulsory at least at “(school) foundation level”, with 2 hours per week over two years.   The time of 2 years is far too short and precious, in my view, to play with any further refinement of pathways for those who may need mathematics in their future professions. Having to make a choice between such pathways would be premature for most students at age 16 anyway.

By the way, a two-tier system with a basic and an advanced maths course for the two or three years before Abitur has worked well in Germany’s high schools for many years.

My personal criticism of the ways in which school mathematics is treated goes deeper: Rather than being concerned with introducing more refined provision, one should give up the fixation on league tables and the life lie that wants to make us believe in the ever-increasing quality of A-level performance (and the ever-increasing intelligence levels of the population that one might need to assume to explain this phenomenon). League table pressures have led to a situation where many schools drill their students to pass exams (“jump hoops”) rather than help them understand mathematics. One should instead focus on ways to convey to students the experience that maths is something that one CAN in fact understand.

For many years (in my case 14 since I started working at a UK university) we have seen increasing numbers of first-years who have only learned to mechanically perform pre-formatted and long-rehearsed tasks without really knowing the what and why. Very often student feedback reflects the expectation that we should continue to treat them that way.  As a colleague’s anecdote has it: challenged by students, he told them that he had to set them some unseen exam questions to test whether they were able to apply what they had learned and think for themselves to solve a problem; the students replied: if you had taught us properly in the first place, we would not need to think.

It seems to me that often it takes the students and us almost into their 3rd year of study before that mind-set has been broken and they do actually start to think on their feet. I would like to dream that one day a school system has been put in place with teachers able and allowed to induce the students to enjoy doing and understanding maths. When my youngest daughter started her final two years of high school in Canada after her GCSE in the UK, she came home one day saying excitedly how thrilled she was that one could actually understand subjects like maths and physics!

That the opposite seems to happen more is evident from anecdotes such as the above or this one: having learned that besides sin(x) and sinh(x) there are also functions cos(x) and cosh(x), some students have in fact concluded that besides sign(x) there also has to be a function called cogs(x).  This is not a joke, nor an isolated instance. It shows what kind of thinking may develop in schools and is brought into universities, on the strength of good enough grades in A-level maths. When my daughter was exposed to trig functions in year 9 the first time, she was just instructed to perform calculations on her calculator. When she asked her teacher what this “sin(x)” meant, the teacher said it would take too long to explain, this would come in a later year.

So, I’d rather wish to see the real issues being addressed instead of being contented with the chimera of ever improving A-level statistics. Introducing a “vocational” maths pathway is not the answer; managing three different maths streams is bound to cause excessive administrative burdens on teachers and schools and takes away even more the ability of teachers to focus on their job.

Results of elections to contested posts in the LMSCouncil as announced at today’s AGM:

General Secretary: Hyland

Education Secretary: Budd

Members-at-Large:

Barrow-Green

Donaldson

Laptev

Segal

Totaro

Wilson

Chandler-Wilde

Nominating Committee:

Etheridge

Liebeck

With all the business concerning the proposed merger and the events that  followed its rejection by the Society members, I was amazed by the lack of information provided to the members through the Society official channels, the LMS website and the Newsletter. There was a clear impression of an internal censorship. Information have been appearing in homoeopathic doses;  till now, all the “official” announcements on the website have been cryptic and often had an obvious bias. (For example, what have appeared about the Council meeting in August where the nomination of the President-Designate was confirmed — and some officers resigned “as a consequence of this”.) I had lived a substantial part of my life under the Soviet communist regime. At those days, I, as well as many my compatriots, had learned how to read the official reports about the Politburo meetings published by Pravda and then republished word by word by all other newspapers, and similar party texts. It was a certain art to look through those lines composed by an anonymous trusted high-ranking party journalist (and thoroughly checked by several people before it could appear in press) and to figure out what was happening in reality. Everything mattered: the order of words, the very vocabulary used (sometimes the appearance of a new word might be a sign of a new campaign), how precisely the names of party bosses were quoted there, and so on.  Unfortunately, I had to apply that art again for reading the recent LMS announcements. I do not think it is healthy. The new LMS Council should change the situation completely. It is a learned society, not a business corporation. Openness is essential. To avoid turning the London Mathematical Society into something totally alien to its goals and dominated by the managerial (or “inner party”) spirit, was, I think, the main motivation for many who voted against the merger. The merger is dead; but we have to think about the future. The elections on the 20th November may be crucial from this viewpoint. After the elections, with the new Council, we want back the spirit of the society of mathematicians. Small grants, good publications, work mainly done by officers on a volunteer basis, openness, discussions, — yes; “lobbying”, spending money on bureaucracy, handling matters in secrecy, promoting the “party line”, and similar things, — thank you very much, no.

