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

BCME – Celebrating Mathematics Education


April 3-6, 2018

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

BCME 9 is ” 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.

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?