what does primary stage mean? 6-10 year olds?
at that age I recommend just getting them to master the basic skills. And to practice reading problems and translating them into mathematical computations.
real mathematical thinking for high school or junior high students should involve thinking about how we measure various quantities, i.e. what do we mean by length, area, volume.
some logical principels should be learned, such as the difference between "if A then B", and "if B then A". This seems obvious, but it is not. most high schoolers think that solving x -y = 4, and x+y = 2 is done by adding the equations, and concluding that 2x = 6, so x = 3.
they do not realize that this reasoning shows only that 3 is the only possible solution, not that it actually is one. I.e. they do not distinguish between "if there is a solution, then it equals 3", and "if x = 3, then this is a solution".
this becomes more important in exampels like sqrt(x-2) = -3, so x-2 = 9, so x = 11. i.e., assuming sqrt(u) means the non negative one as usual, then x = 11 is actually not a solution of the problem.
