This article presents an instructional idea that facilitates the students' active participation in the problem analysis process using insufficient or contradictory problem contexts. (Contains 1 figure.)

Provides a model for teachers to engage children in understanding problems and communicating their solutions in order to lead them toward becoming mathematically powerful learners. (Author/NB)

Explores how an elimination game played for fun turned into an extended exploration of mathematical problem solving and reasoning. (Author/NB)

Presents two problems posed to kindergarten children to challenge and to encourage discourse among the students working in small groups of 8 to 10 children. Results showed various levels of understanding and demonstrated various approaches which serve to give the teacher insight into the level of understanding of the class and the possible need to…

Explains how critical thinking, communication, and estimation can be incorporated into an exciting problem-solving unit for first-grade students. Presents four related activities. (ASK)

Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system. (PVD)

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…

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…