This paper aims to give detailed insights of interactional aspects of students’ agency, reasoning, and collaboration, in their attempt to solve a linear function problem together. Four student pairs from a Norwegian upper secondary school suggested and explained ideas, tested it out, and evaluated their solution methods. The student–student interactions were studied by characterizing students’ individual mathematical reasoning, collaborative processes, and exercised agency. In the analysis, two interaction patterns emerged from the roles in how a student engaged or refrained from engaging in the collaborative work. Students’ engagement reveals aspects of how collaborative processes and mathematical reasoning co-exist with their agencies, through two ways of interacting: bi-directional interaction and one-directional interaction. Four student pairs illuminate how different roles in their collaboration are connected to shared agency or individual agency for merging knowledge together in shared understanding. In one-directional interactions, students engaged with different agencies as a primary agent, leading the conversation, making suggestions and explanations sometimes anchored in mathematical properties, or, as a secondary agent, listening and attempting to understand ideas are expressed by a peer. A secondary agent rarely reasoned mathematically. Both students attempted to collaborate, but rarely or never disagreed. The interactional pattern in bi-directional interactions highlights a mutual attempt to collaborate where both students were the driving forces of the problem-solving process. Students acted with similar roles where both were exercising a shared agency, building the final argument together by suggesting, accepting, listening, and negotiating mathematical properties. A critical variable for such a successful interaction was the collaborative process of repairing their shared understanding and reasoning anchored in mathematical properties of linear functions.

本文旨在详细探讨学生的代理，推理和协作之间的相互作用，以期共同解决线性函数问题。来自挪威高中的四对学生提出并解释了想法，对其进行了测试，并评估了其解决方法。通过描述学生的个人数学推理，协作过程和行使的代理能力来研究学生与学生的互动。在分析中，两种互动模式是从学生如何参与或避免参与协作工作的角色中产生的。学生的参与通过两种交互方式揭示了协作过程和数学推理如何与他们的代理机构共存的各个方面：双向交互和单向交互。四个学生对阐明了他们在协作中的不同角色如何与共享机构或单个机构联系起来，以便将知识合并在一起形成共同的理解。在单向互动中，学生与不同机构进行互动，作为主要代理人，领导对话，提出有时基于数学属性的建议和解释，或者作为次要代理人，由同伴表达和倾听并尝试理解想法。次要代理很少进行数学推理。两名学生都尝试合作，但很少或从未不同意。双向互动中的互动模式突显了双方合作的共同尝试，其中两个学生都是解决问题过程的驱动力。在共同行使代理权的情况下，学生扮演相似的角色，通过建议，接受，聆听和协商数学属性来共同构建最终论点。如此成功的交互的一个关键变量是修复他们在线性函数的数学属性中固定的共识和推理的协作过程。