These activities explore classification and logical reasoning by providing students with opportunities to generate multiple answers and engage in multiple classifications of the same item. No solutions are suggested so that students will look to themselves as the mathematical authorities. Sample items for classification include birthday months,…

Describes a mathematical investigation centered on collecting and analyzing data in a scientific setting. The first experiment teaches the basics of data collection--students should be able to identify variables that might have affected experimental results. The second activity includes designing an experiment to control for these variables. The…

Offers a problem for teachers to try with their students. The problem is presented visually as a row of 15 connected squares and the task is to determine the number of rectangles. The goal is to encourage teachers to reflect on students' work and analyze classroom dialogue. (PVD)

Presents ways to stimulate teachers to try several techniques for having students write their own problems and verify their meanings with others to become effective mathematics problem solvers. These techniques include sharing self-generated problems in a Mathematician's Circle and publishing problems on worksheets. (PVD)

Presents activities having to do with data generation, organization, interpretation, representation, drawing conclusions, and making predictions on the basis of data which students have collected. (ASK)

Presents a problem drawn from real life that addresses finding a way to cross all seven bridges of Konigsberg, Russia. Illustrates a set of simple examples and an instructional approach in order for students to make sense of a seemingly impossible problem. (ASK)

Presents activities for students to explore mathematical literature. Argues that through books, students come to view mathematics as a meaningful and valuable tool for solving problems. Highlights books that present an authentic and real context for using mathematics and literature to support open-ended exploration of mathematics in real life.…

Presents an investigation using data collected by students to explore timelines and pie charts. The activity begins with having students keep a chronological record of their activities for one 24-hour period to create and analyze pie charts that show how they have spent their time. Activity sheet also included. (ASK)

Describes a unit of study that promotes environmental mathematics. Automobile license plates are used for practice in classifying, examining the place value of digits, analyzing the numbers on the plates, and measurement. (AIM)

Describes a problem suitable for grades 1-6 where students utilize a hundreds chart and counters. Students cover any numbers that contain only the digit 1, then cover any numbers containing only the digits 1 and 2, and follow this pattern until they can determine how many digits are needed before the hundreds chart is half covered. (AIM)

Using the children's book "Tops and Bottoms" by Janet Stevens--an adaptation of the classic fable of the Tortoise and the Hare--students are given opportunities to build connections between a problem-solving situation and mathematics and to communicate solutions through writing, symbols, and diagrams. A key concept is to demonstrate to students…

Discusses a sixth-grade assignment to conduct an interview with someone to find out as much as possible about that individual's profession as well as ways in which mathematics are used in that profession. Peer teaching, communication, and reasoning were natural consequences of this activity. (AIM)

Presents activities that demonstrate how technology can help students discover the mathematics in nature. Claims that these experiences can clarify students' vision of the symmetry of beauty that fills the world beyond the computer. Concludes that the use of flexible software tools helps students explore how a shape is affected when they change…

Presents a problem suggested for students in grades one through six concerning the concepts of grouping, reasoning, and pattern finding. Discusses the student problem-solving process. (ASK)

Describes typical student strategies for counting cubes in cube buildings and explains why these problems are difficult for students. Suggests instructional tasks that can help students develop more powerful ways of thinking about such problems. Lists two action research ideas related to this issue. (ASK)