Hard Sums blog started!

This blog will provide a platform for publication and discussion of the Scholarship of Teaching and Learning (SoTL) activities in the Division of Maths at the University of Dundee.

Hard Sums is in part an acronym: SUMS standing for Scholarship of University Mathematical Studies. (Yes, it’s a stretch!)

My uncle, (who never enjoyed the maths he took at university), once introduced me as his “nephew who does hard sums”. Maybe this blog is about the ‘hard’ part of the title.

John McDermott

Why don’t students use effective learning strategies?

I attended a TILE (‎@TILEnetwork) talk with the above title yesterday.

Dr Flavia Shechtman-Belham (Seneca Learning) spoke about some of the most effective learning strategies – Dual Coding, Spacing and Interleaving, and Retrieval Practice. She also discussed reasons why students don’t tend to use these  – they are perceived to be ‘hard work’, or unnecessary, (students think their current methods work), etc. The message I took away from this excellent talk was that pointing my students to effective strategies for learning is my responsibility.

Actually no, my responsibility goes further than that. The published evidence Flavia discussed suggests that students cannot easily be persuaded to use these strategies. Chatting with a colleague who made earnest efforts in this direction during a course he delivered last year reinforced that impression. A full-on campaign in one course seems likely to single out that course in students’ minds, as awkward and difficult. So my responsibility might be not only to inform – but to nudge students towards the best strategies.

Nudges have a chance of working.  I feel that an approach mixing evidence from the literature (in small doses) with some reinforcement, in occasional short practical sessions, could provide the right environment for students to decide to adopt (some of) these strategies for themselves. My idea is to intersperse such sessions in occasional 15-20 minute bursts, into ‘regular’ maths workshop hours. These will take a little planning.

Maybe this will help – but maybe I would then single out my teaching as awkward and difficult! An ideal approach would then involve a coordinated effort involving other colleagues, perhaps covering the teaching across a whole level.

Lecture Capture – Moving towards ‘opt-out’ at Edinburgh

Dr Melissa Highton

A talk at LCS2018 (search for this tag in the blog).

Speaking from a dual role as Edinburgh University’s Director of IT and Vice-Principal of Online Learning,  Melissa discussed how Edinburgh is moving towards an ‘opt-out’ policy for LC. Opt-out means that by default, all lectures at the institution will automatically be recorded unless a special case is put forward which provides for an exception.

Edinburgh have been rolling out facilities for LC, with 100 teaching rooms fully ready, 200 more coming online this summer and the final 100 coming next year. This roll-out had been planned and announced but was reported in the student newspaper under the headline “All Edinburgh lectures to be captured from 2017.” The mis-understanding caused some complaints from students whose lectures were not yet being captured. This highlights a theme across the talks: students will increasingly come to expect lectures to be captured and may come to feel poorly served by institutions or individual departments which do not provide LC.


Lecture Capture Symposium

University of St Andrews

2 May 2018

I attended “LCS2018” in St Andrews. This afternoon-long symposium featured presentations by academics from a number of Scottish HEIs on the topic of Lecture Capture (LC). Various aspects were considered, including policy, implications, evidence and possible future directions. Several speakers related their own teaching experiences using LC and discussed implications for good practice.


I will post short pieces about each of the talks using the blog tag “LCS2018”.

BCME – Celebrating Mathematics Education


April 3-6, 2018

Two members of the Maths Division, Rachael Carey and John McDermott, attended the ninth British Congress of Mathematical Education (BCME) in Warwick.

BCME 9 is described as “a celebration of mathematics education attracting delegates from every phase (early years through to university) and aspect (teaching through to research, policy and public engagement), as well as high profile plenary speakers.”

With over 500 delegates, 350 papers / sessions and seven high profile plenary speakers, this four-yearly event is the largest Mathematics Education Conference in the UK.

Various talks delivered at the conference will be highlighted on this blog using the tag ‘BCME’

What makes examples exemplary for students? – John Mason

Mathematics Division Seminar

19 February 2018

Prof Mason has been teaching university mathematics for 40 years and during this time he has extensively investigated how to teach and learn mathematics effectively. He led the Open University’s Centre for Mathematics Education for fifteen years and has published numerous useful textbooks about maths educations that have become standard texts for students and lecturers.

This talk examined many of the ways in which the examples and ‘model solutions’ we provide to students might be more or less helpful to them, perhaps not working in the way that we expect! A number of techniques for engaging students within a session were discussed and even used during the talk.


Using Cognitive Science to Teach Mathematics in Higher Education – Carolina Kuepper-Tetzel

Mathematics Division Seminar

16 October 2017


Cognitive Science has revealed a number of learning and memory
phenomena that have direct, practical implications for learning and teaching.
I will highlight the most promising strategies alongside their original research
findings and will elaborate on ways on how to implement these in large
lectures and small seminars in mathematics. The talk will conclude with an
opportunity discuss the feasibility of implementation and ways to overcome
potential obstacles.

Automatic Assessment of Reasoning by Equivalence – Chris Sangwin

Mathematics Division seminar

Monday 27 February 2017


Deductive reasoning and proof is one of the hallmarks of mathematics, and is an important factor in distinguishing mathematics from empirical sciences. Fluency in calculation, including symbolic manipulation in algebra and calculus, sit alongside deduction, reasoning and problem solving. “Core pure mathematics” is that essential amalgam which is universally studied by all mathematics, science and engineering students. It starts with traditional algebra, trigonometry and calculus, culminating with De Moivre’s theorem and its consequences while stopping short of real analysis. Presentations of core pure mathematics often contain little explicit “proof” beyond formulaic proof by induction, but it is where proof starts for pure mathematicians.  Core pure mathematics contains a key activity “reasoning by equivalence”. This is reasoning and is key in many of the deductions at this level, but it is very close to a calculation. Indeed, in many situations it can be treated formally as a calculation. This talk will look at the interplay between calculation and reasoning, with a focus on automatic assessment. To what extent can we automate the assessment of reasoning now, and where are the limits of automatic assessment in the future?