Activity Theory Research Papers - Academia.edu (original) (raw)

In this paper, I present and discuss findings from a research study the aim of which is to investigate the activity of proving as constituted in a Cypriot classroom for 12 year old students. Through Cultural-Historical Activity Theory (CHAT), the influence of research literature, curriculum prescriptions, the students and critically the teacher is documented. The evolution of objects, in particular the aims of the teacher, and other components in the activity systems is traced. Perceiving the mathematics classroom as a nested activity within educational context levels, this paper considers the role of the broader social context in which this classroom is situated. Theoretical framework. It is now acknowledged that proof and proving should become part of students' experiences throughout their schooling (Hanna, 2000; Stylianides, 2007; Yackel & Hanna, 2003). It is also argued that argumentation, explanation and justification provide a foundation for further work on developing deductive reasoning and the transition to a more formal mathematical study in which proof and proving are central (Yackel & Hanna, 2003). But what is meant by proof and proving? Mathematical argumentation is a discursive activity based on reasoning that supports or disproves an assertion and includes the exploration process, the formulation of hypotheses and conjectures, explaining and justifying the steps towards the outcome and the proof of the statement. Thus, proof is at the core of mathematical argumentation, as a justification, an explanation and a valid argument. Research has responded to the need to conceptualize proof and proving in such a way that it can be applied not only to older students but also to those in elementary school (Stylianides, 2007). The challenge remains however to understand how proof and proving is shaped by the practices in the mathematics classroom. This is in accordance with Herbst and Balacheff (2009), who argue that the focus should not only be on proof as the culminating stage of mathematical activity, but also on the proving process and how this is shaped by the classroom environment. Thus, in understanding how proving is constituted in the classroom, a wider network of ideas is required as these ideas no doubt have an impact on how proof in the narrow sense is constituted. To address this issue, I refer to pre-proving, that aspect of mathematical reasoning that might nurture proving. What are the roots of proving? The purpose of this study is to investigate proof and proving in the naturalistic setting of the classroom and the way the structuring resources of the classroom's setting shape this process. Instances of students proving statements have been identified in this classroom community but instances where the argument was not in the conceptual reach of the classroom have also been identified. However, this study also points to those aspects of reasoning that appear to have the qualities of proving, even though they may not be proving in themselves. That is, analyses of video-recorded whole class discussions show how processes of explaining and exploring are key subsystems within the central activity of proving as they provide a key pathway, which often includes defining. Thus, pre-proving refers to those elements that direct mathematical reasoning towards the ultimate goal of formal proving, namely exploring, explaining,