Cardinal rules for putting things in order

Q: This week I have included letters from three readers, all relating to the same topic but for different year groups. The first letter gave rise to the creation of some software to support learning about subitising; the others were from readers who agreed to trial this software with their pupils. The software was created for general use but it has become apparent that it is also useful for students with special needs.

* Please could you tell me what is meant by subitising numbers and what is the difference between cardinal and ordinal numbers? I have been supporting a Year 3 boy and he doesn't seem to get numbers at all. Have you any ideas?

* I teach a Year 2 boy who is still struggling with number recognition. I have a few other pupils who may also benefit from any ideas.

* I teach in a special school and teach numeracy to Years 7 and 8.

Some of the pupils I have had for two years and it looks like I will be keeping them in my group next year. I have tried every method I know to get them to recognise numbers to 20 with little success. They have real problems counting up to 10 objects and recognising written numbers too.

A: A cardinal number tells you the quantity of a group, the counting numbers. For example, in "two horses", the "two" is the cardinal representation of the group of two horses.

An ordinal number demonstrates rank or position - first, second, third... Have a look at the arrangement of dots below. What is the cardinal number associated with the whole group?

Think about how you did it: did you count each individual dot or did you "chunk" the dots into groups and then add them together to get 20? This chunking process is called subitising - recognising arrangements of groups of objects as a number. Research shows that, for most people, seven is about the largest number that can be thought of as a single group. Being able to subitise contributes to developing higher maths and problem-solving.

Look at this example. The dots make a pattern that is instantly recognisable as five from playing cards and dice. But there are other arrangements where the same number is made from different groupings.

The question is: how do you get pupils to build a memory of these visual pictures? The Jigsaw software uses jigsaw puzzles which pupils can complete by grouping the same number in different ways. Here is a partially completed puzzle, can you see what number it is?

I tried these jigsaws with a boy who had just turned three. He got very excited about completing them. I didn't think he would be old enough and was very surprised when he finished. What was important, I found, was to say the number on completion and to count the objects in the picture with the learner.

When the player is happy with the subitising, it is time for arrangements of objects, as in this example with the fish. When I worked with the young boy, he traced the number with his finger on the screen when he had completed the puzzle.

The third letter writer suggested that we link the arrangements in the subitising to the cardinal number, so when the puzzle is finished the number appears visually as well as being said. She also said that her children, who were working below national curriculum levels, "needed lots of support to complete the jigsaws despite being able to view the finished photo".

* Activities and more information:

* Journal of Vision reports research suggesting subitising deteriorates with age: www.journalofvision.org66783

* Hugh Beere created the software at my request to help with subitising and recognising the cardinal form of number with number bonds naturally integrated. He has kindly made five copies available free to the first five readers who email me.

* The full Jigsaw number software, and Jigsaw spelling, Jigsaw Shape and Jigsaw Money cost pound;5 for a single user licence and pound;10 for a whole-school licence from Tarquin Publications Tel: 01727 833866

* The number of the incomplete jigsaw mentioned earlier is eight.

Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.

Email your questions to Mathagony Aunt at Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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