This article reports on efforts, in a middle school mathematics methods course, to implement activities to support PTs in learning about students’ mathematical thinking as well as students’ funds of knowledge—the culturally developed knowledge, skills, and experiences of children in their homes, with their families, and in the community—and using that information to revise a high-level mathematics task to be more culturally relevant for one student who is socio-culturally different from them.

This article describes an intervention with preservice mathematics teachers intended to address the use of Interactive Geometry Software (IGS) for mathematics instruction. A unit of instruction was developed to support teachers in developing mathematical tasks that use IGS to support students’ high-level thinking (Smith & Stein, 1998). Preservice teachers used the IGS Framework (Sherman & Cayton, 2015) to evaluate 3 tasks, to revise a task, and ultimately to design a task using the framework. Results indicate that a majority of preservice teachers in this study were successful in creating a high-level task where IGS was instrumental to the thinking demands, and that the IGS Framework supported them in doing so. The article concludes with suggestions for use by fellow mathematics teacher educators.

In an effort to elicit elementary preservice teachers’ mathematical noticing, mathematics teacher educators at 6 universities designed and implemented a 3-step task that used video, writing, and animation. The intent of the task was to elicit preservice teachers’ mathematical noticing—that is, noticing specific to mathematics content and how students reason about content. Preservice teachers communicated their noticing through both written accounts and self-created animations. Findings showed that the specificity of mathematical noticing differed with the medium used and that preservice teachers focused on different mathematical content across the methods sections, illuminating the importance for mathematics teacher educators understanding of the noticing practices of the preservice teachers with whom they work. This report includes implications for using the task in methods courses and modifying course instruction to develop noticing following task implementation.

This research study was designed to evaluate the extent to which professional development (PD) designed around a learning trajectory (LT) on geometric measurement of area was successful in helping teachers use the LT to conduct formative assessment. Six 3rd-grade teachers from the Midwest participated in 20 hours of PD centered on the LT. Data to evaluate the PD were obtained from a set of questionnaire prompts administered before and after teachers’ participation in the PD. The results suggest that teachers increased their ability to elicit and interpret student thinking and use assessment results to make instructional decisions. We consider the design and evaluation of this PD to be valuable for future efforts aiming to use LTs to support teachers in their formative assessment practices.