Your calculating is improving and you actually like it. We play with numbers together. Two times ten is twenty. Six plus five is eleven. Ten minus 2 equals eight. It is all very playful. You learn how to figure out calculations by making drawings of dots, lines, squares on the whiteboard. You don’t just learn what the outcome of a calculation is, you learn how to prove it with confidence.
Don’t worry, we won’t plough through Bertrand Russell and Alfred North Whitehead’s Principia Mathematica in its entirety. The most fundamental proof that one and one equals two is indeed rather complicated and requires many of its pages. For the sake of the not very rigorous math education I will give you, we are just going to assume it.
But I won’t let you off the hook all the time! When we get to square numbers and, for example, you observe a pattern when you make a series of the difference between to adjacent squares, (1, 4, 9, 16, 25, 36, 49, 64) => (1, 3, 5, 7, 9, 11, 13, 15) it will not be enough. We will prove why the pattern is there. I will teach you about prime numbers and some of the wonderful maths that involve them, something I learned much too late in the development of my numeracy because I was subjected to a primitive form of rote-learning that lacked inspiration or creativity, the kind of learning that destroyed so many children’s appetite for numbers and mathematics.
I am already very proud when you can teach me that six plus six equals twelve and you can also draw a 3 by 4 square to make twelve.