Maths GCSE: repeats are of low values

As this table from Education Data Lab shows, show, retakes are of low value.

Cqs043qW8AA0WXKRead the whole article: Repeat After ‘E’: the treadmill of post-16 GCSE maths and English retakes, by


Hamid Naderi Yeganeh: Fractal Africa

New mathematics artwork from Hamid Naderi Yeganeh.


This fractal is constructed by an Africa-like octagon and its lateral inversion.:

If we count the number of octagons of different sizes we get the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, … (see this animation:

The height of the biggest octagon is φ times longer than the height of second octagon; where φ is the golden ratio. (see the following image) It is a necessary and sufficient condition to see the white triangles in this fractal.


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 at
  • 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:  Information about Umeå Mathematics Education Research Centre:  Information about Umeå University:

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<> 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.