Preservice teachers’ creation of dynamic geometry sketches to understand trigonometric relationships

Dynamic geometry software can help teachers highlight mathematical relationships in ways not possible with static diagrams. However, these opportunities are mediated by teachers' abilities to construct sketches that focus users' attention on the desired variant or invariant relationships. This paper looks at two cohorts of preservice secondary mathematics teachers and their attempts to build dynamic geometry sketches that highlighted the trigonometric relationship between the angle and slope of a line on the coordinate plane. We identify common challenges in the construction of these sketches and present examples for readers to interact with that highlight these issues. Lastly, we discuss ways that mathematics teacher educators can help beginning teachers understand common pitfalls in the building of dynamic geometry sketches, which can cause sketches not to operate as intended

Curricular noticing: A comprehensive framework to describe teachers’ interactions with curriculum materials

Building on the work of Professional Noticing of Children’s Mathematical Thinking, we introduce the Curricular Noticing Framework to describe how teachers recognize opportunities within curriculum materials, understand their affordances and limitations, and use strategies to act on them. This framework builds on Remillard’s (2005) notion of participation with curriculum materials, connects with and broadens existing research on the relationship between teachers and written curriculum, and highlights new are as for research. We argue that once mathematics educators better understand the strategic curricular practices that support ambitious teaching, which we refer to as professional curricular noticing, then this knowledge can lead to recommendations for how to support the curricular work of teachers, particularly novice teachers

Supporting noticing of students’ mathematical thinking through 360 video and prompt scaffolding

360 video records a complete, spherical view of a scenario and allows the viewer to manipulate what is viewable in each frame. We incorporated 360 video into a teaching mathematics course and used prompts that directed prospective teachers’ attention to students’ mathematical thinking. Results indicated that prospective teacher noticing was more specific when they responded to prompts about students’ thinking as compared to more general prompts. With focused prompts, prospective teachers had increased attention to students’ mathematical thinking and were more likely to make interpretations about students’ mathematical thinking. The findings show promise for the combination of 360 video and student-focused prompts to support prospective teacher noticing

Negotiating mathematical goals in coaching conversations

Content-focused coaching aims to focus the coach-teacher conversations on the quality of mathematical goals and associated activities while co-planning a lesson. The coach’s role is to support the teacher to articulate a mathematical goal that represents an important mathematical idea, to plan activities in support of that goal, and to anticipate how students will respond to the mathematical activities. We use a framework that emphasizes the dialogic and mediated nature of the coach-teacher conversations. We found that coaching conversations focused primarily on instrumental aspects of lesson planning and only less so on deeper articulations of content, and we found differences across coaches’ practices. The findings provide nuance to empirical findings of coach-teacher conversations

Identifying and supporting teachers’ robust understanding of proportional reasoning

Accepted manuscrip

Noticing before responding

This article provides a framework for integrating professional noticing into teachers' practice as a means to support instructional decisions. An illustrative example is included based on actual use with secondary students.Accepted manuscrip

Proportional reasoning: visualizing a knowledge resources framework

Supporting documentatio

One task, multiple proportional reasoning strategies

Tasks and materials that allow for different approaches can help teachers incorporate student reasoning and can promote connections across different mathematical ideas.Accepted manuscrip

Texas Lifestyle Limits Transmission of Dengue Virus

Urban dengue is common in most countries of the Americas, but has been rare in the United States for more than half a century. In 1999 we investigated an outbreak of the disease that affected Nuevo Laredo, Tamaulipas, Mexico, and Laredo, Texas, United States, contiguous cities that straddle the international border. The incidence of recent cases, indicated by immunoglobulin M antibody serosurvey, was higher in Nuevo Laredo, although the vector, Aedes aegypti, was more abundant in Laredo. Environmental factors that affect contact with mosquitoes, such as air-conditioning and human behavior, appear to account for this paradox. We conclude that the low prevalence of dengue in the United States is primarily due to economic, rather than climatic, factors