ABSTRACT
The mathematics that children learn is an interesting mix of universal principles, such as inferences, on the one hand, and inventions, such as counting systems, measuring systems, trigonometry and calculus, on the other. This combination is always a significant one in developmental psychology. Where there are universals, it is possible (though not necessary) that children do their learning for themselves without much help from anyone else: some of their knowledge of these universals may even be innate. Inventions, in contrast, are unlikely to be re-invented by each generation of children. They have to be communicated to the next generation: they have to be taught. So, mathematics learning is a suitable case for treatment in a book about Piaget and Vygotsky, since it raises the two central issues associated with these two giants’ theories— the development of logic and the transmission from one generation to the next of cultural inventions and achievements.
