As part of a longitudinal study focused on mathematical play, we (Melissa, Amy, and Anita) are often faced with questions about what counts as play and what mathematics (and other learning) we see in play, and whose play is most likely to be seen or dismissed. Rather than discuss our findings from classroom videos of kindergarten children engaged…

This paper presents Big Ideas of Measurement as a framework of students' thinking about measurement. Drawing from research-based evidence, the framework is a collection of key concepts that students must develop for a robust understanding of measurement and, as such, are key aspects of students' thinking teachers should learn to notice. In a case…

Preservice teachers (PSTs) often demonstrate difficulty learning to attend to content-specific student actions in-the-moment. However, machine learning algorithms applied to PSTs' viewing of 360 videos provides a potentially useful tool for teacher educators. In this paper, we describe the initial development of such a tool and the implications…

This study examined how mathematics coaches leverage written annotations to support professional discourse with teachers about important classroom events during synchronous debriefing conversations. Coaches and teachers created the annotations while asynchronously watching video of an implemented lesson as part of online video-assisted coaching…

Remaining continually curious about students' mathematical thinking is challenging, yet worthwhile, in teaching practice. This paper describes and analyzes two video-based professional learning (PL) activities designed to help teachers go beyond their initial perceptions of what students understand and to identify what else they might learn about…

We share results of a study on the analytic stances of coaches' and teachers' as they annotated key moments from classroom video of the teacher's lessons. In the analysis, emphasis was on the analytic stances of the coaches and how their annotations related to trends in teachers' annotations. Findings indicate differences in how coaches and…

Prospective elementary mathematics teachers (PTs) were asked to analyze 28 videos of cognitive interviews. The purpose of this study was to determine if experiences analyzing videos would lead to improvements in PTs' professional noticing skills. Using a coding schema that reflected three levels of understanding (periphery, transitional, and…

Covariational reasoning and the creation and interpretation of graphs of covariational situations are important skills in math and science. Unfortunately, research shows that students often struggle to make meaningful connections between graphs and the covariational situations they represent. Educational activities designed to help students…

Along with the rapid development of technology, videorecording teachers' lessons for professional development or educational research have become commonplace. Although the benefits of the use of videorecording has been well documented, few studies have attended to teachers' affective experiences in relation to videorecording. In this study, we…

In solving mathematics problems in collaboration, students encounter a range of mathematical and social struggles. As teachers cannot possibly respond to every such struggle, they may need to respond to those with which students require most support. Yet, little is known about students' success in overcoming the various types of struggle they…

In this study, we explored enacted task characteristics (ETCs) that supported students' quantitative reasoning (QR). We employed a design-based methodology; we conducted a teaching experiment with eight secondary school students. Through ongoing and retrospective analyses, we identified ETCs which supported students' quantitative reasoning. The…

Opportunities for students to share their thinking with the class--which I refer to as "work-sharing practices--require a profound shift in who is positioned with intellectual authority in mathematics classrooms. This study explores work-sharing practices in one sixth grade mathematics classroom through an interactional lens. Video analysis…

In this plenary discussion, Dr. Chao presents his research framework and reflections from engaging in Digital Mathematics Storytelling within Black, Asian American, and Asian American communities in multiple countries. The framework, based heavily around storytelling, counter-storytelling, and Critical Race Theory, has been employed as a workshop…

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,…

What are the substantive differences between flipped and non-flipped instruction? This study examined the instruction of two teachers who have worked together within the same school using the same Algebra 1 curriculum for years. One teacher flipped his instruction (creating lecture videos assigned as homework), while the other teacher continued…