Have you ever studied hard but had a crushing disappointment when you looked at the test paper and couldn’t answer most of the questions? You might think this is due to test anxiety but there is a more likely explanation. You might have been doing the wrong type of learning. The following diagram shows some of the different types of learning required for good marks.

If you are studying one of the Victorian VCE maths subjects, you will need to climb to the top of the pyramid and do all these types of learning. In fact, this is true of most subjects, particularly in VCE, vocational education and higher education.

Awareness

Awareness is a trap for people who reread the textbook and the teacher handouts a few times. The content makes sense and you develop a comfortable feeling of familiarity. Unfortunately, you haven’t stored anything in your long term memory, and you don’t notice it all fading away.

You have learned something when it is stored in your long term memory and you can recall it when you want to. To find out if it is in long term memory, you have to practise remembering it.

Learning what

You need to know facts, such as the equation of a circle or the multiplication tables in maths or the road rules when you are learning to drive. You need to know the theory of evolution or the concept of infection if you are studying biology. You should be able to describe and explain these concepts, facts and theories in your own words, or represent them graphically with a diagram, graph, timeline, flowchart or any of hundreds of other techniques. Learning involves reorganising or restructuring knowledge. You need to think hard about what you are learning.

If you can’t put something into your own words, or transform it into a picture or equation, then you probably don’t understand it.

Learning how

Learning is pointless if you can’t use it. Applying your knowledge involves carrying out procedures. Whether it is solving quadratic equations in maths, cooking a cheesecake or driving a car, aim to practise the procedures until you can do them without thinking. This is called automaticity.  Once a procedure is automatic, it is difficult to forget and takes real effort to change.

When practising maths procedures, check the answer after every question. This prevents you from automatically getting it wrong in the future.

Learning which

Imagine employing a chef who used the same procedure for every food, and served up roast turkey, roast soup, roast grapes and roast ice cream! People who can choose the appropriate procedures for a range of situations are much more desirable employees.  You learn how to pick the right procedures by practising with lots of different types of problems.

Interleave different types of problems when you study. This feels harder, but there is evidence that it improves test results.

Learning why

There is often more than one way to solve a problem. How do you choose? You might consider which is

• cheaper
• faster
• safer
• more compliant with regulations
• more fun
• more elegant (important to many mathematicians)
• easier
• more interesting
• more challenging

If you are studying maths, I recommend learning two ways of solving each type of problem.  Use one to demonstrate the knowledge the assessor wants to see, and the other to check you got the answer correct.

Making mistakes is a good way to learn why some procedures are inappropriate.

More information

References