Students who engage in mathematical arguments in classrooms take part in an important practice involving reasoning and justification. As a mathematical practice, argumentation involves using both conceptual and procedural reasoning to justify a claim. Even though argumentation can occur in discussions where one asserts and defends their claim orally or through a written format, the majority of the literature regarding argumentation in school mathematics has considered arguments only as they develop orally through whole class discussions. This study sought to describe the development of 8th grade students' written arguments and the teaching moves that supported the development of students' convincing arguments within two algebra units. To do so, a case study of teaching arguments was conducted in a low-tracked 8th grade classroom using a curriculum in which students were expected to support their claims in both oral and written work. Identifying promising teaching moves that supported students' argumentative writing required a scheme for categorizing written work according to their level of persuasiveness. Accordingly, I created a scheme by taking into consideration several relevant sources: Toulmin's model of argumentation (1978), Morselli and Boero's aspects of proof (2009), and Driscoll's (1999) definition of and criteria for arguments. The first has been used extensively when analyzing arguments as they occur in discussions in mathematics classrooms. The second considers three aspects of proof that students must understand in order to successfully write an argument: epistemological, teleological, and communicational. These three aspects aligned with Driscoll's criteria that arguments be tied to the original context, convincing, and inference-free. Combined, this resulting framework offers a tool to categorize students' written arguments and provides an important resource to teachers and researchers interested in promoting students' written arguments.Once students' written arguments were categorized with this new framework, I considered instructional moves that explicitly promoted students' written arguments. Specifically, I analyzed features of the writing tasks, how students responded to these features, and ways in which writing assignments were introduced to consider what factors may have influenced students' written work. Findings suggest that although students attended to the features of the task, the features did not have a clear impact on the persuasiveness of their arguments. Conversely, as more time was devoted to setting up the writing tasks, students' written arguments became more convincing. The most significant impact on the persuasiveness of students' arguments occurred when students were involved in peer-review activities with the aid of rubrics created by the cooperating teacher. These findings suggest that students can be successful at writing arguments when significant time is devoted to instruction that is specific to writing convincing arguments. This is important, because engaging in arguments is a complex task that requires ongoing attention and support from teachers. Through the consideration of written arguments, this study sought to begin to fill a gap in the literature by describing ways in which one teacher helped students articulate written justifications to claims, an essential part in "creating viable arguments" (CCSSI, 2010).
Read
