I gave a talk on Fermi problems and a method for approaching them using the approximate geometric mean at the Maths Jam gathering in 2017. This post is a write up of that talk with some extras added in from useful discussion afterwards.
Enrico Fermi apparently had a knack for making rough estimates with very little data. Fermi problems are problems which ask for estimations for which very little data is available. Some standard Fermi problems:
- How many piano tuners are there in New York City?
- How many hairs are there on a bear?
- How many miles does a person walk in a lifetime?
- How many people in the world are talking on their mobile phones right now?
Hopefully you get the idea. These are problems for which little data is available, but for which intelligent guesses can be made. I have used problems of this type with students as an exercise in estimation and making assumptions. Inspired by a tweet from Alison Kiddle, I have set these up as a comparison of which is bigger from two unknowable things. Are there more cats in Sheffield or train carriages passing through Sheffield station every day? That sort of thing.
On 31st January 2008, I gave my first lecture. I was passing my PhD supervisor in the corridor and he said “there might be some teaching going if you fancy it, go and talk to Mike”. And that, as innocuous as it sounds, was the spark that lit the flame. I strongly disliked public speaking, having hardly done it (not having had much chance to practice in my education to date – I may have only given one talk in front of people to that point, as part of the assessment of my MSc dissertation), but I recognised that this was something I needed to get over. I had just started working for the IMA, where my job was to travel the country giving talks to undergraduate audiences, and I realised that signing up to a regular lecture slot would get me some much-needed experience. I enjoyed teaching so much that I have pursued it since.
I just noticed that last Wednesday was ten years since that lecture. It was basic maths for forensic science students. I was given a booklet of notes and told to either use it or write my own (I used it), had a short chat about how the module might work with another lecturer, and there I was in front of the students. That was spring in the academic year 2007/8 and this is the 21st teaching semester since then. This one is the 15th semester during which I have taught — the last 12 in a row, during which I got a full-time contract and ended ten years of part-time working.
I have this awful feeling this might lead people to imagine I’m one of the people who knows what they are doing.
P.S. The other thing that I started when I started working for the IMA was blogging – yesterday marks ten years since my first post. So this post represents the start of my second ten years of blogging.
A couple of weekends ago was the big MathsJam gathering (I might call it a recreational maths conference, but this is discouraged). Two of the delightful sideshows, alongside an excellent series of talks, were the competitions. The Baking Competition is fairly straightforward, with prizes for “best flavour, best presentation, and best maths”:
The first will reward a well-made, delicious item; the second will reward the item which has been decorated the most beautifully and looks most like what it’s supposed to be; and the third will reward the most ingenious mathematical theming.
You can view the entries from this year on the MathsJam website.
Welcome to #104 of the Math Teachers At Play (MTaP) blog carnival. A blog carnival is a regular blogging round up coordinated by someone (in this case Denise Gaskins) that moves around different blogs each edition. This time, I’m taking a turn.
The BBC biography series Great Lives covered in its most recent episode Srinivasa Ramanujan. In the closing minutes of the programme, host Matthew Paris said this, which I found quite interesting (or at least, interestingly expressed):
I’m so far from understanding the mind of a mathematical genius that it’s simply inconceivable that you could tell a person an apparently random number and he could intuit or deduce the kind of fact that he deduced about that taxi license number. I mean, I can’t run a four-minute mile, but I once ran a five-minute mile, and I can extrapolate from my own experience, in a way understand how someone might just be a lot better than me at something that, in an inferior way, I can also do. But Ramanujan isn’t like that. It’s as though this man were a different species, not just a superior example of the same species. Can you learn to do this kind of thing? Could I, if I had applied myself? Or is it that goddess again, is it really just genius?
Answers on a postcard!
Readers of The Aperiodical are probably familiar with the Carnival of Mathematics, a monthly blog roundup which takes any maths-related content. Did you also know there is a related blog carnival called Math Teachers at Play?
The Math Teachers at Play (MTaP) blog carnival is a monthly collection of tips, tidbits, games, and activities for students and teachers of preschool through pre-college mathematics. We welcome entries from parents, students, teachers, homeschoolers, and just plain folks. If you like to learn new things and play around with ideas, you are sure to find something of interest.
I’ll be hosting the January 2017 edition of MTaP here at Travels in a Mathematical World. Of course, a blog carnival is only as good as its submissions, so if you join me in aspiring to the claim “you are sure to find something of interest” then please keep your eyes open for interesting blog posts and submit them to MTaP. Please submit posts you’ve enjoyed by others or yourself. Posts you wrote that are appropriate to the theme are strongly encouraged. Submit through the MTaP submission form, leave a comment here or tweet me. Thank you!
Submissions are open now, and anything received by Friday 20th January 2017 will be considered for the edition hosted here.
One of the nice things about working in mathematics at Sheffield Hallam University is the environment in which I work. The maths department is a big, open learning space for students surrounded by staff offices. It’s a busy place, full of activity and plenty of opportunities to interact with students and other staff.
This space was renovated for mathematics a little before I arrived. It was designed to enhance student engagement and to create this sense of community, to allow collaborative learning and encourage inter-year interactions.
Over the last year, we conducted a study of use of the space. This included observations of use of the space as well as questionnaires and interviews with students about their use of the space, including students who had studied in the department in the old and new locations.
The results have just been published as ‘The role of informal learning spaces in enhancing student engagement with mathematical sciences‘ by Jeff Waldock, Peter Rowlett, Claire Cornock, Mike Robinson & Hannah Bartholomew, which is online now and will appear in a future issue of International Journal of Mathematical Education in Science and Technology (doi:10.1080/0020739X.2016.1262470).