This paper examines the existence and impact of theoretical mathematicalfoundations on the teaching and learning of whole numbers in elementary school inFrance. It shows that the study of the New Math reform–which was eventually itselfreplaced in the longer term–provides some keys to understanding the influence ofmathematical theories on teaching and learning. The paper studies changes related toplace value, a notion that was deeply impacted by the introduction of numerationbases other than ten in 1970, and their subsequent removal in the 1980s. What theauthor terms‘numeration units’(ones, tens, hundreds, thousands, etc.) and‘powers-of-ten written in figures’(1, 10, 100, 1000, etc.) are key tools for describing andunderstanding changes. The author identifies two theories that have formed the basisfor place value teaching in the twentieth century, and examines some aspects of theirinfluence. The paper also addresses epistemological issues in the relation betweenacademic mathematics and school mathematics, and highlights the role of units in theteaching of basic arithmetic

• The influence of theoretical mathematical foundationson teaching and learning: a case study of whole numbersin elementary school