Ted Voronov

P.S. On a slightly different but related topic. There has been an apparent fall in standards in the recent time. I did not receive the October issue of the Newsletter with the voting papers. Initially I thought I have lost it myself, mysteriously, so it was my own fault; but then I have learned that one or possibly two of my colleagus did not receive that issue with the electoral papers either. Eventually I have obtained the ballot papers after I requested them from the secretary. Now, differently from the past, there is just a single small envelope for putting the ballot paper, on which we are supposed to write the name “in block capitals” and sign it. Before, there was a large second external envelope. It is just a detail, but it has probably played a role. Actually, it would be a good idea for the future to ask the Electoral Reform Services to help us to establish a secure and simple electronic voting system to avoid all this hassle with the paper ballots.

An open letter to Research Councils UK  [From Donald W. Braben, University College London; John F. Allen, Queen Mary, University of London; William Amos, University of Cambridge; and 45 others in a personal capacity, including ten Nobel laureates; Full list] (Times Higher Education, 5 November 2009).

The research councils have decided that research proposals should include details of their “potential economic impact”, a term that they stress embraces all the ways in which research-related knowledge and skills could benefit individuals, organisations and nations.

Peer reviewers will be asked to consider whether plans to increase impact are appropriate and justified, given the nature of the proposals. However, academic researchers are primarily responsible for the impartial pursuit of knowledge. Richard Haldane acknowledged this many years ago, and the application of his famous principle, by which governments did not interfere in scientific policymaking, was spectacularly successful for decades.

Science is global, of course, and until relatively recently policies of non-interference flourished everywhere. The result was an abundance of unpredicted transformational discoveries, including the structure of DNA, the genetic code, the laser and magnetic resonance imaging, almost all of which came from pure research. These discoveries also stimulated unprecedented economic growth.

Chris Budd’s post suggests that the LMS lost its independence in the way its policy responses are presented. There is still no explanation to the “Use of Maths A-level” debacle, when a joint LMS-IMA press release of 10 July 2009 prepared by the MPU (Mathematics Promotion Unit) clearly contradicted the position of the LMS Education Committee. It was as though MPU (which is 80% financed and housed by the LMS) operated as a de-facto agency for an outside body, ACME, Advisory Committee On Mathematics Education.

This is part of a more general pattern: over the last few years, a plethora of organisations were created, mostly for lobbying purposes on behalf of mathematics. The LMS financially supports some of them, sometimes to a considerable extent, but appears to have no influence over their output.

As Another Anonymous asked on this Blog in respect of the REF “impact” proposals,

“How about the LMS’s own response as a professional society?”

My answer to Another Anonymous: Council have delegated responsibility to an outside body, CMS (Council for Mathematical Sciences), to provide the final response to the consultation. No time has been set aside for Council to discuss the matter collectively. A committee of two has been constituted to discuss the response with the LMS Research Policy Committee, but as far as is known there is no plan to seek the LMS Council approval before the deadline of December 16.

This is an abnormal situation, and it has to be corrected. While working to speak with others where possible and contributing to preparation of responses of outside bodies and co-operating with them, the LMS should retain its own voice, widely publicise its own policy responses and base them on a wide consultation with the LMS members.

Following the recent posting by Tony Gardiner, I am happy to try to summarise some of the issues related to the proposed Use of Maths A2 A-level (some of which were covered in my earlier posting).

It is important to consider the overall context of the Use of Maths A-level. Most importantly, it is not a replacement for the usual Maths and Further Maths A-levels, and the LMS continues to support these latter qualifications and the need to make them challenging for the students that take them and to prepare such students to take mathematically rich degrees at HE. Returning to Use of Maths. Since its publication in 2004, the LMS has broadly supported the conclusions of the Smith Report ‘Making Maths Count’ into post-14 maths teaching. One of the conclusions of this report was that too many students stop studying mathematics post-16. This is potentially bad both for them and for the future health of UK science and technology. A recommendation of the Smith Report was that there should be different ‘Pathways’ for students studying maths post-16 (of which the ‘first pathway’ would be ‘traditional’ Maths and Further Maths A-levels) so that students of different levels of mathematical attainment could study a mathematics course up to the age of 18 which is best suited to their needs and abilities. The LMS Education Committee has supported this approach, whilst being very mindful of the resourcing issues that are involved.  The Use of Mathematics (current AS and proposed A2) qualifications have been considered as a possible ’second pathway’ for students who want to do a good amount of mathematics post-16, but who would not be going on to do a degree with a high mathematical content.  The Education Committee recognises the potential advantages of doing this, but is also concerned about the potential dangers in that (i) teaching a full A-level in Use of Maths  could lead to a reduction in the resources available for teaching the traditional Maths and Further Maths A level courses and (ii) students might take Use of Mathematics who instead should be taking a usual maths A-level and this might cause problems to subsequent university entrance. The Education Committee is also concerned that the pilot examination papers for the A2 level in Use of Maths were not well designed or challenging.

