Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

The rapid growth of digital technology, including the worldwide adoption of mobile and embedded computers, places new demands on K-grade 12 educators and their students. Young people should have an opportunity to learn the technical knowledge of computer science (e.g., computer programming, mathematical logic, and discrete mathematics) in order to…

The combined seventh-grade and eighth-grade class began each day with a mathematical reasoning question as a warm-up activity. One day's question was: Is the product of two odd numbers always an odd number? The students took sides on the issue, and the exercise ended in frustration. Reflecting on the frustration caused by this warm-up activity,…

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

This article provides the rationale for using Fermi questions with eighth graders studying algebra. It describes the students' reaction to such questions as well as their thinking processes and solutions to questions posed to them by their teacher. (Contains 1 figure.)

This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

Explains how middle school mathematics topics are often taught as separate, discrete topics without a unifying thread. Discusses the importance of proportionality as a concept with the potential to untie, relate, and clarify many important, complex middle grades ideas into a cohesive theme. (YDS)

Focuses on mental strategies for computing in the middle grades. Describes what they are and why they are important. Refers to relevant research and presents some teaching ideas for developing these strategies beyond the primary grades. Includes a discussion of the role of mental calculation in everyday life both past and future. Contains 27…

Describes how open-ended writing prompts provide a window into student understanding and mathematical thinking. (YDS)

This article describes connections between chess and mathematics, including examples of activities that connect chess with set theory, patterns, algebra, geometry, combinatorics, and Pascal's triangle. The author observes that competitive games play a dual purpose in advancing the work of mathematics educators: to reinforce a specific skill and to…

This article discusses relationships between the development of an understanding of algorithms and algebraic thinking. It also provides some sample activities for middle school teachers of mathematics to help promote students' algebraic thinking. (Contains 11 figures.)

Three pieces of literature are used to launch mathematical investigations. The tasks provide opportunities for students to apply proportional reasoning skills, explore linear relationships, calculate a unit rate, and find the relationship between the volume of a cylinder and a cone. A poem, a short story, and a young adult novel are discussed.…

Spatial visualization is an important skill that deserves instructional attention. Strong evidence supports the claim that "measures of mathematical ability tend to be strongly correlated with spatial ability" (Anderson 2000). Thus, there is every reason to believe that time spent helping students develop their spatial visualization skills will…

Describes a professional development program for upper elementary and middle school teachers that includes a sequence of four activities designed to foster improved understanding of the connections among measurement, ratio, scale, and proportion. (YDS)

Describes a professional development project to increase teachers' understanding of proportional reasoning, the thinking patterns associated with proportional reasoning, and the applications of proportional reasoning across the middle-grades curriculum. (YDS)