The two sequences of development be

The two sequences of development beginning with object and action are quite distinct. I therefore hypothesise that, rather than view growth in elementary mathematics as a single development in the manner of a neo-Piagetian stage theory, an alternative theory is to see two different developments which occur at the same time. One is visuo-spatial becoming verbal and leading to proof, the other uses symbols both as processes to do things (such as counting, addition, multiplication) and also concepts to think about (such as number, sum, product).