Throughout the 1990s, I have observed the development of the secondary mathematics curriculum of the Fayette County Board of Education. From time to time, I have directed staff development courses focusing on updating and upgrading both content and instructional strategies of mathematics teachers. These activities have been professionally rewarding for me for several reasons.

First, curriculum and instruction are a top priority of the Fayette County Board of Education. (Note that I have been in this business for more than 30 years. This position of the school system is unique in my experience).

Second, Fayette County's secondary mathematics teachers are the most professional and most dedicated to good mathematics instruction of any school system in the area.

And, finally, the adopted textbooks are among the very best that money can buy. For many years, these materials were the only ones available based on research in how students learn mathematics.

It is unfortunate, indeed, that some of the consumers of this fine program are being unduly critical of it, the teachers, and/or the school system. In my view, this criticism is unjust.

Perhaps what is at the heart of this matter is that good mathematics instruction today is quite different from the instruction which most of us experienced when we were in school.

The arithmetic of those days was likely to be basic for a 1940s shopkeeper when the most prevalent problem solving tool was a pencil. In those days, everyone needed a solid foundation in computing. Our teachers gave us an algorithm. We memorized the steps; practiced the routine on dozens, if not hundreds, of exercises; and perfected the skill. We became proficient in adding, subtracting, multiplying, dividing, and could even take square roots, but we had little notion of why we were doing this or where we should use it!

In those days, algebra was a course for ninth graders who were college-bound. Moreover, the course concentrated on the algorithms of polynomial arithmetic that was necessary to be successful in the calculus. In fact, the entire high school mathematics curriculum focused on providing skills needed for the calculus, although less than 30 percent of those taking Algebra I would ever enroll in a calculus course.

Even so, we became proficient in performing algorithms with no idea of why we were doing this or where we should use it! This is quite different from what occurs in good mathematics classrooms today.

Those of us engaged in research that centers around the teaching and learning of mathematics believe that basic facts are still basic. However, there is more to mathematics than simply memorizing mindless procedures.

Students should model, explain, and develop proficiency with these basic facts and with algorithms. (Of course, there are many different algorithms. Depending on the student's learning style, the teacher is the most able to help the student determine which is best).

The world today is a much different place than it was when we were is school. To be successful in today's world, students need proficiency with basic facts and they must be adept in reasoning, problem solving, and communicating mathematically.

Today's basic skills are much more extensive than merely memorizing facts and procedures. Of course, advances in technology have brought about what is basic today. Surely none of us wants to return to the day when we had little, or no, technology. I expect none of us would pay to ride on an airplane that had no computer systems.

We must educate our students to live in a technologically rich world. In that world, estimation is much more basic than memorizing a needless algorithm. Today's students must experience multi-step problems that require reasoning, inventing, generalizing, abstracting, and applying mathematics.

We must sequence the curriculum carefully to develop the mathematical ideas over time in a connected way. The students should see how the mathematics they are learning this week relates to the mathematics they learned last month.

Our kids should always know that the mathematics they are learning is useful. To make this happen we need excellent textbooks, skillful teachers, and a school system dedicated to providing a strong instructional program for all students. In reality, this describes the situation in Fayette County.

It is impossible to please all of the people all of the time. However, in today's world the Fayette County Board of Education is making an admirable effort to provide mathematics instruction that reflects what we know about how we learn, makes use of current technology, and responds to the needs of an industrialized society. I commend the Fayette County Board of Education and The Mathematics Supervisor for a job well done.