ABSTRACT
This chapter broadly addresses what it means to “do,” to “teach,” and to “learn” mathematics, describing the discipline from a problem-solving approach. Eight Standards for Mathematical Practice (SMPs) are described, with evidence from national and international testing that motivates the need to teach students to think mathematically, an expectation that moves beyond simply asking students to perform mathematical procedures. The SMPs are derived from previous work published by the National Council of Teachers of Mathematics, and the need for reform in mathematics education is presented, along with 21st-century skills demanded of all students as they move to advanced schooling or to the workplace. Examples of the types of problems that elicit mathematical thinking are presented throughout the chapter and set the tone for the rest of the book’s contents.
