A second common answer is "the writings of Martin Gardner" in the 1960s and 1970s. Gardner's prolific work in recreational mathematics not only kindled the interest of thousands of potential mathematicians; it put Scientific American, the magazine that carried his monthly column, on the consumer map. Gardner's work remains widely available and is still fresh. Schools, however, are making little use of his marvelously motivating material. I can't imagine an adequate middle or high school library that doesn't contain every one of his books. Fortunately, Gardner's place as a key motivator of new mathematicians will not remain unique. Modern authors such as Calvin Clawson, Ivars Peterson, Clifford Pickover, and Ian Stewart are moving in that direction. School libraries should have their books as well.

The third common answer is "personal computers" in the 1970s and 1980s. That's when computers really were personal. The user wasn't connected to the Internet and wasn't limited to six or seven major applications. Internet access and today's applications have become almost indispensable, but the personal part of computing has been unnecessarily lost. The computer is personal when you can make it do exactly what you want it to— when you can use it as a precision tool to investigate exactly what you want. When doing mathematics, this is often done by writing simple programs.

There is overwhelming evidence that students prefer learning material that challenges them. That doesn't mean they won't moan and groan when it's presented. It does mean they will engage their minds when they are working on challenging material and that they will enjoy doing so—although they aren't always willing to admit that this is the case.

The REAL Mathematics™ series combines recreational mathematics and modern technology. Students will almost certainly need a simple calculator to do many of the problems. If they can use a computer, that's even better. However, they do not need to use a computer to get the full value of the material.

The REAL Mathematics™ series is based on successful lessons that have been used with students in grades 6-14. This material works! It instructs and it motivates. The series is intended for average and above-average students. It can be used by above-average students for independent study, but, as with most material, it is best when presented by a teacher.

Some of this material "looks hard." There will be instances when your students have most but not quite all of the background necessary to complete a problem. Don't hesitate to assign the problem! You will very likely create a "teaching moment." When a student comes to you with a question, he or she will listen carefully to the answer. That's a much more effective teaching technique than telling students about new material according to your presentation schedule. You may present, but there's little assurance that many students are listening. If students fill in the background on their own, that's even better.

The REAL Mathematics™ series can also be used as the basis for professional development programs for teachers. The books do an excellent job of communicating the kind of thinking we all hope to teach in the classroom.