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 7: Developing Students’ Thinking in Number and Operations
Developing Students’ Thinking in Number and Operations
Work with number and operations forms the foundation of the K–12 mathematics curriculum. Many of children's first experiences with mathematics involve counting. In early elementary school, students work on combining sets of objects and removing objects from sets. Methods for multidigit addition and subtraction are studied in the elementary grades as well. Young students also learn how to represent fractions and begin to solve problems with them. These ideas in number and operations account for a large amount of the time students spend studying mathematics before entering middle school.
Although the study of number and operations is most intense in the early years of school, students’ understanding in this area should continue ...