Tony Gardiner: Teaching mathematics at secondary level

A. D. Gardiner, Teaching mathematics at secondary level. The De Morgan Gazette 6 no. 1 (2014), 1-215.

From the Introduction:

This extended essay started out as a modest attempt to offer some supporting structure for teachers struggling to implement a rather unhelpful National Curriculum.  It then grew into a Mathematical manifesto that offers a broad view of secondary mathematics, which should interest both seasoned practitioners and those at the start of their teaching careers.  This is not a DIY manual on How to teach.  Instead we use the official requirements of the new National Curriculum in England as an opportunity:

  • to clarify certain crucial features of elementary mathematics and how it is learned — features which all teachers need to consider before deciding `How to teach’.

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Campaign to change UK immigration practices that deter foreign students

Please sign this petition to the Home Secretary and Minister of
Education https://you.38degrees.org.uk/p/foreignstudents to implement
the House of Lords Science & Technology Report recommendations
http://tinyurl.com/nbqbvca
international_students[1]

When we really need to send the message that international STEM students
will get a warm welcome in the UK, they’re getting the cold shoulder and
they are heading elsewhere. We’ve seen over the last few years how
international student numbers have fallen dramatically. As a result
we’re missing out on the talent and the economic and cultural
contribution that international students bring when they come here to
study, and our competitors are reaping the rewards.

Please sign the petition and ask your friends to sign it. The more
support we can get behind this campaign, the better chance we have of
succeeding.

MY REASON FOR STARTING THIS PETITION
The LMS June newsletter drew my attention to the House of Lords Science
and Technology report (April 2014) http://tinyurl.com/nbqbvca that
recommends a change in immigration practices relating to foreign
students.

This is a campaign of national and international importance, and not just
about a few individuals, but I decided to act because this week some
friends of ours from Chennai met with the unpleasant face of UK
immigration practices, and academic visitors coming to work with us have
had similar experiences. Mandira, age 17, who has permanent residency in
the UK, and was on her way to the UK to do a 2 week course for High
School students in Cambridge that starts this week, was turned back and
put on a plane back to India because she has not been in the UK for 2
years. She was with her mother and younger sister, and they also planned
to visit some other universities because Mandira wants to apply to UK
universities to study medicine starting in September 2015. This was
probably a mistake on the part of some officious individual but
never-the-less it is typical.

Can you also take a moment to share the petition with others? It’s
really easy – all you need to do is forward this email or share this link
on Facebook or Twitter: https://you.38degrees.org.uk/p/foreignstudents

Thank you! Toni

Toni Beardon OBE Retired from University of Cambridge NRICH/MMP
http://mmp.maths.org
& African Institute for Mathematical Sciences Schools Enrichment Centre
(AIMSSEC) http://aimssec.aims.ac.za

Programmes of study for Mathematics at Key Stage 4

Programmes of study for  Mathematics at Key Stage 4, which will be taught in schools from September 2015 alongside the new English and mathematics GCSEs, are published today. This appears to be the final pack of statutory documents:

Can you pass the maths test for 11-year-olds?

A sample KS2 test based on the official publication from Standards and Testing Agency,
2016 key stage 2 mathematics test: sample questions, mark scheme and commentary,
was published in The Telegraph. One question attracts attention. In The Telegraph version, it is

A question as published in The Telegraph.

The answer given is £12,396.

And this is the original question from 2016 key stage 2 mathematics test: sample questions, mark scheme and commentary

The official version of the same question

In my opinion, both versions contain serious didactic errors. Would the readers agree with me?

And here are official marking guidelines:

Official marking guidelines

And the official commentary:

In year 6 pupils are expected to interpret and solve problems using pie charts. In this question pupils can use a number of strategies including using angle facts or using fractions to complete the proportional reasoning required.
Pupils are expected to use known facts and procedures to solve this more complex problem. There are a small number of numeric steps but there is a demand associated with interpretation of data (or using spatial knowledge). The response strategy requires pupils to organise their method.

Mathematics after 16: the state of play, challenges and ways ahead

On Wednesday 02 July the Nuffield Foundation published report Mathematics after 16: the state of play, challenges and ways ahead. It argues that reforms to GCSEs and A levels risk undermining the government’s goal of universal participation in post-16 mathematics education, particularly if new ‘Core Maths’ qualifications are not backed by universities. The report brings together a wide range of evidence and warns that plans to make GCSE Maths more demanding, detach AS from A levels, and replace the modular structure in favour of terminal exams could actually discourage students from continuing to study the subject beyond the age of 16.

The report is available to download from the Nuffield Foundation website.

The Math Myth

D. Edwards,   The Math Myth, The De Morgan Gazette 5 no. 3 (2014), 19-21.

Abstract

I’ve been concerned with what skills those who are working as scientists and engineers actually use. I find that the vast majority of scientists, engineers and actuaries only use Excel and eighth grade level mathematics. This suggests that most jobs that currently require advanced technical degrees are using that requirement simply as a fi lter.

[A version of this text appeared in the August, 2010 issue of The Notices of The American Mathematical Society.]

