In the extension from the use of natural numbers with zero to integers, i.e. the introduction of directed numbers including negative numbers, much experimental work is now being done with the use of mathematical structure. Some attempts are being made to give this as the initial treatment at about the age of 12, and some teachers are getting their children very interested and consider it a correct method. For other children the formal treatment will come later, when they are more mature and begin to query the rules they are using. This may be when they are starting to work ahead of their O level syllabus, the beginning of a more advanced course with work on groups. It could give work for those doing some mathematics when they are beginning to specialise in some other subjects and want to try to understand more about the mathematics they have learnt.