When I did my A levels we did not really look at the exam papers until the end. There was very little support for the students on ‘how to do’ exams. My teachers focused on what we should learn and then expected those who had learned the most, doing the best. I’m not sure I ever saw a copy of the specification, or had any indication of what I was going to be examined on, beyond what we had covered in the lesson. My teachers loved logarithms and matrices, and we did lots of questions on those. But now we embed the assessment process through the course and make it clear what you need to do to be successful, give feedback, set targets, and .. And it makes a difference. I used to do a set of lessons around the theme of the 3 legs of exam success. The analogy was that the shortest leg always limits the usefulness of a 3-legged stool. In the same way as the outcome of your exam is limited by your weakest area. But in refinement over the years, 3 became 4 and 4 became 5 so here we are.. the analogy falls down, but the philosophy remains sound.
My five columns:
1. Fine Detail Memory
Students have to be able to remember what they learned today and carry it with them into the back end of next year. They need to have the FINE DETAIL at their fingertips. Students need to know the facts. That formula, that process, that set of operations. Knowing how to do something on a mechanical level. Our department does a great exercise stolen from Hattie (Visible Learning) based on his six principles of memory retention (p116) and how knowledge is stored (p126). By the end of this block of lessons each of the students has a set of revision strategies to try and develop over the course. We collect our ‘Fine detail’ facts on the wall as we go through the course.
2. The BIG picture
This is where many of my students initially struggle. They can understand the sections of the course in isolated detail. They can follow the instructions for one topic, but faced with a question that crosses over two or more parts of the course, they start to doubt themselves. They keep flying at the same window repeatedly, and wondering if they do that same thing next time, will they get a different output?.. They seldom do.
In order to make these synoptic links you need to have a grasp of the big picture. The top level, ‘what is the point of Pythagoras’. Understanding the BIG PICTURE is crucial to prevent maths being a set of operational processes. Without it you can’t make the high level synoptic links between one topic and the next. How does angle relate to vectors? How does probability link to fractions?
I play this game with them. For it to work best it needs to be pressured, because stress affects perception.
I say I’m going to show you an image of 5 black shapes. I’ll give you 15 seconds to look hard at the black shapes and remember them. Then I will give you 30 seconds to draw it from memory.
Go, tick, tick, pressure, tick, tick, time constraint, stop. Now draw it…
Some of the students will see 5 black shapes (the fine detail) and try to remember each one and its size and its location. They will really struggle and really find it hard to retain all this in their short-term memory. Others will see the big picture, they will see the white word behind the black shapes and be able to do this exercise easily.
And when they complain that it’s not fair?
Well, that’s LIFE isn’t it! (try seeing the word in the shapes if you have not done so yet)
3. What you are being asked to do? (what do questions mean? Exam paper interpretation)
“You know all the words and you sung all the notes, but you never quite learned the song she sung”
Students need to know what they are being asked. They must know the difference between the words used in questions. Calculate, state, and explain. All have very specific and very distinct meanings. You need to know what you are being asked if you want to give the answer. But not only that, you need to be able to look at the question structure and the marks, is it a 2-part question, with 4 marks? How are these marks distributed? Why? We do lots of practice marking their own questions, marking questions for others. Writing questions ‘in the style’ of an examiner for this topic. And definitely, definitely looking at exam mark schemes and examiners reports. We identify the straightforward questions. Those that you see and know just what to do, and hopefully can then do it.
4. What not to learn
How do you introduce the specification to the students? Students need to know if something is a novel, maybe ‘one off’ problem. This gives you license to have a guess at it. Otherwise, it is reasonably familiar, we’ve done it and you should know how to approach it.
Also students should be able to track their progress through the course, and through their revision. To do this they need to know how big ‘all of it’ is. I adapt and chop and colour code parts of the specification, but I use the same source material throughout.
I’ve blogged about mathitude a lot recently. It’s my fifth column. Though actually it is my most important. You can train a monkey to jump, or a robot to scan for predetermined values, but students need mathitude if they are to be mathematicians. Read more in my blog, but this is how you help students to be more… creative, curious, celebrating of mistakes, communicative, supportive, humorous, resilient, and valuing of effort and feedback. If you can get this right, then you can build the other 4 columns around it.