Carol Vorderman's report on maths has the excellent idea of separating the arithmetic needed for adult life and work from the more abstract pure maths that is needed for other purposes. Unfortunately, it doesn't say enough about how skills in arithmetic develop, or about how they are best taught.
Above all, I can find no mention of multiplication tables. After accurate addition and subtraction, multiplication tables are the key to accurate calculation. Without them, people can only add and subtract one digit at a time. How tables are best learned, and their contribution to calculation, requires research. The reason we have no research evidence is that large numbers of academics don't consider arithmetic to be the basis of mathematics, and don't consider tables to be important. They are wrong, and we need some proper investigation of the issue.