Towards an effective national structure for teacher preparation and support in mathematics


A new paper at The De Morgan Gazette:

A. D. Gardiner, Towards an effective national structure for teacher preparation and support in mathematics, The De Morgan Gazette 10 no. 1 (2018), 1-10.


The fragmented, learn-on-the-job English model for ITE is not working.
About this there is little dispute.  We analyse why such a system cannot 
possibly work for mathematics teaching.  We also suggest the need for an improved national framework for teacher preparation and development, based on a limited number of specialist centres, which accumulate expertise over time, and through which planned programmes might be effectively  delivered.

The teacher labour market in England: shortages, subject expertise and incentives

This Report from Education Policy Institute made news today: BBC, The Guardian, The Independent. PDF File.

Some of key findings (edited with focus on mathematics):

Teacher shortages and other pressures

  • Pupil numbers have risen by around 10 % since 2010 – while teacher numbers have remained steady. This means that pupil-to-teacher ratios have risen from around 15.5 in 2010 to nearly 17 by 2018.
  • Teacher training applications are down by 5%, while training targets have been persistently missed in maths and science.
  • Exit rates have also increased, and are particularly high early on in teachers’ careers. Only 60% of teachers remained in state-funded schools five years after starting.  For ‘high-priority’ subjects like physics and maths, this 5-year retention drops to just 50%.
  • Teacher pay has declined by about 10 % in real-terms since 2010 – but the recent announcement of pay rises of up to 3.5 % from September 2018 will halt this real-terms decline.
  • With many able to earn more outside of teaching, England faces a great challenge recruiting new graduates. In maths, average graduate salaries are £4,000 above those of teachers.

Highly-qualified teachers: variations by subject

Levels of teacher quality in secondary schools vary considerably depending on the subject:

  • Maths and most science subjects in particular struggle to attract highly-qualified teachers – with as little as half of teachers holding a relevant degree. Under 50% hold a relevant degree in maths and physics. These subjects, with the lowest proportion of highly-qualified teachers, are also those with the greatest recruitment and retention problems. […]

Highly-qualified teachers: London and the rest of England

There are stark differences in how highly-qualified teachers are represented in the most, and least deprived schools in England (at KS4). The socio-economic gap is much greater outside of London:

  • In areas outside of London, just over a third (37%) of maths teachers […] in the poorest schools had a relevant degree. In more affluent schools outside of London, the proportions are far higher for maths (51%) and chemistry (68%). […]

In London, differences in how highly-qualified teachers are represented are far smaller:

  • In maths, the proportion of teachers with a degree ranges between 40-50% for all schools, regardless of deprivation level […]

Tackling teacher shortages: introduce financial incentives

  • There is strong evidence that providing salary supplements to teachers in some subjects would alleviate shortages – such as in maths and science.
  • Schools in England are able to make such payments already – however, they would have to be drawn from existing budgets, which would present financial challenges.
  • The government should therefore consider a national salary supplement scheme, centrally funded and directed by the Department for Education.
  • Bonus payments of £5,000 for maths teachers are currently being trialled – yet this programme is limited in scope, and the pilot process may be lengthy. It also fails to target many local authorities that are the most in need of highly-qualified teachers.
  • Given the scale and severity of shortages in the teacher labour market, and the known links between teacher quality and pupil outcomes, the government should introduce salary supplements in hard-to-staff areas and subjects without delay.

A degree of uncertainty: an investigation into grade inflation in universities

“Universities are essentially massaging the figures”: this assessment  by an unnamed expert is quoted in the short on-line version of the report A degree of uncertainty: an investigation into grade inflation in universities from Reform, a UK think-tank. A fuller quote:

There is considerable evidence to suggest that ‘degree algorithms’ (which translate the marks achieved by students during their degree into a final classification) are contributing to grade inflation. Approximately half of universities have changed their degree algorithms in the last five years “to ensure that they do not disadvantage students in comparison with those in similar institutions”. Research has also identified serious concerns about how these algorithms treat ‘borderline’ cases where a student’s overall mark is close to the boundary of a better degree classification. One expert concluded that “universities are essentially massaging the figures, they are changing the algorithms and putting borderline candidates north of the border”.

