This paper is part of a broader research initiative examining algebraic thinking. It presents a case study involving a 4 year-old female student, examining her functional perspective through individual work. Our interest lies in early childhood functional thinking. Specifically, our research objective is to describe how the child completed two tasks involving linear functions and their respective inverse functions. We posed questions related to specific near numbers, specific far numbers, and the generalizations themselves. We gathered data from her individual written work on the two tasks and from an individual interview. We analyzed the strategies she employed to generalize, the representations and generalizations she made, and how she established relationships between variables. We observed that she used pictorial and verbal representations to complete the proposed tasks and successfully achieved generalization. As a strategy, she counted drawings; however, when verbalizing her approach, she created groups of similar elements and innately distributed them into equal groups when working with the inverse function.

本文是研究代数思维的更广泛研究计划的一部分。它提出了一个案例研究，涉及一名 4 岁的女学生，通过个人工作研究她的功能观点。我们的兴趣在于幼儿功能思维。具体来说，我们的研究目标是描述孩子如何完成两项涉及线性函数及其各自反函数的任务。我们提出了与特定近数、特定远数和泛化本身相关的问题。我们从她关于这两项任务的个人书面工作和个人访谈中收集了数据。我们分析了她采用的泛化策略、她所做的表示和泛化，以及她如何在变量之间建立关系。我们观察到她使用图片和语言表示来完成提议的任务并成功实现了泛化。作为一种策略，她数着图纸;然而，在用语言表达她的方法时，她创建了相似元素的组，并在使用反函数时天生地将它们分配到相等的组中。