Principles of instruction - Teaching Geometry

The following principles of instruction are relevant in teaching Geometry and Spatial Sense :

• Student talk is important. Students need to talk about and talk through mathematical concepts, with one another and with the teacher.

• Representations of concepts promote understanding and communication. In Geometry and Spatial Sense, concepts can be represented in various ways (e.g., using manipulatives, familiar objects, illustrations, diagrams). As students investigate geometric ideas, it is important that they manipulate concrete materials and do not simply view pictures and diagrams of two-dimensional shapes and three-dimensional figures. As well, students should be encouraged to make their own representations of mathematical ideas using concrete materials, pictures, and diagrams.

• Students learn through problem solving. Problem-solving situations provide opportunities for students to reason about mathematical ideas and to apply concepts and skills in meaningful contexts.

• Students need frequent experiences using a variety of learning strategies (e.g., playing games, using movement, sorting, classifying, constructing) and resources (e.g., using models of two-dimensional shapes and three-dimensional figures, geoboards, pattern blocks, or tangram pieces). A variety of learning strategies should be used in instruction to address the learning styles of different children.

• Teachers can help students acquire mathematical language by using correct mathematical vocabulary themselves. Beginning in Kindergarten, teachers should model appropriate mathematical terminology as they discuss geometric ideas with their students. They should encourage students to use mathematical vocabulary that will allow them to express themselves clearly and precisely.

• Progression from one level to the next is less dependent on students’ age or maturation than on instruction that promotes reasoning about geometric ideas. Teachers of primary students need to provide the kinds of instructional activities that help students move beyond merely recognizing two-dimensional shapes and three-dimensional figures to understanding the properties of shapes and figures .