Meanings, representations and language: Fractions in three generations of textbooks for primary

Abstract

This article presents the results of a documentary research developed with the aim of highlighting valuable aspects and weaknesses of three curricular proposals for the teaching of fractions. The analysis is done by identifying the sub-constructs of the rational number considered in each opportunity, as well as the transition between informal (ethnomathematical) and technical-symbolic knowledge observed in the three official curricula and textbooks of the Mexican Primary Education used between 1960 and 2011. The approach is based, essentially, on the conceptualization of Thomas Kieren regarding: a) the sub-constructs that constitute a thorough knowledge of the fractions, and b) the desirable path between the informal knowledge and the technical-symbolic also suggested by this researcher. It is considered that the work provides a useful methodology to analyze the curricular proposals and the teaching of these numbers, it also highlights that it is pertinent to recover the lessons of the past if the interest is not innovation but the improvement of teaching.