Challenges for UK mathematical scientists in HE

This invitation for a dialogue is written by Professor Ken Brown, Vice-president of the LMS and  is published on the  LMS Members Blog.

Some current developments in UK Higher Education Institutions raise serious concerns for mathematicians. The issues involve complex changes in the relationships between career development, the impact agenda, and external funding. While many of these changes affect academics in other fields, I will concentrate here on their particular effects on those working in the mathematical sciences. These effects are, broadly speaking, of two sorts: changes in our working conditions as individual mathematical scientists, and changes in the overall structure of academic mathematical science in the UK. Here are some examples of the sort of thing I have in mind: the first 6 predominantly concern individuals, at least initially, while the remainder are more structural.

  1. award of sabbatical leave only to those winning Research Council (RC) grants;
  2. allocation of PhD students only to those winning RC grants;
  3. supervision of research student(s) a necessary condition for promotion;
  4. substantial external research income a necessary condition for promotion;
  5. move to “tenured” status dependent on winning external income and/or PhD supervision;
  6. non-submission of an individual’s outputs to the REF, despite availability of a full set of internationally-published outputs;
  7. departmental decisions on number of outputs submitted to the REF influenced by the number of sufficiently strong Impact Statements;
  8. decisions on research fields to support or appointments to make dependent on likelihood of future Impact Statements being generated;
  9. loss of service teaching leading to reduced student FTE numbers and reductions in staffing.

The purpose here is not to provide a detailed analysis of each of the above issues—rather, I want to open a dialogue, letting others develop topics which they feel are of particular concern, whether from the above list or not. Instead, I’ll simply comment briefly below on a couple of the points.

Of course, not everyone will think that each of these developments is by definition “a bad thing”. Regarding point 8, for instance, areas of research focus and consequently of appointments must change over time if our subject is to remain vital. The increased focus on Impact in the UK is part of a world-wide trend which we as mathematical scientists cannot and should not try to oppose—rather we must continue with and redouble our efforts to make funders’ definitions of and ways of measuring impact more in tune with the full range of our activities. We must also continue to emphasise the huge long-term impact of the mathematical sciences, as catalogued for example in the Deloitte report; and we should develop a portfolio of examples of the profound influence of the mathematical sciences on all aspects of our lives—one excellent example is the USA’s National Research Council report “The Mathematical Sciences in 2025”. (This is available as a free download at http://www.nap.edu/catalog.php?record_id=15269.)

On point 4, we all know that RC grant income in the mathematical sciences is very low compared to many other STEM subjects. This is in part because the main costs of much of most of the research in the mathematical sciences has been for people and for time, costs which, though very significant, have in the past been adequately covered for many of us in the UK by the dual support system of funding.  Perhaps also it is the case that what we do has historically been undervalued, thanks to long lag times for impact, but also—let’s be honest—thanks to our sometimes relaxed attitude in the past to the need to make the case for more funding. The LMS, both on its own and in conjunction with the Council for the Mathematical Sciences, has been working hard to make these cases and to assemble relevant data, for grant income and more broadly: for example, the Deloitte report, produced with CMS backing last year, has generated a lot of publicity, and the LMS is producing data documents on UK HEI staffing in the mathematical sciences (November 2013 http://www.lms.ac.uk/policy/statistics-mathematics), and on UK research funding in the mathematical sciences (to be published July 2014).  A CMS report on the “people pipeline” in the mathematical sciences will come out later this year.

I should also briefly explain what I have in mind with the point 5. At least two Russell Group universities have recently introduced contracts for newly-appointed lecturers, which lead the appointee through a career path set up to complete probation in 2-3 years, with an expectation of promotion to Senior Lecturer or Reader (possibly called something different),  within 5-7 years of initial appointment. All to the good, you might think—except that milestones expected to be passed en route to promotion include winning substantial RC grant income, and supervising a PhD student to completion. The consequences of failing to achieve these targets in the specified time frame are left unclear.

So, why am I writing this article? The first and very important reason is to gather information. At the moment our community has no way of knowing how widespread are these and similar changes. Those of us directly affected can feel isolated, powerless and undervalued. I’m therefore inviting two sorts of response. First, I will very much welcome information about particular cases along the lines of those listed above. It will be equally valuable to learn of examples of good practice with regard to these issues. Naturally, I’ll treat all such communications in the utmost confidence, but will hope to share what global data I can gather, in due course. More generally, it will be good to hear other views on the issues raised here: perhaps, for example, some of these changes should be welcomed? Most importantly, we need to consider what we as a community should be doing in the face of these developments. What should the LMS be doing?

Comments can be placed at the blog, sent to newsletter@lms.ac.uk for inclusion in the Newsletter, or, in the case of more confidential material, sent to me atKen.Brown@glasgow.ac.uk.

Ken Brown

Vice President, LMS

Consultation on Key Stage 4 mathematics

The government response to consultation for key stage 4 English and mathematics on December 2nd 2013 can be found here; pdf.

DfE are now consulting on the draft Order and Regulations that will give effect to the new programmes of study for English and mathematics at key stage 4 from September 2015 and to extend the disapplication of the key stage 4 science programme of study for a further school year (2015/16).