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Partially-automated individualised assessment of higher education mathematics

A while ago I wrote an article based on my work in partially-automated assessment. The accepted manuscript I stored in my university’s repository has just lifted its embargo, meaning you can read what I wrote even if you don’t have access to the published version.

Thinking about assessment, it seems there are methods that are very good at determining a mark that is based on a student’s own work and not particularly dependent on who does the marking (call this ‘reliability’), like invigilated examinations and, to some extent, online tests/e-assessment (via randomised questions that are different for each student). These methods tend to assess short questions based on techniques with correct answers and perhaps therefore are more focused on what might be called procedural elements.

Then there are methods that are probably better at assessing conceptual depth and broader aspects that we might value in a professional mathematician, via setting complex and open-ended tasks with diverse submission formats (call this authenticity and relevance ‘validity’). People are often concerned about coursework because it is harder to establish whether the student really did the work they are submitting (not an unreasonable concern), which impacts reliability.

It is hard to ask students to complete high-validity coursework tasks (that might take weeks to complete) in exam conditions, and diverse submission formats do not suit automated marking, so two ways to improve reliability are not available. The idea with partially-automated assessment is that an e-assessment system can be used to set a coursework assignment with randomised elements which is then marked by hand, gaining the advantageous increase in reliability via individualised questions without triggering the disadvantage of having to ask for submission in a format a computer can mark. The payoff is that the marking is a bit more complex for the human who has to mark it, because each student is answering slightly different questions.

In the article I write about this method of assessment, use it in practice, and evaluate its use. It seems to go well, and I think partially-automated assessment is something useful to consider if you are assessing undergraduate mathematics.

Read the article: Partially-automated individualized assessment of higher education mathematics by Peter Rowlett. International Journal of Mathematical Education in Science and Technology, (published version; open access accepted version).

Aperiodical News Roundup – September 2021

Here’s a collection of some things that have been happening (and will be happening) in maths this month (and next month).


The British Society for the History of Mathematics have announced their annual Neil Bibby Awards, which have been awarded to Ciarán Mac an Bhaird and Michael Barany. The award winners receive £400 each, and will be expected to deliver some schools talks and produce resources for the BHSM website. More information about the Bibby Awards can be found on the BSHM website. (via @MathsHistory on Twitter).

The British Society for the History of Mathematics have also announced the winners of their annual schools and undergraduate essay prizes:

  • Schools Writing Prize (11-15 category): Daria Gal (Notting Hill and Ealing High School, London) for ‘Mathematics and the mysterious world of creating gold’;
  • Schools Writing Prize winner for 2021 (category 16-19): Carys Williams (Monmouth School for Girls, UK) for ‘A story of secrecy and security: the key to unlocking prime numbers’;
  • Undergraduate Prize winners, jointly: Ellen Flower (Oxford University) for ‘The “analysis” of a century: Influences on the etymological development of the word “analysis” in a mathematical context to 1750’ and George Waters (London School of Economics) for ‘Exploring the use of mathematics to obtain consensus’.

These winners and the runners up for each prize are announced in this Twitter thread: “Our Schools and Undergraduate Prizes announcements!!!”.

Money, Dollars, Sack, Bag, Icon, Bag Of Money

Carnegie Mellon University has been gifted $20 million by blockchain pioneer Charles Hoskinson to establish the Hoskinson Center for Formal Mathematics. The center will be part of Dietrich College and will “advance mathematical research by improving global access to knowledge and resources for mathematics researchers, educators and learners”. For more information read the press release here. (via @KevinZollman on Twitter).


This coming Ada Lovelace Day, Tuesday 12 October, the organisers of Ada Lovelace Day live are putting on a series of online webinars on topics including engineering, tech and games, and the science of hypersleep. Tickets are free, and the events will be streamed live on YouTube and Facebook.

School student stage show outfit Maths Inspiration are putting on a special online show during COP26, themed around the mathematics of climate. Schools can pay a flat fee of £75+VAT to have as many students as they want join and watch live, and speakers include Matt Parker, Sammie Buzzard and Hugh Hunt. (via @MathsInspiratn on Twitter).

Screenshot from the MathsCity website, with text: 'EXPLORE - DISCOVER - SOLVE; MathsCity is the home of hands-on maths, located in the heart of Leeds. Coming soon to Trinity Leeds, the UK's first Mathematics Discovery Centre.'

It’s finally happening! The UK’s first hands-on maths discovery centre, MathsCity, will be opening in Leeds on 5th October. Open from 10am-5pm Tuesday-Sunday, in Leeds Trinity Shopping Centre, the mathematical wonderland will include giant bubbles, a laser ‘ring of fire’ and puzzles to solve. Go go go! (via @MathsCityLeeds on Twitter).

On 15th October, the Royal Irish Academy is hosting the Hamilton Lecture 2021, featuring Professor Caroline Series, who’ll be talking about Glimpses in Hyperbolic Geometry. The lecture will take place online, followed by a Q&A, and tickets are free but booking is required. And look, they did such a cool poster (above)!

Mathematical Objects: A sheep, at least one side of which is black

Mathematical Objects

A conversation about mathematical jokes, humour and folklore inspired by a sheep, at least one side of which is black. Presented by Katie Steckles and Peter Rowlett.

The jokes sent to Peter on Twitter that we mention can be found in the replies to this tweet.

A black sheep in a field

Mathematical Objects: Plate of biscuits with Alison Kiddle

Mathematical Objects

A conversation about mathematics inspired by a plate of biscuits. Presented by Katie Steckles and Peter Rowlett, with special guest Alison Kiddle. What do you notice? What do you wonder?

Alison’s Noticing and wondering page.

We also mentioned A Problem Squared Episode 014 = Final Cheese Drama and Quick-Fire-O-Rama.

You can see Peter’s kitchen floor in this tweet.

Plate of biscuits described in the episode in two configurations.

Mathematical Objects: Spirograph

Mathematical Objects

A conversation about mathematics inspired by a Spirograph set. Presented by Katie Steckles and Peter Rowlett.

Katie’s Spirograph GeoGebra file.

Travel Spirograph kit, with blue and red pens

Mathematical Objects: Balancing bird with Alom Shaha

Mathematical Objects

A conversation about mathematics inspired by a balancing bird. Presented by Katie Steckles and Peter Rowlett, with special guest Alom Shaha.

Alom’s video and template about the balancing bird.

Paper bird balancing by its beak on a finger.
Photo by Alom Shaha.