Mathematics for teachers of mathematics

Featured

A new paper at The De Morgan Gazette:

A. Borovik, Mathematics for teachers of mathematics, The De Morgan Gazette 10 no. 2 (2018), 11-25. bit.ly/2NWECtn

Abstract: 

The paper contains a sketch of a BSc Hons degree programme Mathematics (for
Mathematics Education). It can be seen as a comment on Gardiner (2018) where
he suggests that the current dire state of mathematics education in England cannot
be improved without an improved structure for the preparation and training of
mathematics teachers:

Effective preparation and training requires a limited number of national institutional units, linked as part of a national effort, and subject to central guidance. For recruitment and provision to be efficient and effective, each unit should deal with a significant number of students in each area of specialism (say 20–100). In most systems the initial period of preparation tends to be either

  •  a “degree programme” of 4–5 years (e.g. for primary teachers), with substantial subject-specific elements, or
  • an initial specialist, subject-based degree (of 3+ years), followed by (usually 2 years) of pedagogical and didactical training, with some school experience.

This paper suggests possible content, and didactic principles, of

a new kind of “initial specialist, subject-based degree” designed for intending teachers.

This text is only a proof of concept; most details are omitted; those that are given
demonstrate, I hope, that a new degree would provide a fresh and vibrant approach
to education of future teachers of mathematics.

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

Featured

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. bit.ly/2N9NU7W

Abstract:

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.

UKRI: Accelerating the transition to full and immediate Open Access to scientific publications

Yesterday, 4 September 2018, UKRI announced their

Plan S: Accelerating the transition to full and immediate Open Access to scientific publications

Since the LMS critcally depends on income from publishing, it has serious implications for out Society.

The key principle of the Plan is as follows:

“After 1 January 2020 scientific publications on the results from research funded by public grants provided by national and European research councils and funding bodies, must be published in compliant Open Access Journals or on compliant Open Access Platforms.”

IN ADDITION:

  • Authors retain copyright of their publication with no restrictions. All publications must be published under an open license, preferably the Creative Commons Attribution Licence CC BY. In all cases, the license applied should fulfil the requirements defined by the Berlin Declaration;
  • The Funders will ensure jointly the establishment of robust criteria and requirements for the services that compliant high quality Open Access journals and Open Access platforms must provide;
  • In case such high quality Open Access journals or platforms do not yet exist, the Funders will, in a coordinated way, provide incentives to establish and support them when appropriate; support will also be provided for Open Access infrastructures where necessary;
  • Where applicable, Open Access publication fees are covered by the Funders or universities, not by individual researchers; it is acknowledged that all scientists should be able to publish their work Open Access even if their institutions have limited means;
  • When Open Access publication fees are applied, their funding is standardised and capped (across Europe);
  • The Funders will ask universities, research organisations, and libraries to align their policies and strategies, notably to ensure transparency;
  • The above principles shall apply to all types of scholarly publications, but it is understood that the timeline to achieve Open Access for monographs and books may be longer than 1 January 2020;
  • The importance of open archives and repositories for hosting research outputs is acknowledged because of their long-term archiving function and their potential for editorial innovation;
  • The `hybrid’ model of publishing is not compliant with the above principles;
  • The Funders will monitor compliance and sanction non-compliance.

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 (https://eams.ncl.ac.uk/).
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 eams@ncl.ac.uk
– 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.

Musings of a Mathematical Mom

[Reposted from Alexandra O Fradkin’s blog Musings of a Mathematical Mom; listed in reverse chronological order]

Witnessing the woes of math homework

Highlights of 2017

Discovering the area of a trapezoid

“Math you can play” – books with games

Isometric graph paper and 3D pictures

Fun with pentacubes

Funville Adventures launched!

Counting crocodile legs

Drawing heads, tails, knees, and toes – useful?

Counting beads

Playing Broken Telephone

A figure with pointy things and a line, a line, and a line

Protecting against magic

Skip counting or word skipping?

Numicon – combining geometry and arithmetic

Discussing the meaning of “almost” with an 8 year old

From math-hater to mathematician and computer scientist: The story of Allison Bishop

A number talk that turned into an investigation

Funville Adventures live on Kickstarter!

Logical Fun, Part II

Get ready for Funville Adventures!

Games with the multiplication table

Logical Fun, Part I

Arithmetic games – is that boring?

Playing with symmetry in kindergarten

The joys of peas and toothpicks for all ages!

Math enrichment – what is the value?

3-digit numbers are tricky! Part II

Entertaining kindergartners with caterpillars, dots, and monsters

3-digit numbers are tricky!

Games with tanks and mirror books

Measuring everything in sight!

Functions in Kindergarten – A favorite

Avoid Hard Work! – A book for problem-solvers of all levels (toddler to mathematician)

Lots of fun with Tiny Polka Dot

Conservation of fingers and toes

Dots in a Square from Math Without Words

Double perfect squares

Four colors or more?

The Piaget Phenomenon

Time, symmetry, and unexpected turns

Why not count on our fingers?

Fibonacci Trees

Numbers on a Line

PME 42 in Umeå, Sweden

From Maths-Education mailing list:
Psychology of Mathematics Education (PME) is an annual conference where scientific research in mathematics education is the focus. PME welcomes all who are interested in how students learn mathematics, how teachers teach mathematics, and how mathematicians, teachers and students do mathematics.
PME 42 will be held at Umeå University in Umeå, Sweden, from July 3 to July 8, 2018.
The First Announcement of PME 42 is now available. You can download it from the home page of the conference website: www.pme42.se
The ConfTool system, used for submissions and registrations, will open before the end of November.
For continuous updates about PME 42 you can follow or like the conference Facebook page: www.facebook.com/pme42
Best wishes,
Ewa Bergqvist and Magnus Österholm
Co-chairs for PME 42

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

BiBTeX: 
@article{UTTL201722,
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 = "http://dx.doi.org/10.1016/j.stueduc.2016.08.007",
url = "http://www.sciencedirect.com/science/article/pii/S0191491X16300323",
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"
}