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Tackling mathematics revision
By David Hanson
24 Aug

Revision! The word, usually associated with the realisation that an examination is imminent, can bring on feelings of apprehension, and even panic if the available time is short.

‘Where do we start?’ Well, that is the easy part! What can be much more difficult to determine is ‘Where do we finish?’ Where to start can be the same for all children, but where the revision finishes will vary from child to child, depending on a number of factors, not just when the syllabus for the intended examination has been revised.

It is assumed that you will have a good revision guide and supplies of paper.

So, where do we start? I think it a good plan to start with the lowest of the six levels of 'Bloom's pyramid' for mathematics and then progress steadily upwards through the levels.

Bloom Level 1:  Remembering (Knowing)
I believe that there are two essentials here:

1. Reading through a comprehensive glossary (such as that in the Galore Park ISEB Mathematics 13+ Revision Guide) can provide a very useful reminder of key words. Using these key words as a basis for questioning can be most helpful and each glossary entry can provide at least two questions.

Example: Acute angle

Question 1: "What is an acute angle?"
Question 2: "What name is given to an angle measuring less than ninety degrees?"

Admittedly, these are very simple questions, but considering the whole glossary, this exercise will revise, thoroughly, the basic knowledge that is essential before progressing through the mathematics revision.

2.  Practising recall of basic multiplication facts at speed.

A jumbled 3 to 9 (or better 3 to 12) multiplication square, of the type below, should be attempted regularly, with the time recorded.

 
 

  X

6

4

8

5

9

7

3

8

 

 

 

 

 

 

 

4

 

 

 

 

 

 

 

7

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

5

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

9

 

 

 

 

 

 

 

 

You may be surprised how this exercise will increase speed, accuracy and, above all, confidence. Ability in this does not make a child a mathematician, but it will certainly be a significant factor in examination success.



Bloom Level 2:  Understanding (Comprehension)
Following on from Bloom Level 1, a child should be able to explain how, and why, a process works.
Examples:
Why is the sum of the exterior angles of a polygon always 360 degrees but the sum of the interior angles varies according to the number of sides of the polygon?
Why do the numerators need to be the same when adding and subtracting fractions?


Bloom Level 3:  Applying
Here we move on to the application of the knowledge and skills to the solving of problems. It is important to know which method to use from a variety of strategies, and decision making can play an important part in answering examination questions.

It is possible for an unprepared child to race off along an inappropriate path and, sadly, on occasions, along no path at all!

Children should be able to explain what they have done, and why.
This might be the best time to try a few questions from books of practice questions or past papers.


Bloom Level 4:  Analysing
In the light of experience from applying the knowledge and skills, it is a good idea to reflect on the progress so far.

  • Would there have been a better way to tackle a particular problem?

  • Would it have helped to break the problem down into simpler parts?

  • Would rearranging things have been helpful?

Looking at a problem in a different way can lead to a more efficient solution.


Bloom Level 5:  Evaluating
Children can be asked to make a general rule, for example with number or spatial patterns.

They may be asked to draw conclusions, for example by comparing two sets of data.


Bloom Level 6:  Creating (Synthesis)
Children may be expected to do some original, creative thinking and come up with new ideas.

Bloom Levels 5 and 6 are sometimes reversed, or placed side by side, and these may be more appropriate for CE Level 3 and Scholarship candidates, but this is where mathematics can become more exciting. It can be very satisfying for a child to make up an examination question.


So, where do we finish? Of course, revising all the topics in the current syllabus for the intended examination level is important and it is probably a good idea to progress just a little beyond the basic requirements, so that the examination questions may seem, reassuringly, well within the child's capability and experience. Scholarship candidates can show 'flair' and an insatiable appetite for mathematics. For these children, there is no finishing line and they will be carried forward by a momentum of their own. For children who find mathematics a struggle, reliable recall of knowledge, confidence and competence in basic number work, and understanding of important processes, will be the main focus of attention in revision. This should provide children with the resources and confidence to tackle problems, but I think it is very important to have realistic expectations and it is essential that any possibility of causing confusion is avoided.

Revision can, and should, be fun. Good luck!
 
 
 
 Many thanks to David Hanson, author of a number of Galore Park Maths textbooks and revision resources.
You can see a selection of his books here

 
 
 
 

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