I think of it like this - all of mathematics is a 'pattern' which can be created - we agree the ground rules of the aspects we are working with, we explore the unknown and we come accross new generalisable patterns - which we can then prove. This for me is mathematics. Negative numbers were developed from looking at positive numbers - start counting backwards 5, 4, 3, 2, 1, 0, then as we carry on taking away one we get -1, -2, -3, -4 and so on. Once we have discovered negative numbers we need to understand how to operate with them. Again we can start with what we know. Draw a multiplication grid with -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 along the top and the same down the right hand side. Fill in the part of the grid that you know for example 1 x 1 = 1. When you have filled in all the parts you know, use the pattern of the mathematics to find out what you don't know.
Another way in is to look at the history of negative numbers, how they were discovered. One of our RCs has a brillian history web site on mathematics, there may be something there. I don't think that we should ever let students 'accept' things - why can't they have the same joy of mathematics in discovering rules and formulas that the original mathematicians have - once they discover things for themselves they will always remember it - that is the beauty of being a mathematician.