Middle

This article offers six suggestions for middle school principals to implement or strengthen mathematics intervention classes at their schools, based off the findings of the authors' NSF-funded research.

In this article, we report on the development of a novel, video-based measure of teachers’ moment-to-moment noticing as knowledge-filtered perception. We developed items to capture teachers’ perception of similarity of their own teaching to the teaching shown in three short video clips of authentic classroom instruction. We describe the item design and relate teachers’ moment-to-moment noticing to their reflective noticing as measured by judgements of similarity teachers provided after viewing each video.

Numerous studies have reported positive outcomes of noticing interventions on the development of prospective mathematics teachers’ (PMTs) noticing of a range of important aspects of classroom instruction. Less is known, however, about whether noticing skills that are developed during an intervention transfer to support PMTs’ in-the-moment noticing during their own teaching practice.

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.

Being nice is difficult to critique. Niceness is almost always portrayed and felt as a positive quality. In schools, nice teachers are popular among students, parents, and administrators. And yet Niceness, as a distinct set of practices and discourses, is not actually good for individuals, institutions, or communities because of the way it maintains and reinforces educational inequity.

Butcher, K. R., Runburg-Larson, M., & Lane, M. (2019). Making critical thinking visible for student analysis and reflection: Using structured documentation to enhance effective reasoning and communication. Science Scope, 42(8), 44-53.