The teaching of numerical extensions: the case of negative numbers

Some results of a study on the teaching of negative numbers are presented. Attention is concentrated on a unified view of the teaching of numbers. This ideais based on three dimensions of the numerical knowledge: abstract, contextual and number line. The research was carried out with 127–13-year-old students and is focused on the identification of addition and subtraction, the use of the number line, additive problem solving and the possibility of following several sequences of numerical extensions. Results show the importance of previous ideas on positive numbers and how these ideas influence the knowledge of negative numbers. Also included are the resolution procedures used by the students for additive problems. Interviews with 11 students allow analysis of their different levels of understanding of the objectives of the experience.