Teacher Preparation: 25 May, De Morgan House, Russell Square

LMS Education Day 2017

Thursday 25th May, 11am – 3pm

De Morgan House, London

Teacher shortages in mathematics: how can HE mathematics departments help reverse the trend?

University mathematics departments depend on teachers to prepare their
own students, and they have an important role in training future generations of mathematics teachers. To do this effectively at a national level, it is critical that colleagues from across the sector understand the current state of Initial Teacher Training and the challenges that face teacher recruitment.

The day will be split into two parts. During the morning, participants will have the opportunity to learn about the challenges of teacher recruitment and find out how a number of maths departments have attempted to encourage students to think of mathematics teaching as a career. We are delighted that Simon Singh has agreed to introduce this session. After lunch, discussion, led by Tony Gardiner, will be focused around a document being developed by the LMS education committee on this subject for which input and feedback is sought. A detailed programme, including information about invited contributors, will follow in the coming weeks.

Whilst the theme for the day may seem somewhat removed from everyday teaching and learning activity within mathematics departments in HE, we do hope to get participants from a large number of mathematics departments to participate in the event and share their experiences and ideas.

The event is free to attend and a light lunch and other refreshments will be provided.

Please register interest in attending the event by emailing

Musings of a Mathematical Mom

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

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

Blind people use brain’s visual cortex to help do maths

From New Scientist, by Colin Barras, September 2016:

“It’s actually hard to think of a situation when you might process numbers through any modality other than vision,” says Shipra Kanjlia at Johns Hopkins University in Baltimore, Maryland.

But blind people can do maths too. To understand how they might compensate for their lack of visual experience, Kanjlia and her colleagues asked 36 volunteers – 17 of whom had been blind at birth – to do simple mental arithmetic inside an fMRI scanner. To level the playing field, the sighted participants wore blindfolds.

We know that a region of the brain called the intraparietal sulcus (IPS) is particularly active when sighted people process numbers, and brain scans revealed that the same area is similarly active in blind people too.

“It’s really surprising,” says Kanjlia. “It turns out brain activity is remarkably similar, at least in terms of classic number processing.”

Read the whole story. Journal reference: PNAS, DOI: 10.1073/pnas.1524982113

From the original research paper:


Human numerical reasoning relies on a cortical network that includes frontal and parietal regions. We asked how the neural basis of numerical reasoning is shaped by experience by comparing congenitally blind and sighted individuals. Participants performed auditory math and language tasks while undergoing fMRI. Both groups activated frontoparietal number regions during the math task, suggesting that some aspects of the neural basis of numerical cognition develop independently of visual experience. However, blind participants additionally recruited early visual cortices that, in sighted populations, perform visual processing. In blindness, these “visual” areas showed sensitivity to mathematical difficulty. These results suggest that experience can radically change the neural basis of numerical thinking. Hence, human cortex has a broad computational capacity early in development.


In humans, the ability to reason about mathematical quantities depends on a frontoparietal network that includes the intraparietal sulcus (IPS). How do nature and nurture give rise to the neurobiology of numerical cognition? We asked how visual experience shapes the neural basis of numerical thinking by studying numerical cognition in congenitally blind individuals. Blind (n = 17) and blindfolded sighted (n = 19) participants solved math equations that varied in difficulty (e.g., 27 − 12 = x vs. 7 − 2 = x), and performed a control sentence comprehension task while undergoing fMRI. Whole-cortex analyses revealed that in both blind and sighted participants, the IPS and dorsolateral prefrontal cortices were more active during the math task than the language task, and activity in the IPS increased parametrically with equation difficulty. Thus, the classic frontoparietal number network is preserved in the total absence of visual experience. However, surprisingly, blind but not sighted individuals additionally recruited a subset of early visual areas during symbolic math calculation. The functional profile of these “visual” regions was identical to that of the IPS in blind but not sighted individuals. Furthermore, in blindness, number-responsive visual cortices exhibited increased functional connectivity with prefrontal and IPS regions that process numbers. We conclude that the frontoparietal number network develops independently of visual experience. In blindness, this number network colonizes parts of deafferented visual cortex. These results suggest that human cortex is highly functionally flexible early in life, and point to frontoparietal input as a mechanism of cross-modal plasticity in blindness.

Tim Gowers: In case you haven’t heard what’s going on in Leicester …

[Reposted from Tim Gowers’ Blog, 15 Sept 2016]

Strangely, this is my second post about Leicester in just a few months, but it’s about something a lot more depressing than the football team’s fairytale winning of the Premier League (but let me quickly offer my congratulations to them for winning their first Champions League match — I won’t offer advice about whether they are worth betting on to win that competition too). News has just filtered through to me that the mathematics department is facing compulsory redundancies.

The structure of the story is wearily familiar after what happened with USS pensions. The authorities declare that there is a financial crisis, and that painful changes are necessary. They offer a consultation. In the consultation their arguments appear to be thoroughly refuted. The refutation is then ignored and the changes go ahead.