The story was picked by the mass media: The Times, BBC

E-Assessment in Mathematical Sciences (EAMS)

Registration is open for the international conference on E-Assessment in Mathematical Sciences (EAMS), a three-day academic conference organised by Newcastle University, taking place 28th – 30th August 2018.
The call for talk and workshop proposals closes on 31st May. If you have some research or an innovative technique related to mathematical e-assessment that you would like to present, EAMS 2018 is the perfect venue.
Building on the success of EAMS 2016, the conference aims to bring together researchers and practitioners with an interest in e-assessment for mathematics and the sciences, with an emphasis on enabling attendees to have a go at creating material, and getting an opportunity to share expertise directly. It will consist of a mix of presentations of new techniques, and pedagogic research, as well as live demos and workshops where you can get hands-on with leading e-assessment software.
The conference will feature keynote talks from Mohamad Jebara, founder and CEO of MathSpace and Paul Milner, development manager at National Numeracy.
The conference fee is only £75 and includes a conference dinner. You can find out more about EAMS, and the forms to register for the conference and propose a talk, at the conference website (
We hope that EAMS 2018 will be an inclusive conference environment that invites participation from people of all races, ethnicities, genders, ages, abilities, religions, and sexual orientations. We’re actively seeking to increase the diversity of our attendees and speakers through our call for talk proposals and other conference communication.
Please consider helping us in our goal in creating a more diverse conference through any of the following actions:
– Recommend appropriate speakers to us by contacting any of the session organisers, or at
– Forward our call for proposals to colleagues or potential speakers, with the message that we are looking for a diverse programme of speakers.
– Suggest ways that the conference experience can be more welcoming and inclusive.
– Share your ideas and best practices with us.

Evaluating students’ evaluations of professors

This paper contains some bizarre observations:

Michela Braga, Marco Paccagnella, Michele Pellizzari, Evaluating students’ evaluations of professors. Economics of Education Review 41 (214) 71-88.
Abstract: This paper contrasts measures of teacher effectiveness with the students’ evaluations for the same teachers using administrative data from Bocconi University. The effectiveness measures are estimated by comparing the performance in follow-on coursework of students who are randomly assigned to teachers. We find that teacher quality matters
substantially and that our measure of effectiveness is negatively correlated with the students’ evaluations of professors. A simple theory rationalizes this result under the assumption that students evaluate professors based on their realized utility, an assumption that is supported by additional evidence that the evaluations respond to
meteorological conditions.

Meta-analysis of faculty’s teaching effectiveness: Student evaluation of teaching ratings and student learning are not related

An interesting paper:

Bob Uttl, Carmela A.White, Daniela Wong Gonzalez, Meta-analysis of faculty’s teaching effectiveness:  Student evaluation of teaching ratings and student learning are not related. Studies in Educational Evaluation, Volume 54, September 2017, Pages 22-42.

Abstract: Student evaluation of teaching (SET) ratings are used to evaluate faculty’s teaching effectiveness based on a widespread belief that students learn more from highly rated professors. The key evidence cited in support of this belief are meta-analyses of multisection studies showing small-to-moderate correlations between SET ratings and student achievement (e.g., Cohen, 1980, 1981; Feldman, 1989). We re-analyzed previously published meta-analyses of the multisection studies and found that their findings were an artifact of small sample sized studies and publication bias. Whereas the small sample sized studies showed large and moderate correlation, the large sample sized studies showed no or only minimal correlation between SET ratings and learning. Our up-to-date meta-analysis of all multisection studies revealed no significant correlations between the SET ratings and learning. These findings suggest that institutions focused on student learning and career success may want to abandon SET ratings as a measure of faculty’s teaching effectiveness.

The epigraph is great:

For every complex problem there is an answer that is clear, simple, and wrong.” H. L. Mencken

title = "Meta-analysis of faculty's teaching effectiveness: Student evaluation of teaching ratings and student learning are not related",
journal = "Studies in Educational Evaluation",
volume = "54",
number = "",
pages = "22 - 42",
year = "2017",
note = "Evaluation of teaching: Challenges and promises",
issn = "0191-491X",
doi = "",
url = "",
author = "Bob Uttl and Carmela A. White and Daniela Wong Gonzalez",
keywords = "Meta-analysis of student evaluation of teaching",
keywords = "Multisection studies",
keywords = "Validity",
keywords = "Teaching effectiveness",
keywords = "Evaluation of faculty",
keywords = "SET and learning correlations"

