Contour lines between a model as a theoretical framework and the same model as methodological tool
The flow of theoretical and methodological paradigms which determine the frames for research work in science and mathematics learning has become rich and more and more sophisticated. However, it seems that more than in the past, researchers today do not feel obliged to and/or satisfied with sticking to one methodological paradigm. Research trends in our area are nowadays characterized by flexibility and creativity in combining research methods and methodological tools, which fit the researchers’ theoretical framework and meet their goals and needs to explain and answer some ‘big questions’ emerging from their explorations (e.g. see the chapter by Saxe et al. in this volume). In this chapter I first discuss issues concerning the contour lines between the theoretical framework and the methods and methodological tools within the same research work. I argue that in more and more research work these boundaries are flexible and even a bit vague in the sense that the same scheme or model may serve as a theoretical framework in one piece of research, as a methodological tool in a second one, and as both of them in a third piece of research. I will discuss these issues via two examples, which illustrate dynamic relationships between theory and methodology in two different research domains of mathematics learning. In each example, the questions will emerge from analyses of the above relationships in a few research papers concerning a particular topic, looking at differences and similarities between theoretical and methodological frameworks. The first example is taken from research on argumentation in mathematics learning, and the second example is taken from research using the RBC+C model for abstraction in context.