In a recent outline report to the Joint Mathematics Council (JMC) I have stated the following in response to various questions asked by the JMC. In particular:

1. Which of these positions (Unconditional agreement, Agreement subject to safeguards, Unconditional rejection) does your society hold ?
   “Within the LMS there are varying opinions as to whether the risks of UoM being classed as a full A-level outweigh the benefits, but there is support  for providing  qualifications which lead to fewer students dropping maths at 16. The LMS is in favour of more students doing A level Maths and A level Further Maths and in stretching and challenging the students that do these courses. It also strongly supports all initiatives to get more highly motivated maths teachers into schools so that this can be possible. There is a wide range of views about the Use of Maths.  As such, there is not a simple answer to the various questions that would really reflect the views of the LMS membership.”
2. What sort of safeguards would your society want ?
   “Whilst there are various views within the LMS about the merits of Use of Maths, there is unanimity in the view that if it were to be introduced it should be subject to very strong monitoring so that:
   1. students should only do it if they would otherwise be dropping maths post 16
   2. it should in no way draw students away from doing A level Maths and hence should never be offered unless A level Maths is also being run at the school
   3. great efforts should be made to carefully inform the students taking maths post 16 of the differences between Use of Maths and A level Maths.”
3. Would you like to see more piloting for this or any other reasons?
   “The LMS Education Committee was concerned about the detailed nature of the trial examination papers and hope that if a decision to take UoM forward was agreed that HE (especially those members very experienced in teaching maths and maths modeling service courses) should be closely involved in the design of the new course and papers so they should be better fit for purpose.”

I hope that this gives a useful summary of the current situation regarding Use of Maths. I should say that overall debate about Pathways continues apace. The Advisory Committee for Mathematics Education (ACME) is currently having a consultation into the pathways model to which the LMS has been invited to contribute. I encourage anyone who wishes to contribute to this debate to email me at mascjb@bath.ac.uk.

My own personal (and strong) belief is that many of the concerns about the Use of Maths A-level are secondary to the much bigger concern about a lack of teaching and other resource for teaching mathematics at schools. We can only have good teaching if we have a good number of good teachers. I believe strongly that the LMS should do everything that it can to lobby for more resources to teach maths at schools and that its members should constantly seek ways to support, encourage and develop both current and future maths teachers at all levels.

Kevin Buzzard is probably not alone: one suspects that almost everyone who is going to vote has by now already voted.  So this post should not be seen as “touting for votes”: it is rather an extension of the “communication” theme – a plea for whoever is elected to leave behind the presumptuous era of “Aunty knows best”, and to work to establish renewed contact with members.

• Tim Gowers supported Kevin Buzzard’s plea for some way of giving members a voice.  Edmund Harris elaborated on this issue.
• The current Education Secretary also writes that “it is important that all LMS members have the opportunity to make their views known in the education debate”.  Yet actions speak louder than words: I cannot be alone in finding this assertion hard to square with the experience of recent years.  The “Use of mathematics” debacle suggests a need to rethink not only how different parts of the LMS machine articulate with one another, but how those who speak on behalf of members can make sure that they do not ride roughshod over members’ views (even though the most appropriate response may not exactly reflect many members’ views).
• One gets the impression that over the last five years the LMS Education Committee has been repeatedly sidelined by small, relatively unaccountable “units”.  LMS responses to important consultations which the committee has no doubt laboured over appear to be unavailable.  (In his “manifesto”, the Education Secretary writes: “in recent years the Education Ctee has addressed such issues as the changes to GCSE, Diplomas, post 16 and A-level teaching, enrichment and engagement activities with schools, benchmarking of undergraduate degrees, training of maths lecturers, the issues related to the Bologna agreement and the popularisation of mathematics”.  At the time this was written I could not find any of the detailed responses referred to on the LMS website: the single exception today – which proves the rule – is the response to the A-level consultation, which was submitted many months ago, but which was quietly posted a week ago, presumably in response to unseen pressures.)
  Most public statements on key educational issues seem to originate from such groups as CMS, LMS-IMA, MPU: this would be fine if members could see how these statements articulated with, and reflected the detailed work of the Education Committee.
• On 18 October, “Anon” asked the current Education Secretary if he “could say something about “Use of Mathematics”, which seems to be quite a controversial topic, and on which it seems entirely unclear what the LMS position actually is.”  The resulting silence indicates the awkwardness of the question – and one could be forgiven for guessing that the sudden unannounced appearance of the official submission may be a sop to those who feel unable to answer publicly.
• So I hope that whoever is elected as Education Secretary will (a) use the website to advertise imminent business, and to invite contributions from interested and experienced members; (b) make final submissions publicly available as soon as practicable, and where time allows make draft responses available as widely as possible for comment; (c) insist that statements on educational matters that emerge from other LMS affiliated groups be checked out with, and take due account of the deliberations of the Education Committee.

