Acting is learning: focus on the construction of mathematical concepts

The purpose of this paper is to focus on the nature of the thinking processes supporting pupils' construction and understanding of mathematical concepts. We assume that interaction with reality plays a crucial role in learning. In particular, human perception and action and, more generally, interaction with artefacts, are very important for mathematics learning and doing mathematics. We analyze the construction of meanings related to the concept of function, as developed through a teaching experiment carried out with pupils of 11- to 12-years-old attending the fifth (the last year of primary school) and sixth grade (the first year of middle school) of an Italian school. The experiment started in the fifth grade and lasted into the sixth. Our main focus is the analysis of the 'schemes of use' (in the sense of Rabardel) activated by the pupils during the activities. In particular, we are concerned with the passage from perceptuo-motor activities to their representations, both in the paper and pencil environment and on the spreadsheet. © 2005 University of Cambridge, Faculty of Education.