Developing argumentation in mathematics: The role of evidence and context

Abstract

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 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: 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. 3Data 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 understanding...

Research Trends in Science and Mathematics Education in South Korea 2014–2018: A Cross-Disciplinary Analysis of Publications in Selected Local Journals

“…There are examples of cross-fertilization in the opposite direction. Wells (2014) is an example where argumentation research in science education informed a mathematics education project. Problematizing the focus of argumentation in MER on formal logic to "arrive at a correct answer" (p. 2), she attended to the power of argumentation in supporting ill-structured, ambiguous, and open-ended problems in mathematics.…”

Task design for online learning: the case of middle school mathematics and science teachers

“…The situation of argumentation included three types of argumentation: argumentation during the teacher's introduction of the topic, argumentation during students' investigation of mathematical or scientific ideas, and argumentation investigated through technological programs. Wells (2014) argued that it is possible to focus students on the importance of quality evidence if argumentation structures and practices are introduced, and this could lead them to become more interested in math content.…”

Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom

“…Translating these into an argumentation-based inquiry classroom, normative practices would focus on having a shared goal of authentically responding to the inquiry question, generating a legitimate and justifiable solution, being explicit about the evidence and process of solution, anticipating critique, and privileging expectations to think and reason mathematically. The use of mathematical evidence takes on particular meanings in each stage of an inquiry (Wells, 2014). In the initial stages, students imagine a possible outcome and attempt to consider what evidence may be needed to respond to the inquiry question.…”

“…Scaffolding classroom talk in small group and whole class discussion is a key concern for classroom-based inquiry because of its emphasis on sense-making (Brown et al, 1989;Goos, 2004), collaboration (Quintana et al, 2004), and the need for making thinking visible (Wells, 2014;Linn, 2000). Elaborating on the research of Brown and his colleagues (1989), a scaffolding end-goal of handover to independence in an inquiry-based environment would focus on students' confidence to use peers as social and cognitive resources.…”