I was asked to give extra lessons to a 5 year old boy who loves math (he says he likes 3 sports: football, swimming and math). However, I have never taught at this age and I am unfamiliar with the best theoretical way to proceed.
Hence, I would like some references on teaching at this age, particularly to gifted children.
EDIT: as requested, I did take a time with him and tried to assess what he knows. He is fluent in:
- addition, subtraction
- knows fractions (in a intuitive way, he knows nothing about the notation and relation to division)
- he knows that negative numbers are ok in math but cannot account for a 'real' thing. In his words "there cannot be -2 me's".
- he has great intuition: knowing there's not a largest number and that infinity isn't a number either.
- he has trouble with problems which don't have a "precise" answer- such as: "if I toss a die many times, which number will appear the most?", to which he replied "one", but could not justify why.
That's about it; as mentioned, I am not even sure how to properly assess what he knows, so everything helps.