Geometric Figures California State University, （几何图形加州州立大学,）.pdf

CHAPTER 2 Geometric Figures This chapter describes how elementary students are introduced to the world of geometry. As we have seen, children first learn to measure lengths and angles and to solve arithmetic problems with measurements. By the middle of elementary school they are prepared to start studying geometry as a subject in its own right. Already by grade 2, geometry means much more than simply identifying figures and naming their parts. In grades 2–4, children learn about parallel and perpendicular lines and solve prob- lems involving supplementary and vertical angles. Every year children do drawing activities using rulers and, later, protractors, set squares, and compasses. In grade 5 they begin solving problems involving lengths and angles within triangles and quadrilaterals. The elementary geometry curriculum focuses on clear reasoning and simple geometric facts. There are no proofs; instead, facts are introduced using paper-folding or symmetry arguments. Reasoning skills are developed through daily problem sets — problem sets that can be great fun for both children and teachers. 2.1 Fundamental Geometric Ideas As children learn to measure in grades K-3 they acquire intuition about segments, angles and other objects of geometry. Sometime near the end of elementary school, intuition is replaced by precise definitions. This section describes how angles, perpendicu