Theorem proving components for educational software

Call for Extended Abstracts & Demonstrations (2nd)
– – – – – – – – – –  – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
Theorem proving components for Educational software
6 August 2017
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
at CADE26
International Conference on Automated Deduction
6-11 August 2017
Gothenburg, Sweden
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

THedu’17 Scope:

Computer Theorem Proving is becoming a paradigm as well as a technological base for a new generation of educational software in science, technology, engineering and mathematics. The workshop brings together experts in automated deduction with experts in education in order to further clarify the shape of the new software generation and
to discuss existing systems.

Invited Talk

Francisco Botana, University of Vigo, Spain, “Theorem Proving   Components in GeoGebra”

Important Dates

  • Extended Abstracts: 18 June 2017
  • Author Notification: 2 July 2017
  • Final Version: 16 July 2017
  • Workshop Day: 6 August 2017

Topics of interest include:

  • methods of automated deduction applied to checking students’ input;
  • methods of automated deduction applied to prove post-conditions for particular problem solutions;
  • combinations of deduction and computation enabling systems to  propose next steps;
  • automated provers specific for dynamic geometry systems;
  • proof and proving in mathematics education.


We welcome submission of extended abstracts and demonstration proposals presenting original unpublished work which is not been submitted for publication elsewhere.

All accepted extended abstracts and demonstrations will be presented at the workshop. The extended abstracts will be made available online.

Extended abstracts and demonstration proposals should be submitted via easychair,
formatted according to

Extended abstracts and demonstration proposals should be approximately 5 pages in length and are to be submitted in PDF format.

At least one author of each accepted extended abstract/demonstration proposal is expected to attend THedu’17 and presents his/her extended abstract/demonstration.

Program Committee

Francisco Botana, University of Vigo at Pontevedra, Spain
Roman Hašek, University of South Bohemia, Czech Republic
Filip Maric, University of Belgrade, Serbia
Walther Neuper, Graz University of Technology, Austria (co-chair)
Pavel Pech, University of South Bohemia, Czech Republic
Pedro Quaresma, University of Coimbra, Portugal (co-chair)
Vanda Santos, CISUC, Portugal
Wolfgang Schreiner, Johannes Kepler University, Austria
Burkhart Wolff, University Paris-Sud, France


The extended abstracts and system descriptions will be published as a CISUC Technical Report series (ISSN 0874-338X). After presentation at the conference, selected authors will be invited to submit a substantially revised version, extended to 14-20 pages, for
publication by the Electronic Proceedings in Theoretical Computer Science (EPTCS).

Ronnie Brown: from Esquisse d’un Programme by A Grothendieck

I just came across again the following (English translation):
 The demands of university teaching, addressed to students (including
those said to be “advanced”) with a modest (and frequently less than mod-
est) mathematical baggage, led me to a Draconian renewal of the themes
of reflection I proposed to my students, and gradually to myself as well.
It seemed important to me to start from an intuitive baggage common to
everyone,  independent of any technical language used to express it,  and
anterior to any such language
– it turned out that the geometric and topo-
logical intuition of shapes, particularly two-dimensional shapes, formed such
a common ground.
(my emphasis)
It seems to me a good idea, and expressed with AG’s usual mastery of language.

Chinese maths textbooks to be translated for UK schools

The Guardian, 20 March 2017. Some quotes:

British students may soon study mathematics with Chinese textbooks after a “historic” deal between HarperCollins and a Shanghai publishing house in which books will be translated for use in UK schools.


HarperCollins signs ‘historic’ deal with Shanghai publishers amid hopes it will boost British students’ performance.


The textbook deal is part of wider cooperation between the UK and China, and the government hopes to boost British students’ performance in maths, Hughes added.

Most likely, an attempt to introduce Chinese maths textbooks in English schools will lay bare the basic fact still not accepted by policymakers. Quoting the article,

Primary school maths teachers in Shanghai are specialists, who will have spent five years at university studying primary maths teaching. They teach only maths, for perhaps two hours a day, and the rest of the day is spent debriefing, refining and improving lessons. English primary teachers, in contrast, are generalists, teaching all subjects, all of the time.

See the whole article here.