Do as I say, not as I do

Working in a sixth form college, this term is all about revision, revision, revision. I appreciate that different approaches work for different people and I acknowledge that many of my students are mature and experienced enough to know what’s best for them. That said, however, I still model the revision process and keep a close eye on their work during the term to ensure they are progressing well.

Modelling Revision for Everyone

It may seem difficult to reconcile the fact that I want to model ‘how to revise’ whilst not prescribing ‘how to revise’. So I begin by explicitly acknowledging that we don’t all learn things in the same way. Of course we don’t. And we don’t all have the same strengths and weaknesses. BUT, there are sensible things to do and some certainly non-sensible things to do.

Mind map? Small cards? Big piece of paper covered in tiny writing? I don’t mind! (I’m a big piece of paper person, if you must know.) Some of the points I make:

  • DO use the textbook as a source of ‘what you need to know’. (Our A level textbooks match the specification.)
  • DON’T copy out every bullet point word-for word.
  • DO scan through the chapter to get an overview of the content, and see what is summarised at the end of the chapter.
  • DO write down the key ideas in your own words.
  • NEVER write something down that you don’t understand – ask first!
  • DON’T assume your revision notes are finished when you’ve been through the book once.
  • DO keep adding to your notes everytime another idea comes to you, or every time you learn more details behind a technique.
  • DO make your revision summary your first port of call when you are stuck on a past paper question. If it doesn’t help you then you know you will need to ADD something once you have asked for help.

To motivate my students that bit more, I allow them to make use of their sheets after one week in a class ‘mock’. The final question on that test asks them how much use they made of their notes, how useful they were and what, if anything, they will need to add.

This process seems to have worked well with all my students: they have mind maps, big sheets and index cards. Some didn’t do much revision at all and learned their lesson when the class test came around. They are all adding extra details, almost on a daily basis.

Here is one such sheet: an S1 summary from one of my AS students. As I mentioned on Twitter, the more I stare at the photo, the more details I notice. (If you look really close you’ll see she’s annotated some things in Thai!)


How Not to Revise

Now it’s time for me to be come clean. My own revision habits have a certain ‘efficiency’ to them which I recognise in one or two of my students each year. I have a very reductionist view that everything in mathematics is essentially definitions and deductions, and rely on that a little too heavily when I sit exams.

Over the past couple of years I’ve been taking a few modules with the Open University – I’ll blog about that bigger picture another day. Today I sat the exam for MT365 Graphs, Networks and Design. This is actually an incredibly interesting (dare I say fun?!) course that has some overlap with the D1 and D2 A level modules. Throughout the course I’ve had 4 assignments to complete: I would cram each of those into a weekend, study the material intensively and just enough to be able to answer the questions, and then lose all memory of it soon after. But today was the final examination and, due to the demands of my teaching job, I left myself little time to prepare. How did I do it?

  • Download the last 3 past papers. I can’t share these as the OU students association use the sale of past papers as a source of revenue.
  • Dig out the ‘module handbook’. This is a life-saver! The OU seem to provide these for many of their mathematics modules: it’s a booklet of key information from the course that you are allowed to take into the examination. You’re even allowed to annotate it beforehand. This reduces the burden of learning reams of definitions and thus questions can focus more on techniques and depth of understanding.
  • Figure out the structure of the exam. (No calculator allowed. Section A, 55%, 11 shorter compulsory questions on all topics. Section B, choose 1 question out of 3 on each of Graphs, Networks and Designs. There is an essay option in each area but you can only do one of those.)
  • Scan-read through the past papers, noting unfamiliar topics and vocabulary – all the things that I need to work on before facing the real exam.
  • Make my own summary notes on all those areas, sourcing the information from the handbook, the course textbooks or even the past paper solutions.
  • Attempt Section A on one paper. Mark it. Annotate summary notes with areas where I lost marks. Repeat for Section A on the next paper, and then the third.
  • Any areas where I was always careless? Yes – bin-packing algorithms. Note to self to work carefully if that topic comes up.

It became clear that there were some key topics that I wouldn’t be able to understand in depth before the exam (maximum flow, Hungarian algorithm, electric circuit analysis, linkages). All I could do is learn enough in case there was a short Section A question and then hope the options in Section B worked out in my favour!

Also, because I began this process 24 hours before the exam, there wasn’t sufficient time for me to write my own answers to the Section B questions. I could only read the mark schemes and, again, add key information to my summary.

On the morning of my exam (that’ll be this morning!) I had another look at my summary notes – 3 sides – and then decided what would need to go into the handbook as annotation. Then I was as ready as I would ever be.


Typical page from the handbook


Some of my annotations in the spare space

The Moment We’ve All Been Waiting For

I am fortunate enough to not get too nervous with exams. As I mentioned before, this comes down to my reductionist faith in being able to figure out maths from the definitions. I took my seat, smiled inwardly as the invigilator read out the spiel just as would be happening to school kids up and down the country. “The time is 2:35, you may begin.”

Scan-read the paper. Section A looks quite ok, just one question on linkages that I had not prepared for at all. Section B Graphs: ok, there’s one on Hamiltonian circuits and planarity which I was comfortable with. Section B Networks: oh ****. One question on maximum flow (a no-go topic) and the other on electrical circuits (even worse). And the essay topic? Critical Path Analysis. Thank goodness. Section B Design: one on linear codes which again I could muddle through. A slight pang of sadness that there was no mention of Prüfer sequences anywhere: I’d made sense of those and was ready for them!

I won’t go through the paper in any more detail, but I’m reasonably sure I’ve scored 70% plus. And for 24 hours revision I feel a slight tinge of guilt that I’ve played the system. One question asked for the ‘thickness’ of a given graph. I didn’t know that term, but the handbook contained a definition that I could work from!

An Interesting Aside

I was intrigued to note that tracing paper would be provided in the examination. One of the course tutors advised us to make use of this, although it would work in different ways for different people. I actually found it incredibly useful for many things: looking for subgraphs, drawing the graph for a linkage, applying Kruskal and Prim’s algorithms when given distances in a table, trying to determine the chromatic number for a graph…

Next time I teach D1, I think I will have a good supply of tracing paper on hand!

No Rest for the Wicked

I’ve actually got another exam next week and it’s a much more difficult module. I’m just hoping a similar approach works again as, sadly, I simply don’t have the time to do these courses full justice.


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