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Introducing hexboard – a LaTeX package for drawing games of Hex

Chris Sangwin and I wrote a LaTeX package for drawing Hex boards and games called hexboard. It can produce diagrams like this.

Hex board with counters.

First: why? Then: how do you use it?

MathsCity Leeds opening weekend

One day in February 2014, I was fortunate enough to battle through London during a Tube strike to attend a reception at the House of Commons for MathsWorldUK – an initiative then just two years in development which aimed “to establish a national Mathematics Exploratorium in the United Kingdom … an interactive centre full of hands-on activities showcasing mathematics in all its aspects for people of all ages and backgrounds”.

That initiative took a huge leap forwards last week with the launch of MathsCity Leeds, which my son and I visited on its opening weekend.

Child holding a transparent dodecahedron through a red light which is showing as a triangle around one vertex

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).

Spooky 007 date coincidence


John Bibby points out a numeric coincidence – “Sean Connery died on 31/10/20. If you add up all the numbers in the date = 007”. Spooky, huh? I’m hoping you’re asking ‘is that unlikely?’ John asks “How many other dates this year add up to 007? What about in 2021?”

This is a fine pen-and-paper activity (or for thinking about in the shower, as I tried this morning), but also a nice little brute-force coding exercise.

nimsticks: LaTeX package for drawing Nim sticks and games

A while ago on this blog I shared a LaTeX macro I had written for drawing games of Nim. I have now taken the plunge and written this into a LaTeX package called nimsticks. (Why? What do you do to relax on a lazy Sunday morning?)

Here is the description of the nimsticks package:

This LaTeX package provides commands \drawnimstick to draw a single nim stick and \nimgame which represents games of multi-pile Nim. Nim sticks are drawn with a little random wobble so they look ‘thrown together’ and not too regular.

What this does it allows commands such as \nimgame{5,3,4} which renders like this:

Three Nim heaps: 5 sticks, 3 sticks and 4 sticks

Prime Climb colouring in with LuaTeX

A while ago, my son did the Prime Climb colouring sheet.