Digital technologies as a means of accessing powerful mathematical ideas. A study of adults with low schooling in Mexico

摘要

This paper derives from a study which main purpose was to investigate how a group of adults with low schooling can have access to powerful mathematical ideas when working with activities that involve the use of technology resources and that take into account the adults' previous experience with mathematics. Specifically, adults' previous experience with area calculation was considered. Principles of the Theory of Didactical Situations (TDS) formulated by Brousseau guided the study design, and Pick's theorem was recreated in a dynamic digital setting, with which it is possible to calculate the area of regular and irregular polygons. In this approach, intuitive notions of area and perimeter are resorted to, seeking to promote the experience with powerful ideas such as 'the generality of a method', 'realizing the existence of different methods used for one and the same end' and 'realizing that each method possesses advantages and limitations'. Analysis of interview protocols from three noteworthy cases (which include both adults' work in the digital setting and their discussions with the researcher) suggests the presence of powerful underlying mathematical ideas, such as the idea of generality and the power of a method and the features of the constituent elements of a geometric figure that are involved in calculating its attributes, attributes such as area.