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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).

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: Hundred square with Susan Okereke

Mathematical Objects

A conversation about mathematics and education inspired by a hundred square. Presented by Katie Steckles and Peter Rowlett, with special guest Susan Okereke.

In the episode, we mentioned the original Prime Climb colouring sheet and Peter’s Prime Climb colouring sheet on GitHub as drawing-primes.

Grid of numbers 1 to 100

COVID-19: moving my maths lecturing online, week 1

I teach maths at university. Last week, I moved to online delivery, in something of a panic. I am writing to share something of how this went.

That which we call an identity

I’m grateful to Jemma Sherwood and Rob Low for reading an early draft of this and for their comments thereon. All opinions are, of course, my own.

This post is inspired by something that I see crop up now and again in discussions with other Maths teachers. It usually manifests itself as a rallying cry to use ≡ in place of = in identities and reserve = for equations. My standard response is to mutter something about identities being equations and leave it at that. But in the latest round, Jemma Sherwood challenged me, in the nicest possible way, to explain a bit further. This is that explanation.

Although I’m going to state my case here, I’m well aware that there are different opinions. In matters of opinion, such as this, agreement and disagreement is less important than that all sides think. So if what I write seems to you wrong, that’s fine so long as it makes you think about why you think that it is wrong.

Mathematical Objects: Stick of Chalk

Mathematical Objects

A conversation about mathematics inspired by a stick of chalk. Presented by Katie Steckles and Peter Rowlett.

A stick of chalk