Often, mathematics teachers do not incorporate whole-class discourse of students' various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students' thinking and develop their collective construction of mathematics. This study explores the…

In this study, we investigated the relationship between teachers' post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We…

Learning to name and notice students' mathematical strengths is a challenging process requiring time and multiple iterations of practice for prospective teachers (PTs) to adopt. Mathematics teacher educators (MTEs) can approximate and decompose the complex practice of naming and noticing students' mathematical strengths so PTs learn to teach…

Interactions around unexpected, incorrect, or dis-preferred responses can be powerful sites of learning for both teachers and students. The information that teachers uncover through probing student thinking can then guide their pedagogical response. We report on a study of prospective teachers' skills and capabilities around a particular problem…

This study examines how teachers' discourse moves influence patterns of authority in the mathematics classroom. We identify changes in authority structure in one classroom taught by a primary mathematics teacher in Hong Kong. This teacher participant was one of 32 who participated in a larger teacher-intervention study that aimed to help teachers…

Mathematics teachers' identities profoundly influence how they interact with and position their students to learn mathematics. In this paper, we examine how a year-long teacher learning intervention supportive of student engagement in mathematics helped shift teachers' mathematics-related identities. We use an implied identity perspective as a…

This paper highlights the second phase of a multi-university research project focusing on improving secondary prospective mathematics teachers' abilities to respond to student thinking. This work is based on an Interview Module, created by the authors, which showed gains in prospective teachers' (PSTs) abilities to attend to and interpret student…

Mathematics teacher educators' (MTEs') written feedback is an instantiation of teaching practice and provides information to support the developing understanding of prospective teachers (PTs), yet no research has been undertaken to characterize such feedback. Research on feedback forms, including written feedback, has focused on information…

The mathematics education field recognizes the importance of noticing children's mathematical thinking as a means for supporting children in learning mathematics (Sherin et al. Mathematics teacher noticing. Routledge, New York, 2010). Using the existing literature base around teachers' knowledge of children's mathematical thinking and…

Professional support in the form of a year-long video club based on teacher noticing of student thinking was provided to three rural teachers who comprised the entire mathematics department of one secondary school (grades six through twelve). The focus of the study was to understand how participation in a video club structure for rural secondary…

The idea that formal learning generalizes, or is transferred, beyond the conditions of initial learning serves as a basis for our educational system. That is, educators hope students will use the learning that develops in the classroom to productively reason about situations they have yet to encounter. Researchers in psychology and mathematics…

This paper explored the following: (1) teachers' ways of attending to students' written responses in pattern generalization tasks and (2) differences in the ways of attending to students' responses associated with different factors. A questionnaire was developed to classify teachers' ways of attending to students' written responses. The…

The discipline of mathematics values precision and teachers are accountable for promoting and supporting their students in attending to precision (ATP), which in the USA is an explicit standard for mathematical practice included in the "Common Core State Standards for Mathematics." This study used thematic discourse analysis to examine…

To teach adaptively, teachers should be able to take the students' level of knowledge into account. Therefore, a key component of pedagogical content knowledge (PCK) is the ability to assume the students' perspectives. However, due to the so-called expert blind spot, teachers tend to misestimate their students' knowledge, such as when estimating…