Student: Female, 16, GCSE

Louise has just had a fabulous lesson with me.

Something has just clicked with her and I watched, beaming, as she began answering exam questions PERFECTLY.  And I mean even the 'workings' she used to check her answers midway through a question were well-placed in the answer space.

It was even a calculator paper and she didn't even reach for one throughout.

Over the past year and a half I've been working with Louise who, at the beginning of our very first meeting, declared herself "terrible at Maths".  Over time our short time together, this has proved to be quite different from the truth.  A slow grow of confidence and an unpicking of the knotty topics with which she was struggling and we found ourselves stumbling around with Exam Craft.

How to answer exam questions, the process of answering.  Making life easier for the examiner marking your question paper.  And picking up all the points for each question.

In this particular lesson we were concentrating on Ratios.  We had a handful of exam questions on Ratios and we read through them all in order to create our 'Leave Me / Watch Me / Show Me' table - where we put questions in columns according to how confident the tutee feels about them.  For example, questions in the 'Leave Me' column means the tutee is confident enough to do the question herself without intervention from me.  Questions in the 'Show Me' column mean she has no confidence and wouldn't even know how to begin answering them.

Leave Me / Watch Me / Show Me table

As she tackled each question I watched her use my "PDR?" technique.  This is where we [P] Plan / Prepare, [D] Do the Maths and workings, [R] Review our answers and [?] ask ourselves whether we should move on to the next question yet.

Louise 'Prepared' by highlighting the words and numbers she wanted to focus on - unpicking the meaning of the question itself.  She then 'Did' the maths - worked out, using a new line for each new change that she made - giving short labels to each of the important numbers she found.

I was watching her arrive at the right answer but INSTEAD of just putting her pencil down with relief that the answer was over she continued by revisiting the wording of question and then retracing the steps of her answer.  'Reviewing'.  She had asked herself "Does this answer feel right?".

It was then that she concluded she didn't need to add to the answer any further and decided to 'Move On'.

It was like watching the perfect answering technique in action. And if I was the Examiner marking her answer here then I would have been in no doubt as to what Louise had done in order to work through the problem - making the Examiner's job as easy as possible and giving them no choice but to award full marks.

Student: Male, A Level

Tony is a hard worker.  Good at maths.  In fact, after the first couple of sessions I wasn't sure what value my presence was offering - usually it's a straight forward case of tackling a topic at a time but Tony knew what he should be doing.  I was barely keeping up with him.

Having said all that, he wasn't always getting things right.  The consistency wasn't there.  Silly mistakes were being made and time was taken up in working backwards through his answers in trying to detect where these mistakes were occurring.

He was very confident in his ability and quite stubborn in his lack of acceptance that his technique was causing him problems.  I noticed that he was doing too much of the working out in his head without writing it down - he didn't want to waste his time writing this stuff when he knew he was right and it didn't seem worthy of committing it to paper.

The Eureka moment for him came when I asked him to pretend that I was a year 10 student and he needed to teach me how to answer a question.  I observed him stumbling over some of the basics as he hadn't had to articulate certain steps before - he just 'did them' in his head.  Having to explain to a year 10 student what he was doing forced him to really think about every bit of information he was processing.

This helped me to convince him to use a new line for every change he made to an equation, or make a note of the narrative that was going through his mind - he resented the way it slowed him down but when he began to realise that he was making fewer 'silly mistakes' [like missing off minus signs or basic multiplication errors] and that his answers were becoming more reliable, and his answering was more disciplined, he started enjoying himself.

I was then able to open him up to the concept of Exam Craft.  His hard work and newly-discovered discipline helped him achieve the A* he wanted.

A Typical Session

I like to have an hour and a half with my GCSE students [14-16 years old].  It's long enough for me to fit in three areas of work for each session.

I like to start each session with a warm up and then we select two further areas from below...

Warm Up

This involves some number work.  Familiarisation with the 12 times table really helps here and so we investigate ways of making this 'stick' with the student.

I also like to use square numbers and, over time, see how far we can get up to 30². We also bring in cubed numbers and can take them up 10³.  It's very rewarding watching a fifteen year old self-declared arithmophobe trot out all the square numbers AND cube numbers in order up to 1000.  While this may sound fanciful for most students it really is achievable by learning the most suitable methods.

This knowledge really helps the student recognise numbers that would otherwise appear random and intimidating when they crop up on Exam Papers, e.g. 729 - this is the square of 27.  It's also the Cube of 9.  From here we can also explore multiplying decimals using these numbers/digits. For example:

0.27 x 0.27 = 0.0729

Or 

2.7 x 2.7 = 7.29

Being able to handle fractions is often an assumption we make of our young students and I like to ensure we don't take this ability for granted.

Factorisation of numbers like 12, 24, 36 and 72 can be done methodically so you can know that you have all the factors in front of you.  This is very useful in making quadratic equations less intimidating.

Depending on what is discovered about the tutee's ability with these 'nuts and bolts' of GCSE maths we might stretch this into the second part of the session.  Otherwise we go on to the two from the following...

1. Specific Topic

The second part of the session is usually given over to an area of Maths with which the student has specific issues.

2. Homework

If a student is having trouble with a set homework then this could also direct us to cover a specific topic.

3. Exam Paper

We can pull apart exam questions and help our understanding of Exam Craft.

4. A4 Revision Sheets

I encourage a student to obtain an A4 folder.  Over the course of my tuition we will be creating an A4 revision sheet for each topic - here I guide the student into writing their own Revision Notes for a particular topic.  I restrict them by using one A4 sheet per topic, so that it is up to them in how they reduce the notes to fit on one piece of paper. 

I make it clear that while they may decide to never return to a revision note it is the mere fact that they have actually written the revision note in their own words that makes the subject 'stick'.  We only write a revision note once the student has 'Got It' and they are able to write it in their own words.  We hope that by the time of their exams we have a healthy looking A4 folder full of their own revision notes.

5. Past Paper Practice

As we approach the exams we increase the number of past papers with which we practice.  We shall learn how to eliminate 'silly' mistakes [like when a minus sign goes inexplicably missing during our 'workings'] and we shall be applying the Exam Craft we have learned.

Exam Craft

Exams are the oddest of things.  Like interviews are for jobs.  Is an interview really the most effective way to determine whether a candidate is the most effective person for the job in question?

No. Not really.  But it's probably the best way we've got.

Likewise: Exams.

Awful things.  Artificial.  And a real pressure point for the young mind.  So, while equipping those young minds with the subject matter to be examined one should also have a bit of an exam strategy to pass on to them. Otherwise known as Exam Craft.

For me it started by wondering how each student approached their first exam question?  Do they read it through and then underline key words?  Do you need to draw a diagram?  What is the question actually asking you?  Have I answered it?  Do I move on?

I tend to use the rather awful acronym 'PDR?' (rising intonation at the end there)

I explain it in more detail here but in a nutshell, it is...

Planning or Preparation
Doing
Reviewing
? [Do I Move On?]

This is quite hard for a student to believe in without them having its benefits demonstrated to them followed by practice in applying it.  It helps the student take charge of each exam question, right up to the point of knowing when they have gone as far as they can with it.