Abstract

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.

中文翻译：

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数字技术是获取强大数学思想的一种手段。对墨西哥低学历成年人的研究

摘要

本文源自一项研究，该研究的主要目的是调查一群低学历的成年人在从事涉及利用技术资源的活动并考虑到成年人以前的数学经验时，如何获得强有力的数学思想。 。具体而言，考虑了成年人以前的面积计算经验。布鲁索提出的“教学情境理论”（TDS）原理指导了研究设计，并在动态数字环境中重新创建了匹克定理，从而可以计算规则和不规则多边形的面积。在这种方法中，我们采用了面积和周长的直观概念，力图通过“一种方法的普遍性”之类的有力思想来促进体验的发展，“认识到存在用于同一目的的不同方法”和“认识到每种方法都具有优点和局限性”。通过对三个值得注意的案例（包括成年人在数字环境中的工作以及与研究人员的讨论）的访谈协议进行分析，表明存在强大的基础数学思想，例如通用性思想，方法的功能和功能计算几何图形的属性，面积等属性所涉及的构成图形的元素。