The authors asked fifth-grade and eighth-grade students to pose stories for number sentences involving the addition and subtraction of integers. In this article, the authors look at eight stories from students. Which of these stories works for the given number sentence? What do they reveal about student thinking? When the authors examined these…

As a fifth-grade mathematics teacher, the author tries to create authentic problem-solving activities that connect to the world in which his students live. He discovered a natural connection to his students' real world at a computer camp. A friend introduced him to Alice, a computer application developed at Carnegie Mellon, under the leadership of…

Data analysis plays an important role in people's lives. Citizens need to be able to conduct critical analyses of statistical information in the work place, in their personal lives, and when portrayed by the media. However, becoming a conscientious consumer of statistics is a gradual process. The experiences that students have with data in the…

Just as ready-made clothes may not provide a perfect fit for all bodies, math lessons may not be a perfect fit for all students. Published instructional tasks, including problems in mathematics textbooks, often need to be tailored to be meaningful, relevant, or accessible to each student. Ways are possible to take high-level reasoning tasks and…

Interactive whiteboards are somewhat unimpressive at first and look like the whiteboards that already hang on the walls of many classrooms. However, integrating interactive whiteboard technology in a unit on adding and subtracting integers enhances student engagement and understanding. In this article, the author describes how she used an…

Mathematics education is replete with activities that explore real-world problems. A variety of these problems are added to lessons in the belief that merely applying mathematics knowledge to everyday contexts will enhance the transfer of that knowledge to other settings. However, these contexts are hypothetical rather than authentic. This…

It is important to use rich problem-solving tasks to develop students' understanding of important mathematical ideas (NCTM 2000). Rich tasks are complex, nonalgorithmic, and nonroutine, requiring reasoning, problem solving, and communication of thinking. Evidence has shown that using rich tasks in student-centered classrooms is especially…

To promote math and science, this author designed an activity to show students that biomedical fields are within their reach. The activity has three distinct goals: (1) To introduce the field of biomedical engineering to students and encourage them in these career pursuits; (2) To give them hands-on experience conducting a biomechanical test; and…

Students appear to be able to see number relationships and patterns but have difficulty recognizing the visual properties of shapes, especially if the shapes are in different positions. Their difficulty in the visual and spatial realm is often linked to a lack of drawing experience and possibly undeveloped fine-motor skills. The author, as a…

Story problems either bring students to a screeching halt or send them into a frenzied search for numbers and operations. They cause greater anxiety, still, in English language learners. These problems are often the nemesis of many a math teacher. This author grappled with this challenge in the context of teaching a series of lessons on integers…

To help fifth- through eighth-grade students develop their deductive reasoning skills, the author used a ten-week supplementary curriculum so that students could answer logic questions. The curriculum, a series of lessons built around language-independent logic puzzles, has been used in classrooms of fifth through eighth grades. In most cases,…

Infinity and infinitely small numbers pique the curiosity of middle school students. From a very young age, many students are intrigued, interested, and even fascinated by extremely large or extremely small numbers or quantities. This article describes an activity that takes this curiosity about infinity into the domain of adding the numbers of an…

The NCTM calls for the use of rich tasks that encourage students to apply their own reasoning to problem situations. When students work through algebraic generalization tasks, their reasoning often elicits a variety of strategies (Lannin 2003; Stacey 1989; Swafford and Langrall 2000). Challenges for teachers include facilitating student awareness…

Developing meaning for symbolic representations is an important part of the middle school mathematics experience for all students. Teachers must not see simply writing symbolic representations as the end goal, but focus on the internal meaning that students ascribe to these symbols. Too often, students lack a deep understanding of the algebraic…

This article describes a semester-long pen-pal project in which preservice teachers composed mathematical problems and the middle school students worked for solutions. The college students assessed the solution and the middle school students provided feedback regarding the problem itself. (Contains 6 figures.)