Additive Conceptual Field: a study on elementary school teachers

Abstract This article discusses the results of a doctoral thesis entitled: “The teaching of additive structures among elementary school teachers.” It aims to identify and understand the contributions associated with the undertaking of a study of the Additive Conceptual Field in mathematics learning of elementary school teachers who participated in a discussion group. The research adopted a broadly qualitative approach, in which quantitative data was also considered. The analyses were based on the resolutions of problems administered to students, problems produced by teachers and those drawn from mathematics textbooks used in the school, as well as data collected during group discussions. The results indicate that, during the study, the teachers amplified their perspectives on the nature of problems associated with the additive field, producing a balanced quantity of problems in the categories: composition, transformation, and comparison.摘要 本文探讨题为《小学教师的加法结构教学》的博士论文研究成果。本研究旨在识别并理解参与讨论小组的小学教师在数学学习中开展加法概念域（Additive Conceptual Field）研究所获得的相关贡献。研究采用以质性研究为主、同时纳入量化数据的研究路径。分析基于三类素材：施测给学生的问题解答、教师自主创编的习题以及取自校内现行数学教材的题目，同时结合小组讨论过程中收集的相关数据。研究结果表明，在本次研究期间，参与教师拓宽了对加法概念域相关问题本质的认知视角，且能均衡产出组合、变换、比较三大类别的习题。