This article presents results of a research study with a pretest, instruction, and posttest design that aimed to identify students' mental models of integers and investigate how these models change based on instruction on the unary and/or binary meanings of the minus sign. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students over-relied on various combinations of whole number principles as they tried to understand negative integers. However, a significant number of students developed formal mental models based on their instruction.

A sizable body of literature exists studying various technologies and pedagogical practices for teaching secondary mathematics curriculum to students with a learning disability in mathematics. However, with the growing footprint of computer-based technologies in today's classrooms, some areas of study, such as the use of virtual manipulatives, lack sufficient exploration. Although concrete manipulatives were studied for many decades for students with a learning disability and are considered a best practice, the research base for virtual manipulatives is notably less. With a specific focus on algebraic instruction, this study sought to compare the benefits of both forms of manipulatives to assist secondary students with a learning disability in mathematics to solve single-variable linear equations using a single-subject alternating treatment design. Over the course of 30 sessions of intervention, three students exhibited over 90% average accuracy solving problems using both virtual and concrete manipulatives, while the concrete manipulative earned higher scores for two of the three students.

Both scientists and policy-makers emphasize the importance of education for influencing pro-environmental behavior and minimizing the effects of climate change on biological and physical systems. Education has the potential to impact students' system knowledge -their understanding of the variables that affect the climate system -and action knowledge -their understanding of behaviors that can impact the system. Research on climate change education has largely focused on system and action knowledge that address mitigation while overlooking equally necessary adaptive responses. This study used a pre/post-test format to identify aspects of middle and high school students' climate system knowledge and action knowledge of both mitigation of and adaptation to climate change. Results indicate that adolescents currently conflate climate change mitigation strategies with unrelated environmental problems far less than in previous surveys. However, students demonstrated limited understanding of adaptive responses to climate change. After engaging in an instructional unit on climate change, students expressed stronger system and action knowledge, but significant misconceptions remained that conflated mitigation of and adaptation to climate change.

This study investigated how elementary teachers in a mathematics lesson study made sense of student learning, teaching, and content, as related to using representations in teaching multidigit subtraction, and how changes occurred over time in their talk and practice. The lesson-study process paved a group talk path along which teacher talk shifted from superficial to deeper consideration of student learning. By providing a context in which interactions of diverse ideas drove teacher learning, lesson study facilitated teachers making connections between the craft knowledge of teaching and scholarly knowledge. Individual teacher talk paths varied within the group path, and one teacher's learning path and the interaction of different learning paths is discussed.

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