In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the…

Assessment is a topic of concern to all stakeholders in our educational system. Pattern Based Questions are an assessment tool which is an alternative to the standardized assessment tool, and they are based on generative learning pedagogy, which shows promise in engaging all learners and usefulness in teaching and learning but validity has not yet…

Mathematics teacher questioning plays a significant role in students' learning. Research has persisted in analyzing teacher questioning from a cognitive perspective. Considering teaching as a relational practice, we explored teacher questioning from cognitive and affective perspectives. Data comprises 14 video-audio recordings, field notes,…

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…

Teacher feedback during the process of students' proving is important to consider because proving is often challenging for students, requiring feedback and support. Additionally, feedback has implications for authority and agency, which are constantly being negotiated. We examined the authority dynamics evidenced in a teacher's feedback actions…

Identifying components of teaching that make a difference in children's learning is an ongoing challenge in our field. Focusing on teaching that is responsive to children's fraction thinking, we decomposed responsiveness into the instructional practices of questioning to support and extend children's thinking, noticing children's thinking, and…

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)…

This research examined the role of the teacher in supporting students to make sense of fraction multiplication when using a problem solving approach. Using a qualitative approach, the teaching of four skillful experienced sixth-grade teachers was examined as they implemented a problem-based unit on fraction multiplication. This paper will present…

In this paper, we integrate a set of theoretical considerations that together serve as a model for investigating how high-leverage practices could be generative of teacher learning. We use the context of rehearsals to investigate how the use of a specified question sequence aimed at eliciting student mathematical thinking can afford opportunities…

As mathematics teacher educators (MTEs), we enact teaching practices in our mathematics methods courses as instantiations of practice for PTs. Questioning is a core practice in teaching (and learning to teach) mathematics that interacts with relationships between MTEs and prospective teachers (PTs). We engaged in a collaborative self-study to…

This study shares two frameworks for analyzing teacher actions that support students in generalizing and examines how those frameworks align with teacher questioning. One classroom teaching episode focused on the mathematical activity of generalizing is shared to illustrate effective generalizing promoting practices. We found several patterns of…

In this paper we offer a review of sorts of the studies conducted around issues of problem posing in mathematics education research. We first ground the work on problem posing in the seminal work of Polya and of Brown and Walter, which influenced most studies on this subject. We then propose two perspectives taken on problem posing: the implicit…

We report on efforts to better understand the questioning practices used by preservice elementary teachers (PSTs), including the range of preferred question types and the values they invoke when evaluating their questions. We sought to determine whether teachers exhibited consistent patterns in selecting questions with certain features, such as…

Our study investigates preservice teachers' perceptions of real-world problems; their beliefs about teaching real-world contexts, especially ones sociopolitical in nature; and their ability to pose meaningful real-world problems. In this paper we present cases of three preservice teachers who participated in interviews that probed their thinking…

In previous publications the authors of this paper identified specific relations between comprehension and convincement. On the basis of Grounded Theory, this research analyzes the changes that arise in said relations as a response to changing conditions. For their study, the authors analyze an interaction, at a distance, between a tutor and a…