Here is a brief summary of the painful changes that are proposed for the Leicester mathematics department. The department has 21 permanent research-active staff. Six of those are to be made redundant. There are also two members of staff who concentrate on teaching. Their number will be increased to three. How will the six be chosen? Basically, almost everyone will be sacked and then invited to reapply for their jobs in a competitive process, and the plan is to get rid of “the lowest performers” at each level of seniority. Those lowest performers will be considered for “redeployment” — which means that the university will make efforts to find them a job of a broadly comparable nature, but doesn’t guarantee to succeed. It’s not clear to me what would count as broadly comparable to doing pure mathematical research.

How is performance defined? It’s based on things like research grants, research outputs, teaching feedback, good citizenship, and “the ongoing and potential for continued career development and trajectory”, whatever that means. In other words, on the typical flawed metrics so beloved of university administrators, together with some subjective opinions that will presumably have to come from the department itself — good luck with offering those without creating enemies for life.

Oh, and another detail is that they want to reduce the number of straight maths courses and promote actuarial science and service teaching in other departments.

There is a consultation period that started in late August and ends on the 30th of September. So the lucky members of the Leicester mathematics faculty have had a whole month to marshall their to-be-ignored arguments against the changes.

It’s important to note that mathematics is not the only department that is facing cuts. But it’s equally important to note that it is being singled out: the university is aiming for cuts of 4.5% on average, and mathematics is being asked to make a cut of more like 20%. One reason for this seems to be that the department didn’t score all that highly in the last REF. It’s a sorry state of affairs for a university that used to boast Sir Michael Atiyah as its chancellor.

I don’t know what can be done to stop this, but at the very least there is a petition you can sign. It would be good to see a lot of signatures, so that Leicester can see how damaging a move like this will be to its reputation.

The Humanistic Mathematics Network Newsletter

The Humanistic Mathematics Network Newsletter (HMNN) was founded by Alvin White in the summer of 1987. The Newsletter was later renamed The Humanistic Mathematics Network Journal (HMNJ). The last issue of the HMNJ was published in 2004. The open access digital archive of the full run of the HMNN/HMNJ (1987-2004) is now available at http://scholarship.claremont.edu/hmnj/.

This journal does not accept new content. A related current journal is the Journal of Humanistic Mathematics.

Jack Abramsky: MathsWorldUK

I am writing to you, friends and colleagues, in an appeal to boost the number of Friends and donor sponsors of MathsWorldUK.
For those of you who are unfamiliar with MWUK, we are a registered company and a registered charity set up with the long-term aim of establishing in the United Kingdom the first National Exploratorium devoted entirely to mathematics and its applications. We will not be in competition with the Science Museum in London, because our philosophy is radically different from that of the SM. The new Mathematics Gallery (to be named the Winton Gallery) at the Science Museum will open in December. It will be essentially static with about 90 exhibits from the permanent collection of artefacts owned by the museum. Each artefact will be accompanied by a short description of around 90 words about some mathematical idea that the exhibit might exemplify. Our approach will be for fully interactive exhibits designed to illustrate some mathematical idea or mathematical application, with the visitor doing his or own individual exploration of the ideas underpinning each exhibit. So one approach is static, the other is active. The two spaces will complement each other, rather than be in competition with each other. A further fundamental difference is that The Science Museum’s primary function is to present scientific achievement, with mathematics as a small subsidiary of that endeavour, whereas the Exploratorium (note the emphasis on exploration, and hence discovery) will  put mathematics in all its manifestations and applications at the very heart of its activity.
Schools Competition MATRIX:  The top two prizewinning schools

Schools Competition MATRIX: The top two prizewinning schools

You can find out more about MWUk on its website (which will shortly be updated)
We have just hosted an extraordinary and wonderful conference at the University of Leeds called MATRIX with over 100 delegates from 15 countries.  This was the second MATRIX conference; the first was held in Dresden two years ago. MATRIX stands for Mathematics, Awareness, Teaching, Resources and Information eXchange. The conference was for museum folk around the world and others interested in improving public awareness and understanding of mathematics. We co-hosted this conference with the National Museum of Mathematics (MoMath) in New York and the University of Leeds. Full details of the conference are on our website, together with the winning entries for a schools competition that was run for the conference. Attached is a photograph of Hanna Fry with the top two school teams; Hannah gave out the prizes.
There are now over 50 mathematics ‘museums’ around the world with about 10 more due to open in 2017. Germany alone has 10 museums, either dedicated to mathematics or with substantial mathematical galleries. The UK has no such mathematical space. The new Musee Henri Poincare is due to open in Paris in 2020. The Director, already appointed, is Cedric Villani; he  is also the Director of the Institut Henri Poincare in Paris. Cedric Villani is a Fields Medallist in Mathematics (the equivalent of being a Nobel Prize winner in maths), who also wrote the recent best-seller Birth of a Theorem: a mathematical adventure. He was at our MATRIX conference.
MWUK has been invited by the Chairman of the House of Commons Select Committee on Numeracy and Mathematics to participate at a Conference on the Northern Powerhouse, to be held in Manchester, on 15th September. We have also recently had a meeting with Sadiq Khan’s mayoral team at City Hall in London.
I am not one who partakes in sponsored walks, cycle rides, marathons, treks or whatever. So I cannot appeal to you to sponsor me to do some incredible feat of physical activity and then denote the proceeds of such sponsorship to a charity of my choosing. Instead I am appealing directly on behalf of our charity. We urgently need donations to support the appointment of a full time director of fund-raising and to purchase some much needed equipment.
On our website you will be able to make a donation directly to MWUK, and also to request a form to become a Friend of MathsWorldUK if you so wish. All donations, large or small, will be greatly appreciated. Also, please forward this message to any of your contacts whom you feel may be interested in the MWUK project.
Thank you, in advance, for your consideration.
Jack Abramsky

