For children, geometry begins with play. Rich and stimulating instruction in geometry can be provided through playful activities with mosaics. Activities with mosaics and others using paper folding, drawing, and pattern blocks can enrich children's store of visual structures. They also develop a knowledge of shapes and their properties.

For young children, geometry is often a skill of the eyes and hands as well as of the mind, and geometric experiences should focus on the manipulation of familiar objects, such as the unit blocks found in many kindergarten and primary-grade classrooms.

This article describes how children learn about geometric objects -- cube, rectangular prism, cylinder, and so on.

A study unit based on a constructivist approach that offers students real-life situations in which to study the mathematical concepts of geometry. When problem-based learning activities, such as the park-design problem, are implemented in the classroom, students connect mathematical and scientific concepts and apply them to real-world experiences.

This study analyzed young children's understanding of the geometric concepts of triangles and rectangles, and defined patterns in the development of this understanding from ages 3 through 6. An understanding of how young children perceive geometric concepts and of how these perceptions develop as the child both matures and receives systematic instruction is imperative if teachers are to improve early childhood geometry instruction.

The episodes presented in this article contribute to the emerging picture of children's developing understanding of geometry and the kinds of teaching that can support it.

Developing spatial sense, as well as number sense, as described in NCTM's Curriculum and Evaluation Standards for School Mathematics (1989), is a central goal of mathematics instruction that engenders problem solving in particular and doing mathematics in general. A strong spatial sense allows students to formulate image-based solutions to mathematics problems. In geometry, having a mental image of a parallelogram is fundamental. Without spatial sense, a student may only act mechanically with shapes and symbols that have little meaning.

The activities described here are designed to enhance students' spatial-reasoning ability, a neglected part of the geometry curriculum, while encouraging them to reason, problem solve, communicate, and make connections between school subjects and between geometry and the real world. These activities involve tasks which, whether done in a large-group setting, smaller cooperative groups, or individually, require students to conjecture and then verify their conjectures as they investigate reflections of objects—letters and words—from the discipline of language arts. The tasks give teachers opportunities to question, listen, and assess decision-making skills, which are all part of the NCTM's vision of effective teaching (1991).