**KNOWING AND TEACHING ELEMENTARY MATHEMATICS**

**BY RICHARD ASKEY**

**THE TITLE** of this article is also the title of a remarkable new book written by Liping Ma.1 The basic format of the book is simple. Each of the first four chapters opens with a standard topic in elementary school mathematics, presented as a part of a situation that would arise naturally in a classroom. These scenarios are followed by extensive discussion by teachers regarding how they would handle each problem, and this discussion is interspersed with commentary by Liping Ma. Here are the four scenarios: Scenario 1: Subtraction with Regrouping Let’s spend some time thinking about one particular topic that you may work with when you teach: subtraction with regrouping. Look at these questions: 52 91 – 25 – 79 How would you approach these problems if you were teaching second grade? What would you say pupils would need to understand or be able to do before they could start learning subtraction with regrouping?