The development of quantitive reasoning

Numbers have two types of meaning: a referential meaning, characterised by the use of numbers to represent quantities and relations between quantities, and an analytical meaning, which is intrinsic to the number system. Each of these meanings relates to a specific form of mathematical knowledge, quantitative reasoning and arithmetic, respectively. After discussing the difference between these two forms of knowledge, I will present in this talk a brief synthesis of research on the development of quantitative reasoning.