The interaction between multimedia data analysis and theory development in design research

Abstract

Mathematics education researchers conducting instruction experiments using a design research methodology are challenged with the analysis of often complex and large amounts of qualitative data. In this paper, we present two case studies that show how multimedia analysis software can greatly support video data analysis and theory development in design research. The software can (a) act as a type of mould for organising large amounts of data; (b) contribute to improving the trackability and reliability of the research; and (c) support theory generation and validation. We propose an integrated model that elucidates the complex process of data analysis by showing how each of the components that are involved in the data analysis procedures feeds into the emerging local instruction theory. The model combines the intricate cycles of coding and analysing raw video data with the cumulative cyclic process that characterises design research in mathematics education. Our experiences with this model may support other mathematics education researchers in the development of thorough and empirically supported local instruction theories from complex qualitative analyses.Design research in mathematics education has both a theoretical and an applied purpose: theoretical in terms of coming to an understanding of mathematical thinking, teaching and learning, and applied in terms of using this understanding to improve mathematics instruction (Schoenfeld, 2000). As a result, researchers do not settle for answers that merely illustrate what works best. Instead, they use methods that both aim to understand why as well as how mathematics instruction works in practice (cf. Freudenthal, 1983;Gravemeijer, Bowers, & Stephan, 2003).What characterises the process of data analysis in design research is the interaction between data analysis and theory development. At a practical level, this interaction is illustrated in Jacobs, Kawanaka, and Stigler's (1999) cyclical process of analyzing video data. Oriented more towards theory development, Gravemeijer (2004) describes design research in terms of a cumulative cyclic process. In this paper, we propose to embed Jacobs et al.'s (1999) model into Gravemeijer's (2004) model for a more encompassing representation of the intricate interactive processes that are essential for theory development in design research. The significance of this integrated model is that it encompasses the steps that are necessary for keeping track of

Tool Use and the Development of the Function Concept: From Repeated Calculations to Functional Thinking

“…The data analyses started with organization, annotation, and description of the data with software for qualitative data analysis (ATLAS.ti 3 ; see van Nes & Doorman, 2010). Initially, the tasks in the learning arrangement served as the unit of analysis for clipping the videos.…”