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Facilitating productive mathematical argumentation is challenging; it is critical to develop a specific guiding vision of practices to help teachers learn to teach argumentation. However, what counts as acceptable classroom-based mathematical argumentation remains an open question. In this study, building on Habermas' theory of communicative action, we developed two analytic frameworks to examine questioning strategies used to support the validity of collective mathematical argumentation. Habermas' three components of rationality allowed us to focus on fine-grained rationality components of teacher questioning as well as teachers' intentions of asking these questions. The theory of validity claims was used to capture different forms of validating argumentation. The frameworks may help teachers to be aware of the types of questions that they are asking when aiming at supporting valid argumentation. [For the complete proceedings, see ED629884.]

Teachers' questioning is a pivotal contributing factor to support students' engagement in productive mathematical collective argumentation. Following Habermas' (1998) construct of rational behavior, we attempted to demonstrate how teachers' questioning can be framed based on this construct. Adapting Habermas' construct with Toulmin's (1958/2003) model for argumentation, we conducted a case study to analyze how a prospective secondary teacher used questions to support collective argumentation in one of her student teaching classrooms. We also explored how the prospective teacher's interpretations of argumentation related to her use of rational questioning. The results suggested that this theoretical integration can be a useful tool to frame teacher questioning based on teachers' intentions and organizations of argumentation. Some educational implications for teacher professional development are provided. [For the complete proceedings, see ED606531.]

Cooney, Shealy, and Arvold (1998) wrote a widely-cited paper that described four belief structures of prospective teachers and argued the structures can aid in describing the ways beliefs change and the influence of authority on the individual. In this paper, we investigate the impact of this manuscript on the field. We first conducted a literature review (n = 48) of journal articles and proceedings published since 1998 covering the same population and goals of Cooney et al. (changing prospective teachers' beliefs). We then conducted an analysis of 106 journal articles citing Cooney et al. to see why the author(s) cited the piece. We conclude the impact of Cooney, et al.'s article differs from that of their results and suggest belief structures should be more carefully investigated by the field. [For complete proceedings, see ED581294.]

Understanding the formation of the professional identities of prospective teachers is important to better understand the decision-making processes of future teachers. Through an exploration of four prospective teachers' visions of practice and designated identities, we found that their images of future students' affective responses while learning mathematics were a strong influence in the prospective teachers' evolving professional identities. [For the complete proceedings, see ED597799.]

As creating and critiquing arguments becomes more of a focus in mathematics classes, teachers need to develop their abilities to facilitate productive arguments. Toulmin's (1958/2003) model of argumentation has been useful in analyzing arguments in mathematics education research, raising the question whether it would assist mathematics teachers as well. In this study, we examine how using the model affected prospective secondary teachers' development of conceptions of collective argumentation. Our findings suggest that Toulmin's model facilitated appropriate understandings of what collective argumentation looks like in the mathematics classroom and provided the prospective teachers with a lens for analyzing their observations of practice. This study suggests the use of Toulmin's model in teacher education can be a promising step in helping teachers develop their conceptions of collective argumentation. [For the complete proceedings, see ED584443.]

We observed a student teacher's practice as she taught one unit of instruction. Using a modification of Toulmin's (1958/2003) diagrams, we analyzed her support for collective argumentation by examining questions she asked, parts of arguments she contributed, and the kinds of warrants her students contributed. Our findings suggest reasons she was identified as an exemplary student teacher and support moves that may be applicable to other teachers' practice. [For the complete proceedings, see ED585874.]