AW | Do you consider yourself a mathematician or a math educator?

SB | I'm both! I'm a mathematician because my degrees and training are in math and I was tenured and promoted based on my math research. But I'm a math educator because my current professional work is devoted entirely to the issue of how to teach teachers.

AW | Most books are organized by number type; yours is organized by operation type. Why?

SB | I think the operations are more important and more fundamental. In fact, the different types of numbers arise because of the operations. For example, you get the fraction 1/2 when you ask the question: what number can I multiply by 2 to get 1? You get the negative number ­1 when you ask the question: what number can I add to 1 to get 0?

AW | Your exercises are set up differently from what most books do. Why?

SB | The exercises (now called practice problems) function like examples but give students the opportunity to solve the problem on their own first, rather than just showing them how right away. Because there are few examples within the text, the text can focus on the ideas and principles of the topic. I think this focus can help students organize their thinking. The detailed answers to the practice problems give students many samples of good explanations.

AW | How do you personally incorporate activities into the classroom?

SB | I use activities every class period. I usually introduce the topic with a brief lecture. I generally ask students to think about the questions in the activity on their own first, and then to consult with a neighbor. We then go over the answers together as a class. We often go over the first problem in an activity before students go on to the rest, just to make sure everybody is heading in the right direction and won't waste time being completely stuck and confused. Some activities are better done together as a class. For example, the activity on the Global Positioning System is a good one for the class to act out together instead of in pairs or groups.

AW | How many activities do you usually do per class period?

SB | It varies a lot, but often about 2 or 3. I don't do every single activity in a section because there is usually not enough time for that.

AW | What do your students think of this approach?

SB | The students like it a lot. They like to be able to discuss ideas with each other. They like that they are not just sitting and listening to a lecture but are actively participating. They like hearing different ways that their classmates find to solve a problem, or different ways others have of thinking about a mathematical idea. They see the value of having to explain math to each other: as teachers they will have to explain math and so they appreciate the practice.

AW | What was your motivation to write this textbook?

SB | I was using one of the popular books. After reading a section I would always think "but what do I do in class to get these ideas across?" So I started writing activities for my students. But then I realized that the activities alone were not enough for the students: the students couldn't always pull the ideas together just from what we'd done in class. Students needed more to help them solidify their understanding. I needed a text to go along with the activities. The text had to include exercises, with sample explanations given in detail, and problems. So I think this book was written backwards from other books: the activities actually came first.

AW | What is one reason why someone should try using your textbook?

SB | If they think their students are not developing a sufficiently deep understanding of the mathematics they will teach and if they don't think the mathematics they are currently teaching their students will "travel into the classroom", then they should try this book.

Mathematics for Elementary Teachers by Sybilla Beckman