Contribution
Description: The study is an inquiry into the structure of argumentation process triggered and mediated by paradox in a community of mathematical inquiry. Its theoretical approach is based on Vygotsky's theory of social cognition, which in turn is grounded in the broader framework of hegelian and Marxist dialectical theries, and systems theory. The study spans three areas of scholarship and research:
1) the use of paradox-resolution as an organizing activity for classroom discusions;
2) collective argumentation and its structure; and
3) (1) and (2) performed in a pedagogical context characterized by communal dialogical inquiry.
Methodology: It is primarily a qualitative study with a quantitative component. The primary data consists of 19 transcripts of classroom discussions in a community of inquiry format in which 21 fifth grade students participated over a period of one year. The research question is concerned woth the development of students' argumentation as a result of thinking together about paradoxes, and with the particular characteristics of argumentation as it is observed in relation to to collaborative discussions. The data analysis is based on the grounded theory approach, executed in both qualitative and quantitative modes. The qualitative mode includes analysis of the macro-level of the argumentation process. The quantitative analysis focuses on eight of the transcribed conversations in comprehensive detail, in an effort to grasp the argumentation process on a micro-level. The coding process is carried out with the software product NVivo.
Conclusions: The study found that different types of paradoxes provided for different structures of argumentation. Further, it was concluded that paradox fostered what was referred to as integrated reasoning in the process of vcollective argumentation-a multidimensional pattern which incorporates formal, informal, interpersonal, and philosophical (metacognitive) reasoning. In addition, the study performed a quantitative analysis of the development of argumentation structure and its transformation over the course of the discussions. The changes registered in argumentation patterns were interpreted as an outcome of a dialectical interplay between the macro- and micro-level resulted in qualitative shifts on the macro-level of the argumentation structure.
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