ABSTRACT
The authors invite the readers to hear real stories from educators around the country about “keeping the end in mind,” from the perspective of a principal, a coach, and a teacher. However, even within a single school, hardworking educators aim for mathematical destinations as different as Des Moines, Los Angeles, and Paris—all at the same time. Just like Spanish, Japanese, or any other language, mathematics has its own vocabulary, its own syntax, and its own sign system or set of symbols. The authors’ goal is always to have a balanced approach to mathematics, to make sure that the pendulum gently sways in the middle around sense-making. These are the goals for students that they promote and that many schools ultimately identify: think and reason effectively; solve problems accurately, flexibly, and efficiently; communicate clearly using mathematical language and representations; and demonstrate skills and knowledge on performance assessments as well as standardized tests.
