Developing argumentation in mathematics: The role of evidence and context [thesis]

Jill Wells
Multiple potential benefits to the introduction of argumentation into classroom environments have been identified and documented, including the potential to extend teaching goals to emphasise cognitive and metacognitive processes, epistemic criteria and reasoning, as well as the enculturation of students into the practices and discourses of a subject. Argumentation structures and practices offer the means to focus students on the need for quality evidence, potentially encouraging students to
more » ... ging students to focus deeply on mathematical content. Much of the work with argumentation that has already occurred in mathematics is associated with justification of procedural choices to arrive at a correct answer. By contrast, mathematical inquiry offers the opportunity for students to engage in ill-structured, ambiguous problems that have neither a defined solution path nor a single correct answer. Thus there is great potential for argumentation to be effective in inquirybased learning environments. However, very little research has focused on argumentation practices of students undertaking inquiry of this nature. The study presented is thus exploratory; designed to both develop deeper understanding of Inquiry-Based Argument practices and possibilities, and to identify how students' developing use of evidence in argumentation could be understood and supported. Specifically, the study sought to address the following research questions: 1. What are key features of an Inquiry-Based Argument model as implemented in a primary (elementary) mathematics setting? 2. What signature elements of Inquiry-Based Argument can serve to guide children's mathematical argumentation? A design research methodology approach was utilised, with iterative cycles of inquiry and argumentation implemented in a single inquiry classroom of Year 4-5 students (n=27, aged 8-10). These cycles introduced the role of evidence, the structure of argument, and evidence and argument quality, to a class environment that embraced a knowledge building culture (Bereiter & Scardamalia, 1996) . Berland and Reiser's (2009) Goals of Argument and McNeill and Martin's (2011) Conclusion-Evidence-Reasoning Framework were used to guide the instructional approach which was modified progressively to meet the developing needs of the students. 3 Data were generated through videos of emerging classroom practices, interviews with students, student work artefacts, teaching notes, and observations over the course of ten months. A Grounded Theory Approach (Corbin & Strauss, 2008) was utilised for data analysis. The analysis identified several significant results of introducing Inquiry-Based Argument into the classroom: 1. Introducing argument practices enabled the ‗visibilising' of student thinking, increasing opportunities to develop and utilise cognitive conflict. 2. An increased focus by students on the need for quality evidence enables them to be able to put forth and negotiate arguments. In turn, these factors appear to enable students to: 1. Develop complex appreciation for argument structure, progressing from intuitive responses to development of qualified arguments. 2. Demonstrate understanding and appreciation of the critical role of evidence and evidence quality in the development of deepened mathematical understandings and argumentation processes and structure. Particular areas that presented difficulty for the students were observed throughout the unit and teaching and learning supports were noted as these offer potential for scaffolding argumentation development. Two tangible contributions from the research include a proposed model of inquiry-based mathematical argumentation, based on integration between Mathematical Knowledge, Argumentation Knowledge and Context Knowledge, and a detailed guideline for measurement of developing argumentation practices with young students in this context. While this research is limited in that it followed one class of students only, restraining the size of the research enabled a deeper analysis of the experiences of these 27 students. This research suggests that there is potential for argumentation to have a significant role in mathematics education and that it is certainly worthy of further research. 4
doi:10.14264/uql.2015.208 fatcat:ylrhtpbz7bclra5ep6gliwliea