Vacancy, Postdoc position, PhD positions

  • A new vacancy for a candidate with a PhD in mathematics and I am sending this email in the hope that you might have recommendations for potential applicants to this job. The job title is “Senior Mathematics Curriculum Designer” and the salary bracket is £36,000–48,000. Full details about the job and a link for interested applicants to apply is available athttp://www.chestnut.com/en/careers/952105480268/.
  • A two year postdoc in Mathematics Education, with a focus on problem
    solving, reasoning and educational design, is announced in Umeå, Sweden. The full announcement:https://umu.mynetworkglobal.com/en/what:job/jobID:111103  Information about Umeå Mathematics Education Research Centre: www.umerc.umu.se  Information about Umeå University: www.umu.se/english

The Digital Turn in Epistemology (DigTEp)
Research Project
DigTEp is a collaboration between the faculties of Science and of Humanities of Utrecht University (UU), and the faculty of Philosophy of Erasmus University Rotterdam (EUR). The multidisciplinary project DigTEp lies on the cross roads of:

  1. philosophy of mathematics (PhD 1)
  2. logic (PhD 2)
  3. ICT development and mathematics education (PhD 3)

All three PhDs will share an office at the Freudenthal Institute<http://www.uu.nl/en/research/freudenthal-institute> in the faculty of Science of Utrecht University.

Embodied, Embedded and Extended Cognition (E3C) marks the recent Turn in Epistemology, the philosophy of knowledge, as well as in Cognitive Science. The three Es indicate that our knowledge and capacities are not located in our skulls, but extend to, and are distributed over:

  1. our bodies, which are always embedded in their environment they interact with;
  2. the artifacts we use, varying from paper notebooks to ICT.

The mediation of knowledge acquisition and application by ICT is becoming so dominant and ubiquitous (smartphone, tablet, laptop, computer, world-wide web) that Epistemology must take a further, Digital Turn. DigTEp concentrates on the following epistemological questions: How to make sense of mathematical knowledge after the Turn in epistemology to E3C, given its abstract character? Does the Digital Turn affect the genesis and the essence of mathematical knowledge? When practical knowledge is primary and propositional knowledge is derivative (E3C), how does this ‘derivation’ work in a digital environment? To answer these pressing philosophical questions, an empirical case study in epistemology will be performed of the acquisition of mathematical knowledge and skills in a controlled ICT-embedded environment, by secondary-school pupils. For a more detailed description of the contents of DigTEp, and of the individual PhD projects, please send an e-mail to the supervisor of the PhD project you wish to apply for.

Normal distribution is the only one normally taught at schools …

A recent paper: Anders Eklunda, Thomas E. Nicholsd, and Hans Knutssona, Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates.
doi: 10.1073/pnas.1602413113,  bit.ly/29j7dKf

sends a pretty grim message:

The most widely used task functional magnetic resonance imaging (fMRI) analyses use parametric statistical methods that depend on a variety of assumptions. In this work, we use real resting-state data and a total of 3 million random task group analyses to compute empirical familywise error rates for the fMRI software packages SPM, FSL, and AFNI, as well as a nonparametric permutation method. For a nominal familywise error rate of 5%, the parametric statistical methods are shown to be conservative for voxelwise inference and invalid for clusterwise inference. Our results suggest that the principal cause of the invalid cluster inferences is spatial autocorrelation functions that do not follow the assumed Gaussian shape. By comparison, the nonparametric permutation test is found to produce nominal results for voxelwise as well as clusterwise inference. These findings speak to the need of validating the statistical methods being used in the field of neuroimaging.

Implications are very serious:

Functional MRI (fMRI) is 25 years old, yet surprisingly its most common statistical methods have not been validated using real data. Here, we used resting-state fMRI data from 499 healthy controls to conduct 3 million task group analyses. Using this null data with different experimental designs, we estimate the incidence of significant results. In theory, we should find 5% false positives (for a significance threshold of 5%), but instead we found that the most common software packages for fMRI analysis (SPM, FSL, AFNI) can result in false-positive rates of up to 70%. These results question the validity of some 40,000 fMRI studies and may have a large impact on the interpretation of neuroimaging results.

Alas, too many people think that everything is normal…