Students spend most of their time assenting to what other people assert mathematically. This does not imply that they have blindly accepted it; indeed they may have worked hard in order to agree with it. But agreement is not the same as understanding. If they are to make mathematical sense themselves then they need to be able to assert things for themselves. They need to use technical terms with facility to express their ideas. In particular when students come to apply a theorem or technique they often fail to check that the conditions for applying it are satisfied. We conjecture that this is usually because they simply do not think of it and this is because they are not fluent in using appropriate terms notations properties or do not recognise the role of such conditions
