From Experiences in a Dynamic Environment to Written Narratives on Functions

Abstract

This study focusses on high school students' written discourse about their experiences in a dynamic interactive digital environment in which functions were represented in one dimension, as dynagraphs, that are digital artefacts in which the independent variable can be acted upon and its movement causes the variation of the dependent variable. After the introduction of the notion of Dynamic Interactive Mediators within the theory of Commognition, we analyze and classify students' written productions describing their experience with the dynagraphs. We present this classification as a tool of analysis that allows us to gain insight into how their writing reflects the temporal and dynamic dimensions of their experience with the dynagraphs. This tool is used to analyze 11 excerpts; finally, epistemological, cognitive and didactic implications of this tool are discussed. ManuscriptClick here to access/download;Manuscript;RevisedPaper_FINAL.docx Click here to view linked References

Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments

“…A constant function is represented with the independent variable that can be dragged by a direct motion and the other variable standing still. The relations existing between the mathematical properties of a function and the properties of its dynamic representation are many and they are very deep from a mathematical point of view, see, for example, [37]. In terms of the Theory of Semiotic Mediation [24], the artifact, that is constituted by dynamic graphs, embeds a mathematical knowledge and it is linked to artifact signs (signs related to the movement of points on the screen) and mathematical signs (signs related to the functions' properties expressed within a mathematical theory).…”

To tell a story, you need a protagonist: how dynamic interactive mediators can fulfill this role and foster explorative participation to mathematical discourse

“…This is particularly true for findings from research conducted in the context of low achievement in mathematics. Recently, a few studies focusing on students' learning within technological environments have started adopting Sfard's (2008) discursive approach (e.g., Lisarelli, 2019;Antonini et al, 2020;Ng, 2016;Sinclair & Heyd-Metzuyanim, 2014) that I introduce in the next section. These studies have started to unveil discourse that develops within such environments, especially in the mathematical context of functions.…”

“…This study builds on research that has used the discursive approach to study digital visual mediators-or DIMs, for short-in students' discourse on functions. Ng (2016) has introduced a distinction between static and dynamic mediators, which Lisarelli, Antonini and Baccaglini-Frank (Antonini et al, 2020;Lisarelli, 2019) have further elaborated, reaching the notion of dynamic interactive mediators (DIMs), digital objects constructed within technological environments that can be manipulated and that give immediate feedback based on such manipulations, in the form of dynamic change; and that for experts in mathematics are realizations of mathematical objects (or aspects of them). Antonini et al (2020) have suggested that DIMs can enable forms of discourse about functions that are not yet formal but that contain meaningful narratives that an expert can "translate" into canonical mathematical discourse.…”

“…Realizations, like graphs and draggable points and lines, can become dynamic interactive mediators (DIMs) (Antonini et al, 2020), programmed by experts by design to react to inputs in ways that are consistent with those expected of a realization of a certain mathematical object. Moreover, there is a well-defined repertoire of admissible actions that an individual can carry out.…”

“…This last case is typical of experts. Antonini et al (2020) present examples of students' written discourse about DIMs that for experts are realizations of functions, showing how such discourse can be "translated" into experts' discourse. For example, students write: "B's position is static while a [A] can move around" (Antonini et al,p.…”