Students first learn to recognize whole shapes and then to analyze properties of a shape. Later they can see relationships between shapes and make simple deductions. Instruction must consider this hierarchy because, although learning can occur at several levels at once, the learning of more complex ideas requires a firm foundation of basic skills. For middle school students the informal exploration of geometry can be mathematically productive. Geometry at this level links the informal explorations begun in grades K 4 to the more formal processes of grades 9-12.
Students draw inferences and make logical deductions from geometric problem situations.
They can also analyze their thought processes and explanations. Geometry has its own vocabulary including terms like rhombus, trapezoid, and dodecahedron, and students need ample time to develop confidence in their use of this new and unique language. Definitions should evolve from experiences in constructing, visualizing, drawing, measuring, contrasting, and classifying figures according to their properties. Students who memorize a definition and a textbook example or two are less likely to remember the term or its application. Explorations of flips, slides, turns, stretchers, and shrinkers will illuminate the concepts of congruence and similarity.