Tracing the change in discourse in a collaborative dynamic geometry environment: From visual to more mathematical

Abstract

In this paper, we investigate what appears to be an intermediate developmental stage in geometrical thinking according to Sfard's commognitive framework. More specifically, we examine the change in three middle-school students' mathematical discourse as they worked on a geometry construction problem within a virtual collaborative dynamic-geometry environment. We trace how their word use, use of visual mediators, and routines changed character during an hour-long collaborative problem-solving session. Our findings indicate that students gradually moved from a visual towards a more formal discourse --one that is primarily characterized by a routine of constructing dependencies. We conclude that interacting with expert interlocutors may not be the only path towards advancing one's mathematical discourse; this process may also take place within a computer-supported collaborative-learning setting. Thus, collaborative dynamic geometry can be viewed as an effective material condition for learning geometry.

Towards an ecological-dynamics design framework for embodied-interaction conceptual learning: the case of dynamic mathematics environments

“…Both the Geometer's Sketchpad and Cabri geometry have been developed to encompass other topics in the mathematics curriculum, and their software has been adapted for implementation in various platforms and devices. A more recent and widely used xDME, GeoGebra (Hohenwarter et al 2009), includes the following features-it is: free and open-source; operable from desktop computers, tablets, and smartphones; translated into 63 languages; integrated into other technological systems, such as the Virtual Math Teams, for remote collaboration (Stahl 2009;Oner 2016); and equipped with automated formative assessment (Olsher et al 2016).…”

Building community together: towards equitable CSCL practices and processes

“…In the first such article, “Data Wrangling Practices and Learning with Aggregated Data in Talk-in-Interaction”, Shiyan Jiang and Jennifer Kahn offer a timely investigation of collaborative sense making regarding data representations, building on past CSCL work in which students similarly worked with interactive visual representations (Ingulfsen et al 2018 ; Davis et al 2015 ; Oner 2016 ). This paper delves deeply into the sense making processes students engage in as they work with novel, interactive data visualization tools that enable them to interact with representations of their respective family histories.…”

An inferentialist account of students’ collaboration in mathematics education

“…To examine and evaluate collaboration as a process, there have been some studies that used at least one framework from the cognitivist perspective (individual) and one from the social perspective (e.g., Mueller et al 2012;Oner 2016;Watson and Chick 2001). Yet, the focus in these studies was predominantly on one facet of collaboration.…”

“…Research has found that collaboration in the mathematics classroom can be a successful approach to foster mathematics learning. A host of positive outcomes that include higher achievement (Melis et al 2010;Oner 2016), greater effort…”