[Reposted from Alexandra O Fradkin’s blog Musings of a Mathematical Mom; listed in reverse chronological order]
PhD studentships in mathematics education at Sheffield Hallam University. Further information and contact details are below – please contact us to discuss your proposal.
Full details and application forms are available here: http://www.jobs.ac.uk/job/AWG226/phd-studentships-4-posts/ Closing date: 17:00 on 1st February 2017
From New Scientist, by , 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.”
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.
[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 (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.
As this table from Education Data Lab shows, show, retakes are of low value.
Read the whole article: Repeat After ‘E’: the treadmill of post-16 GCSE maths and English retakes, by Rebecca Allen
- 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
- A PhD position on embodied, extended and embedded cognition from a philosophical or mathematics educational perspective, http://www.academictransfer.com/35679http://www.academictransfer.com/35679 or 3 positions as PhD students (1,0 FTE) <http://www.peoplexs.com/Peoplexs22/CandidatesPortalNoLogin/Vacancy.cfm?PortalID=4063&VacatureID=849205>
The Digital Turn in Epistemology (DigTEp)
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:
- philosophy of mathematics (PhD 1)
- logic (PhD 2)
- 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:
- our bodies, which are always embedded in their environment they interact with;
- 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.
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…
From the BBC:
Official data shows just over half (53%) of 11-year-olds made the grade in reading, writing and mathematics. […]
Department for Education statistics show:
- 66% of pupils met the standard in reading
- 70% in maths
- 72% in grammar, punctuation and spelling
- 74% in the teacher-assessed writing
The overall figure of 53% relates to the number of pupils who reached the expected standard in all three subjects.
Read the full story.