In the context of early algebra research and as part of a classroom teaching experiment (CTE), we investigated fourth grade (9- to 10-year-old) students’ justifications of how they performed tasks involving the functional relationship y = 2x. We related their written justifications (part of the task) to the task characteristics, which included various semiotic systems (verbal, numerical and alphanumeric, among others) and the demand of different type of justifications. The role of classroom discussion in helping express the functional relationship orally in more sophisticated terms was also investigated. The findings showed that students’ written justifications changed with the semiotic system involved in the task. Oral discussion helped students generalize in more sophisticated terms than in their written justifications, in which they omitted information or used less precise language.

在早期代数研究的背景下，作为课堂教学实验 (CTE) 的一部分，我们调查了四年级（9 至 10 岁）学生如何执行涉及函数关系 y = 2x 的任务的理由。我们将他们的书面理由（任务的一部分）与任务特征相关联，其中包括各种符号系统（语言、数字和字母数字等）以及不同类型理由的需求。还研究了课堂讨论在帮助用更复杂的术语口头表达功能关系方面的作用。研究结果表明，学生的书面理由随着任务中涉及的符号系统而改变。口头讨论帮助学生用比书面理由更复杂的术语概括，