See Piaget's concrete operational stage [1] of human development: "Abstract, hypothetical thinking is not yet developed in the child, and children can only solve problems that apply to concrete events or objects."
In other words, you can only push the mathematical thinking as far as the developmental stage of the child allows you to. Memorization helps though.
My son is 6. He doesn't know the multiplication algorithm, but he does know that 2 x 2 = 4 or that 3 x 4 = 12. That's sufficient for him to do discoveries of his own. 3 x 4 = 3 x (2 x 2) ! Picture that!
In other words, you can only push the mathematical thinking as far as the developmental stage of the child allows you to. Memorization helps though.
My son is 6. He doesn't know the multiplication algorithm, but he does know that 2 x 2 = 4 or that 3 x 4 = 12. That's sufficient for him to do discoveries of his own. 3 x 4 = 3 x (2 x 2) ! Picture that!
[1] https://en.wikipedia.org/wiki/Piaget's_theory_of_cognitive_d...