Constructing shared mathematical meanings in the classroom with digital artifacts that simulate real-world phenomena

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.