Mathematics

Online collaborative and content-focused professional development (PD) is becoming an increasingly important setting for supporting mathematics teachers’ professional learning. The purpose of this study was to better understand the process by which a community emerges in such a PD setting by examining how the cohesiveness of 21 mathematics teachers’ social network evolves and associated shifts in the quality of mathematics teachers’ mathematical discourse.

Teachers’ knowledge of proportional reasoning is important, particularly in the middle grades in the USA. This exploratory study investigated 32 teachers’ use of knowledge resources in two mathematically similar tasks (one a paper and pencil task, the other a dynamic task) around proportional reasoning. The two tasks invoked different knowledge resources by the same teachers. Results suggest questions to the field around how we access or invoke teacher knowledge and the need to more purposefully explore the potential benefits of using a dynamic task to invoke knowledge resources.

The purpose of this study was to investigate how teachers understand one specific aspect of proportional reasoning. We were interested in understanding the extent to which practicing teachers were able to make sense of reasoning that involved the fixed number of variable-sized parts perspective. We used two items, drawn from a larger dataset, that encouraged teachers to reason about proportional situations using a variable parts perspective.

Maass, K., Cobb, P., Krainer, K., & Potari, D. (2019). Different ways to implement innovative teaching approaches at scale. Educational Studies in Mathematics, 102, 303-318.

Well-designed mathematics instruction focused on concepts and problem-solving skills associated with measurement and data analysis can build a foundational understanding for more advanced mathematics. This study investigated the efficacy of the Precision Mathematics Level 1 (PM-L1) intervention, a Tier 2 print- and technology-based mathematics intervention designed to increase first-grade students’ conceptual understanding and problem-solving skills around the areas of measurement and data analysis.

Mathematics interventions aimed at accelerating the learning of students with mathematics difficulties (MD) should be developed through a design science approach such as the Curriculum Research Framework (CRF). Precision Mathematics is a National Science Foundation-funded DRK–12 Design and Development project focused on building mathematical proficiency with the critical concepts and problem-solving skills of early measurement and data analysis among first- and second-grade students with MD.

Students who earned high marks during the proof semester of a geometry course were interviewed to understand what high-achieving students actually took away from the treatment of proof in geometry. The findings suggest that students had turned proving into a rote task, whereby they expected to mark a diagram and prove two triangles congruent.

This chapter explores a way of describing the teacher education curricular materials being developed by mathematics teacher educators through their interaction with the LessonSketch online platform (www.lessonsketch.org). We briefly describe the platform and the larger project and then using the experiences created by two fellows illustrate the kinds of materials being created by the teacher educators.