Preparing teachers to teach mathematics is at the intersection of the three areas where cultural and racial knowledge intersects with content and pedagogical content knowledge. Consequently, preparing teachers to teach mathematics must consider all peoples' practices. This highlights two Black girls marginalized by their teacher, which provides…

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…

We conducted a multimedia survey experiment with a nationally representative sample (n = 405) of secondary geometry teachers. Participants were shown storyboard depictions of instructional episodes and asked to rate the appropriateness of the (hypothetical) teacher's actions using a Likert-like response format. We analyzed participants responses…

For centuries, there has been a debate about the role of undergraduate education in society. Some have argued that universities should focus on practical skills and knowledge to prepare students for the workforce, while others have supported the idea that universities should prioritize providing a broad understanding of disciplinary knowledge and…

There have been many efforts to measure pedagogical content knowledge with multiple-choice survey instruments, but little is known about how different types of items contribute. In this study, we examined interviews with 9 Grade 4 teachers to develop a deeper understanding of how teachers select pedagogical representations in the context of a…

Positioning teachers as designers of curricular resources invites opportunities for exploration at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for preparing teachers to maintain a commitment to their pedagogical vision in practice, this work seeks to cultivate the imagination of humanistic…

This research report describes a Learning Trajectory-based Curricular Design project that engaged teachers and coaches in the design and implementation process. As the project team, we focused on deepening teacher designers' understanding of the learning trajectory (LT) while situating student learning along a continuum to advance student…

Emotions come into play as teachers make decisions, act, and reflect on the different purposes, methods, and meanings of math teaching. In order to learn more about the emotions of mathematics teachers, this paper shows the emotions experienced by 81 Mexican teachers who teach mathematics in middle school and high school. Emotions are…

This paper examines the possibilities of designing a formative assessment that gathers information about novice elementary teachers' skills with modeling content and makes sense of such information. A decomposition of the practice of modeling content was developed and used to design the assessment. Participants included ten first-year teachers who…

The number line is a model that is used to measure, count, order and even operate, which requires a symbolic interpretation. Then, we investigate the conceptions of 72 in service secondary teachers, when they manage the model of the number line associated with order, spatial location and the relative position between numbers and marks. In a…

Like K-12 mathematics teachers, for whom effective instruction requires a full suite of pedagogical and mathematical knowledge and skills, Mathematics Teacher Educators (MTEs) also need a professional knowledge base to facilitate the development of future educators capable of supporting K-12 students' mathematical learning. In this paper, we…

Secondary mathematics preservice teachers enrolled in a methods class at a large Midwestern University were supported to develop their TPACK knowledge. Instructional tasks included engaging with explorations using technology to support reasoning and sense making, creating entries for a technology portfolio, studying theoretical constructs about…

This study investigates how utilizing student-invented strategies in the classroom can inform teachers' pedagogical content knowledge. Two elementary school teachers participated in professional development discussing the benefits of invented strategies. Data was then gathered as the participants implemented this practice in their classrooms. Data…

In this paper, we extend our previous work on challenges teachers face when engaging with proportional reasoning contexts to investigate two contexts that included four problems for middle grades teachers to solve as well as eight student solutions. Analysis included coding for correct solving of the problem as well as making sense of and…

This study presents an extension of the validity argument for the PCK-Fractions measure. PCK-Fractions is designed to assess the effectiveness of professional experiences in facilitating teachers' pedagogical content knowledge (PCK) for children's fraction reasoning in grades 3-5. We examined data across 101 participants from two Midwest…