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 3: Planning Mathematics Lessons
Planning Mathematics Lessons
Prospective teachers frequently put lesson planning at the top of the list of things they want to learn. This is reasonable, since teachers must deliver several lessons each day. However, a cautionary note is in order. It should be understood that there is no single “best” approach to planning a lesson. Some approaches are more effective than others, but none of them is perfect. In mathematics, we often learn algorithms that provide flawless answers every time they are executed correctly. But because of the diverse and variable nature of schools, students, and teachers, no such algorithm exists for planning mathematics lessons. Even experienced and successful teachers find they must implement a lesson several times, polishing it each time. Lesson ...