This paper describes and examines students’ shared construction of meanings while learning about quadratic functions via digital artifacts that simulate real-world phenomena, like the motion of a ball on an inclined plane, focusing specifically on the role of the teacher in that construction process. The study follows the interactions of twenty 15-year-old students and their teacher during the completion of three sequential digital tasks, analyzing how these interactions promote the students’ ability to construct the mathematical meanings of the quadratic function. The study was guided by the theory of semiotic mediation, which treats artifacts as fundamental to cognition and views learning as the evolution from meanings connected to the use of a certain artifact to those recognizable as mathematical. The data analysis showed students progressing from the description of the real-world phenomenon toward a construction of the meaning of the quadratic function that models the phenomenon. While marking the “critical moments” in this progress, we analyze the communication strategies used by the teacher to facilitate it. Our research findings showed evidence that certain types of questions and the strategy “re-voicing” can be particularly effective in prompting students’ construction of mathematical meanings.

本文描述并检验了学生共享的意义建构，同时通过模拟真实世界现象（例如，球在倾斜平面上的运动）的数字人工制品学习二次函数，并特别关注教师在该建构过程中的角色。该研究跟踪了20名15岁的学生和他们的老师在完成三个连续的数字任务期间的交互作用，分析了这些交互作用如何促进学生构建二次函数的数学含义的能力。该研究以符号学调解理论为指导，该理论将人工制品视为认知的基础，并将学习视为从与使用某种人工制品有关的含义到可识别为数学的含义的演变。数据分析显示，学生从对现实世界现象的描述向建模该现象的二次函数的含义发展。在标记此进展中的“关键时刻”时，我们分析了教师为促进这一过程而使用的交流策略。我们的研究结果表明，某些类型的问题和“重新发声”策略可以特别有效地促进学生构建数学意义。