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.

# You're reading: Travels in a Mathematical World

### ‘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.

### You have completed level 8. Game over. Insert coin.

(See QCF.)

That is to say, the university have sent me a degree certificate, and I’ve shown it to the bank. So that’s pretty darn official.

### 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.

Why does 0! = 1 better yet, why does a^0 = 1 I must see a proof! #Mission #Unanswered #MathRage

— Callum Mulligan (@Calified) February 1, 2014

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.

### An Approach That Uses Computers a Bit to Ask Questions on Numbers and Stuff in Big School

Here I attempt to write the abstract for my thesis, ‘A Partially-automated Approach to the Assessment of Mathematics in Higher Education’, “using only the ten hundred words people use the most often“.

### Dynamic generation of maths questions

I was recently asked about my MSc dissertation (by someone who may choose to ‘out’ themselves here, but as it was a personal email I won’t name them). In my dissertation, for a Masters degree in computing in 2003-4, I developed a system for pre-processing MathML code using PHP to include pseudo-randomised values in the questions for an e-assessment tool. The title is ‘Asking Questions With MathML: dynamic treatment of XML and pseudo-randomised mathematics assessment’.

The query was from someone who is training to be a maths teacher and is doing some web development. They had seen mention of my MSc dissertation topic on this blog and asked where they could read more about the underlying web technologies. Here, basically, is what I replied.

### Probability of dealing four perfect hands of cards in a world of random shufflers

A couple of months ago (really? Two years?! Man!) I posted about an extraordinary coincidence: in a game of whist at a village hall in Kineton, Warwickshire, each of four players had been dealt an entire suit each. My post ‘Four perfect hands: An event never seen before (right?)‘ discussed this story. What really interested me was that the quoted mathematical analysis — and figure of 2,235,197,406,895,366,368,301,559,999 to 1 — appears to be correct; what lets down the piece is poor modelling. The probability calculated relies on the assumption that the deck is completely randomly ordered. Apart from the fact that new decks of cards come sorted into suits, whist is a game of collecting like cards together, so a coincidental ordering must be made more likely. Still unlikely enough to be worthy of mention in a local paper, maybe, but not “this is the first time this hand has ever been dealt in the history of the game”-unlikely.

Anyway, last week I was asked where the quoted figure 2,235,197,406,895,366,368,301,559,999 to 1 actually comes from. Here’s my shot at it.