Engaging students in mathematical justification is extremely important from a learning-focused and a disciplinary perspective. Prior research has commonly found that middle grades students struggle to produce viable justifications, arguments, and proofs, yet these studies often consider students' justification in only one modality (oral or…

Two studies (Trautwein 2007 and Dettmers et al. 2010) show a positive correlation between high-quality homework and mathematics achievement. Students who completed their homework assignments scored better on assessments. However, these studies also showed no relationship between time spent on homework and resulting student achievement. This helped…

Students who engage in mathematical arguments in classrooms take part in an important practice involving reasoning and justification. As a mathematical practice, argumentation involves using both conceptual and procedural reasoning to justify a claim. Even though argumentation can occur in discussions where one asserts and defends their claim…

The findings discussed here are a small part of a larger study entitled, "Encouraging Persistence Maintaining Challenge". The paper reports five teachers' observations of the implementation of a task which was new to them. The teachers were asked to identify aspects of the task which they perceived as challenging for the Year 6 students.…

In this study, we considered how four teachers reasoned about proportional situations involving geometry. We used pilot interviews conducted with in-service middle grades teachers around a set of proportional tasks. Analysis relied on a knowledge in pieces lens to uncover the resources that each teacher used in solving the tasks and which…

Assessments of instructional quality based on classroom observations and artifacts have the potential to measure and improve mathematics instruction and learning. This article describes the Instructional Quality Assessment (IQA) Mathematics Toolkit and examines its ability to identify the nature and quality of classroom instruction. The IQA…