Reasoning and sense making are at the heart of mathematics teaching and learning throughout the K-12 mathematics curriculum. Focusing on these skills gives students the opportunity to analyze, interpret, and critically think about the mathematics they learn. The terms "reasoning" and "sense making" are frequently used to describe the wide range of…

Middle school mathematics teachers face unprecedented challenges. Foremost among those challenges is being able to systematically adapt instructional practices to advance student achievement relative to rigorous math standards. These challenges are not likely to be overcome by individual teachers. That said, it is widely argued that collaborative…

This article explores the thinking behind students' thinking. (Contains 2 endnotes.)

This article explores how conceptualization of absolute value can start long before it is introduced. The manner in which absolute value is introduced to students in middle school has far-reaching consequences for their future mathematical understanding. It begins to lay the foundation for students' understanding of algebra, which can change…

Since communication is an important feature of classrooms in which students are engaged in doing challenging mathematics, one concern that might be raised for teachers who are creating discourse-rich learning environments is what students who remain silent during discussions might learn. In this article, the authors consider this issue by…

Geometric pattern tasks can be a useful tool for developing students' capacities to reason algebraically and in helping establish classroom norms and practices at the beginning of the school year. In this article, the authors consider the mathematical and social purposes that pattern tasks can serve by examining one middle school's…

This article examines research to explore whether the use of manipulatives is an effective tool in teaching mathematics concepts and reasoning to middle-grades students.

This article contrasts relational and instrumental understanding and the consequences on the application of mathematics learning. (Contains 3 endnotes.)

Describes the results of a classroom trial activity to encourage communication in mathematics. Students were asked to write a short story or a joke or to create a cartoon about an aspect of mathematics, which was in this case isolating the variable or property of negative 1. The activity revealed creativity and allowed the teacher to determine how…