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.
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 UpThis 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 when they crop up on Exam Papers, e.g. 729 is the square of 27. It's also the Cube of 9. From here we can 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.
1. Specific TopicThe second part of the session is usually given over to an area of Maths with which the student has specific issues.
2. HomeworkIf a student is having trouble with a set homework then this could also direct us to cover a specific topic.
3. Exam PaperWe can pull apart exam questions and help our understanding of Exam Craft.
4. A4 Revision SheetsI 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 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.
No. Not really. But it's probably the best way we've got.
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.
How do you approach your first exam question? Do you 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?