A lot of people seem to be doing a #Nurture1415 post – Sue Cowley (@Sue_Cowley on Twitter) has compiled a long list here.

So here are my, hopefully short, 5 positives and 5 negatives.

5 Positives from 2014

  1. I saw the final completion of my PhD in applied computational mathematics by graduating from The University of Nottingham
  2. I joined Twitter, properly. I had a while a go signed up to Twitter, but never really used it. This year I decided to set up a professional Twitter account (@DrBennison). I was a bit dubious at first, but I now use it all the time. Everyone on Twitter is very welcoming, happy to get involved in discussions and I have learnt a lot from everyone I have interacted with. It was particularly good to meet people I had spoken to on Twitter at Mathsconf2014.
  3. I started working at a great school, with a great department that is very supportive of each other.
  4. I also started a blog in the summer, which I have enjoyed updating!
  5. Doing maths by hand. It has been nice to practice integrations etc by hand again. I had become very reliant on Mathematica over the last few years.
  6. First wedding anniversary. It has been a great first year married to my beautiful wife and I feel very lucky to always have her support.

5 Wishes for 2015

  1. Develop my website properly. At the moment my website just hosts my blog, a few files and a Javascript game – I need to spend time designing a proper homepage.
  2. Do some coding. After 5 years of programming everyday I have been missing doing some programming. I have two projects I would like to work on: 1) an iFEM finite element iOS app; 2) a useful online computer based assessment and grading system. Hopefully if I am disciplined in school holidays I can make a start on these.
  3. Blog more frequently. I’ve learnt loads in the last six months reading other people’s blogs and updating mine, however my posts have been infrequent. My goal for 2015 is to post at least one decent post every week – fingers crossed I can manage this.
  4. Continue learning from colleagues at work, people on twitter and in any other way so that I can be the best teacher that I can be.
  5. Manage a good work-life balance

You got one bonus positive.. sorry for not sticking to the rules.


Merry Christmas

Merry Christmas to everyone who has taken the time to read my posts since I started this blog. I know they have been infrequent recently and I intend to post more often this year.
People always mock me for my inability to colour very well, so here is a Christmas Calculated Colouring I did this morning for you all 😉

Colouring sheet courtesy of 10ticks.

A Level Teaching

Why are there so few derivations in A Level Mathematics?

A thing I have noticed with the A Level textbooks (I use the Edexcel books published by Pearson) is that there are very few derivations of results, with them preferring to just present a formula for the student to use.
I don’t understand why this is the case… I get that there is a lot of content to be covered in a relatively short time (maybe this will improve with going back to terminal exams) but aren’t students missing out on some really important concepts by not including derivations.
I’m sure many teachers do show derivations, but why are they not in the text books we expect students to use to help their studying?
I recently asked my Year 12 FP1 students to derive an expression for the inverse of a general \( 2 \times 2 \) matrix, in terms of the entries of the matrix that you are trying to invert. Of course, a straight forward way to do this is to use the definition of the matrix inverse to derive 4 equations with 4 unknowns which can be solved in two pairs to obtain the entires of the inverse matrix in terms of the original matrix.
I was surprised to find that no one managed to do it. Perhaps the amount of letters floating around put them off, but I think this kind of exercise is important for building confidence and developing fluency with methods used in other modules.
I typed up a solution for them, if it is of interest to anyone it is available on my website here. Of course there are likely to be typos…..
I’d be interested to hear other peoples views / experiences of derivations with A Level maths.