One of the recurring themes in comments on this blog is the importance of communication, normally in the context of communication between members and the executive. Developments in this area are an essential part of taking the society forward, however we should also be considering communication in a wider setting.

Firstly communication as a whole is a rapidly changing area. In particular the internet is opening up opportunities that simply could not have been dreamt about even a few years ago. When this is mentioned in LMS discussions it is normally with a voice of doom as one of the effects is a potential reduction in money from publishing. Mathematics, however has a lot to gain from embracing this and it would be exciting to see the LMS taking a leading role. There are (at least) three different ways that mathematics communication can benefit:

1. Communication between mathematicians and how mathematics takes place. A great example of this is the polymath projects started by Tim Gowers. These aim (already with success) to actually solve mathematical problems through massive collaboration. Another example is the often brilliant expository writing on wikipedia. This leads me naturally to…
2. Making mathematics accessible. This is not just writing up on wikipedia, but videos on YouTube, photos, fractal art, the list goes on. As a simple example this YouTube video on Mobius transforms has been viewed over 1,500,000 times. Even if a small number of those communicated some understanding that is a significant increase in the number of people who know what a Mobius transform is!
3. Finally the internet allows mathematicians to engage with a wider audience. The classic example here is Terry Tao, on his way to becoming a public intellectual through his blog. The readership is very large, but he certainly does not achieve this by dumbing down. Many of his blog posts are incredibly technical.

As Kevin Buzzard and others have intimated, LMS members really do face important choices.

Life is often turbulent; and the wisest stance is usually to hold on tight to what seemed stable yesterday and to proceed *as if* all were well. However, at some point this strategy is no longer appropriate.

In the matter of the LMS, things may have passed this “tipping point” some time back – even if the precise details are still hard to make out.

Norman Biggs (who was Council General Secretary during the key period 2002-2006) has provided some of the background (on this site). This helps put things in a larger context. However, he eschews close-ups which try to make sense of recent events, and wisely sticks to a salutary “long lens”. He writes: “One of the reasons why I was prepared, over a period of thirty years, to give my time and energy to the LMS was because it was, in many respects, a model of how a learned society should conduct itself. Of course, there were many disagreements, but there were very few occasions when the line was crossed, and fortunately they did not impinge on the core purposes of the Society. The Society´s affairs were run smoothly, by people who respected each other even if they did not always like each other. Latterly there was significant progress towards more open procedures, although the mysterious routine for the choice of President has survived.”

There are evident dangers in trespassing on matters which Norman wisely chose to leave unspoken. Much remains unclear; but there are unmistakeable shadows – even if one cannot be sure which are innocent and which are significant (or in what way).

So what follows is simply a collection of “things it is hard to ignore”.

As has been mentioned several times on this blog, a vitally important issue for the continuing LMS is to decide its priorities for spending its limited financial resources. It is of course easy to say that we want more money spent on grants and less on administration, but how can we actually do that in practice?

Financial rules for charities require that salaries of the highest-paid employees are put in the public domain. From the report available from the LMS website, http://www.lms.ac.uk/policy/annualreports/trustees_08.pdf, page 28, we see that last year the salary of one employee was betwen £80K and £90K, which is more than one-third of the *total* amount spent on grants. I would hazard a guess that it was also considerably more than the salary of most mathematics professors, even in London.

The need to appoint a new Executive Secretary gives the LMS the opportunity to reconsider the amount spent on this post. This is a matter which the new Council should look into. My recollection is that this post was created at a time when the LMS felt it was needed, in order to take some of the burdens off the elected Officers, and Council and Committee members. Perhaps now when the LMS is having to look more carefully at costs, it is time to reconsider the scope of duties of the new Executive Secretary. In particular, the LMS should look at which roles are more appropriately taken by elected members. Some roles might even sensibly be farmed out to volunteers among ourselves, the ordinary LMS members, as is already done with much of the editorial work for LMS publications.

This must be done before a job description for the new Executive Secretary is drawn up. In my opinion it should be possible to draw up a job description which adequately relieves the burden on elected Officers, Council and committee members, and which commands perhaps no more than a Senior Lecturer’s salary.

(Let me make it clear again that I am talking only about the job description for the post when it becomes vacant, not about the incumbent Executive Secretary.)