Designing and Investigating Dialogue-Intensive Online Math Videos

• In Event: 29.027 - Designing Digital Environments to Support Mathematical and Scientific Reasoning: Theoretical and Disciplinary Perspectives

Abstract

Despite the enormous number of mathematics videos available online, there is surprising uniformity in use of talking heads or hands to demonstrate step-by-step procedures using a traditional pedagogical approach (Bowers, Passentino, & Connors, 2012). A review of online mathematics videos revealed very few videos created for K-12 student learning (versus for professional development with teachers) that included dialogue with children (Lobato, Walters, & Walker, 2016). In these videos, either children mimicked the script of a traditional teacher, or animated characters were used to discuss how to resolve dilemmas. Thus, one design principle guiding the development of our videos was to feature a pair of secondary school students engaged in dialogue, as characterized by Alrø and Skovsmose (2004) as a conversation that involves the quality of inquiry, meaning that there is an interaction that aims to generate new meaning or to open up different ways of experiencing things.
This design principle is framed by the theoretical assumption that dialogue is central to learners’ enculturation into forms of academic argumentation and that it mediates thinking (Vygotsky, 1978). Although dialogue is well accepted as an important tool for learning, the educational usefulness of watching dialogue has been a matter for debate. There is some evidence that students who vicariously observe a dialogue outperform those who observe a monologue (Craig, Sullins, Witherspoon, & Gholson, 2010; Fox Tree, 1999; Muller, Bewes, Sharma, & Reimann, 2008). One the other hand, in one of the few such studies in mathematics, the vicarious learners (VLs) did not use the video spontaneously when asked to solve a related task (Kolikant & Broza, 2011).
In contrast to the typical use of videos lasting an hour or less, the study presented in this paper examined a pair of 9th graders as they interacted with 8 video lessons over ten 90-minute sessions (see Figure 2). The students were from a diverse high school (87% free and reduced lunch, 46.2% English learners) in a southwestern U.S. city. The conceptually-oriented videos focus on geometry-algebra connections for parabolas, were grounded in prior research, and resulted from iterative cycles of design and feedback from learners.

Research analysis drew upon thematic analysis from systemic functional linguistics (Herbel-Eisenmann & Otten, 2011; Lemke, 1990) to investigate relationships between VLs’ and talents’ (the students in the videos) use of language, inscriptions, symbols, gestures, and ways of reasoning. We report regular appropriation of notational methods, reasoning strategies, and language. Additionally and surprisingly, the VLs personally identified with the talent (e.g., each VL declared that she was more like one of the talent), were able to predict some of the talents’ moves, and appeared to engage in a two-way conversation with the talent (e.g., by wanting to tell the talent when they figured out something that the talent struggled with).
Although vicarious learning is not a replacement for direct participation in dialogue, the study provides some support that watching dialogues can facilitate learning by making sources of confusion visible, modeling ways to resolve confusion, and providing useful resources such as inscriptions and ways of reasoning.

Authors

• Joanne Lobato, San Diego State University

• Carren Senn Walker, San Diego State University

• C. David Walters, San Diego State University