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Guesting on the ‘Wrong, But Useful’ first anniversary episode

You may recall that Samuel Hansen and I used to have a weekly conversation about mathematics in the news and news in mathematics, which we called the Math/Maths Podcast and released through the (still going!) science communication project Pulse-Project. When we put Math/Maths on hiatus (the length of which is still an open question), this left a gap in the lucrative ‘two blokes talking about maths-y stuff’ market. Leaping on the opportunity, plucky young podcasters Colin Beveridge and Dave Gale started Wrong, But Useful (as you may recall from a previous post here). Well, that was a year ago now and, as creatures whose outlook is tied to this planet, that is apparently worth celebrating. Through a careful constructed mock-feud, Colin and Dave reeled in first Samuel and then me to join them in an anniversary recording.

‘Development and evaluation of a partially-automated approach to the assessment of undergraduate mathematics’

Next month I will present at the 8th British Congress of Mathematics Education, the “largest mathematics and mathematics education conference in the UK” which “brings together teachers from early years to higher education, researchers, teacher educators, CPD providers, consultants, policy makers, examiners and professional and academic mathematicians”, according to its website.

My talk is part of the research strand of the conference, organised by the British Society for Research into Learning Mathematics. This society is “for people interested in research in mathematics education”, and I am a member.

I’m presenting the ‘what I did’ portion of my PhD; well, most of it. Anyway, the peer-reviewed proceedings have now been published. My article is ‘Development and evaluation of a partially-automated approach to the assessment of undergraduate mathematics‘. The abstract is below.

Why do $0!$ and $a^0$ equal $1$?

The last two weeks my first year mathematicians and I have covered Taylor series.This means that several times I’ve had the conversation that goes “What’s $0!$?” “It’s $1$.” “Oh, erm, right. Why again?” “Because it works.” This may not be a completely satisfactory answer!

One of my students, Callum Mulligan, tweeted this question.

Saying “by definition” or “because it makes a bunch of stuff work” won’t cut it. So how to answer this question? To give a somewhat intuitive understanding of why this should be the case to a first year undergraduate. It may be obvious, but it wasn’t immediately obvious to me how to explain this, so I share some thoughts here.