E1) From your experience, and what you have studied so far, by which age would-you expect an average child to be ready to acquire the following concepts?

i) Simple classification,

ii) Conservation of length,

iii) Commutatively of multiplication, i.e., ab=ba for any two numbers a and b,

iv) time,

v) chance and probability

The final stage of logical development occurs at the post-primary age, that is, 11 years and above. In this stage a child becomes capable of using formal operations. She is now capable of using words or symbols to denote quantity or objects. The child can now work with hypothetical statements, and explore logical relationships between statements. The ability to cope with abstractions such as concepts of proportionality, variables and algebraic equations depends on how well developed the child's formal operational thinking is.

The problem with learning mathematical concepts is that concrete references are generally not made available to help primary school children learn them. The methodology of primary school mathematics teaching, as practised today, is more appropriate for a formal operational child. But, what the child requires is concrete and meaningful learning experiences for grasping mathematical concepts and skills.