Classic Thinking Games with Java
by Walter Koetke
$29.95

ISBN: 0-922473-02-1
204 pages; comb bound
©2007 Basics & Beyond Inc

Number Wonder
by Walter Koetke
$29.95

ISBN: 0-922473-00-5
172 pages; comb bound
©2003 Basics & Beyond Inc

Authentic Problem Solving

The core of the REAL Mathematics™ series is solving problems. That's also the core of real mathematics. The problems might be related to real-life situations or they might have nothing to do with the real world. Sometimes those that seem to have nothing to do with the real world are later discovered to have compelling real-world applications.

The best way to learn real mathematics is to do it! One learns how to solve real mathematics problems by solving real mathematics problems. Simply put: the best way to learn math is to do math.

Dispelling Mathematical Myths

Real mathematics is not just about manipulating numbers. Real mathematics requires thinking, planning strategies, experimenting, discussing, and writing.

Real mathematics is not memorization. In fact, mathematics requires less memorization than any other subject you might study. Yes, you do have to know the addition and multiplication tables and there are a handful of formulas worth remembering, but that's about all. Many mathematicians were initially attracted to the subject because problems can be solved without a memorized set of facts.

Real mathematics is not just seeing a sample procedure and then practicing it several times. Practice is sometimes a necessary part of learning, but you should be aware that when you are practicing a procedure you are not doing real mathematics.

Challenging Students

The presentation and problems of the REAL Mathematics™ series have been tested with students in grades 6-14 with great success. Students' initial reactions are nicely summarized by "this looks hard." That's a plus for the many unchallenged students
and a source of notable satisfaction for many others. Students rarely find satisfaction when they complete a task that looks easy. The problems may indeed look hard, but all of them can be done—and have been—done by students in grades 6-14.

Integrating Technology

Technology has changed the way mathematics is done. The most important topics and the most appropriate procedures for solving a problem are often different from what they were twenty years ago - or even twenty weeks ago. Learning the mathematical procedures that were important in 1900 may be of historical interest, but that's not real mathematics. Today's calculators, mathematical assistant software packages, and personal computer programming can readily do all of the mathematics now being taught through twelfth grade in most schools. The need to do mathematics without the support of technology diminishes daily.

Reaching the NCTM Standards

The National Council of Teachers of Mathematics recommends five process standards that run across all grade levels from prekindergarten through grade 12. These standards describe the characteristics of a mathematical instructional program that should enable all students to become proficient in:

• problem solving
• reasoning and proof
• communication
• making connections
• representation