Teaching Mathematics in Grades 6 − 12: Developing Research-Based Instructional Practices will provide prospective teachers mathematics in grades 6 − 12 with guidance on what to cover in secondary mathematics courses and how to cover those topics. The text is based on the premise that engaging prospective teachers in the study of students’ mathematical thinking is a powerful and under-utilized strategy for secondary teacher education. The six chapters in Part I of the text provides an induction to the field of mathematics education. The five chapters in Part II describe how students think about mathematical concepts. Borrowing an organizational strategy from the Common Core State Standards, standards documents of the National Council of Teachers of Mathematics, and standards documents of many states, each of chapters in this part is devoted to a specific mathematics content strand.
Chapter 10: Developing Students’ Geometric Thinking
Developing Students’ Geometric Thinking
The teaching of geometry has a long, rich history. One of the most important works in the discipline, Euclid's Elements, dates back to approximately 300 B.C. In it, Euclid compiled and extended the work of his predecessors. Boyer and Merzbach (1989) characterized the Elements as the most influential textbook in history, and speculated that it may be second only to the Bible in terms of number of editions published. Euclid's Elements reflects the Greek commitment to establishing and teaching a deductive system of thought in mathematics. Studying such a system can be contrasted with learning geometry for more practical purposes, such as determining measurements. Even though the Greek word geometria is rooted in geo, meaning “earth,” and ...