I am writing this column in early January. November and December were busy months, with several back-to-back trips, followed by the holiday season. I spent the holidays enjoying family, and, with our son beginning the last semester of his undergraduate college program, reflecting on the upcoming absence of tuition bills and the status of education in general. I will share some of my thoughts on education later in this Message.

For those of you who were unable to attend, you missed a fabulous Conference on Decision and Control in Maui. Many friends from past years came, and it was nice to renew acquaintances in the balmy oceanside atmosphere. Frank Lewis, as the General Chair, Chaouki Abdallah, as Program Chair, and the CDC Operating Committee are all to be commended for keeping everything well organized, with a careful eye on the budget, and providing a very high quality technical program. The weather gods of Hawaii cooperated; Maui had a wet December, but it cleared as we arrived, and the weather was beautiful. I understand that the 2004 CDC in the Bahamas promises to be equally impressive, and we can look forward to the joint 2005 CDC and European Control Conference in Seville, Spain.

As we begin the new year, the news from IEEE headquarters is somewhat mixed. Financially, it appears that the Society is returning to better health. Although due in part to improvements in the investment markets and to cost controls at IEEE headquarters, much of the credit goes to David Castanon's financial prowess as Vice President for Financial Affairs and Cheryl Schrader's leadership as President in 2003.

The news that concerns me is the continued decline in IEEE membership. From November, 2002, to November, 2003, IEEE/CSS membership (all grades) decreased 7.5%. Student memberships decreased even more, at 14.9%. This trend is seen across most IEEE societies, with an overall 5.8% decline in IEEE membership. My concern is that Society membership is no longer as attractive as it once was, especially to students. I suspect that part of the reason is access to IEEE publications through IEEE Xplore, which is available under institutional subscriptions. When I was in college, there was an advantage to having my own copies of transactions, which, as a student, I was able to obtain inexpensively. For many older Society members such as myself, that advantage is still present since I prefer to read printed journals rather than electronic versions. However, for students who are used to obtaining a high percentage of their information through the Internet, electronic distribution is likely to be preferred, and Society, or IEEE, membership is difficult to justify for access to printed publications (this physical Magazine notwithstanding).

I strongly believe that the benefits of membership go far beyond access to publications. The IEEE and the CSS are vibrant entities that greatly affect the technical directions of our profession. Conference participants know that much of the value of conference attendance is gained outside the sessions, where people discuss current work, new ideas emerge, and coalitions form. As most individuals' careers evolve, they discover that their associations through the IEEE often have more permanence and allegiance than their associations with employers, and it is certain that many of us highly value the relationships and respect attained through involvement in IEEE activities. I believe it will be very interesting to participate in the evolution of the IEEE through the coming years, as it becomes more attuned to the changing needs of communities, real and virtual, of practicing engineers. Many of today's engineers move swiftly from project to project, and, with the pace of change, need to rapidly identify information sources that are directly applicable to their work and that can help them adapt their knowledge and skills to their changing workplace. The Information Age has enabled the rapid pace of today's work environments, and it offers solutions that help people step up to this pace. Today, we have IEEE Xplore; over time, I believe we will see additional information products that can be used to locate and use educational content rapidly and easily, providing assistance throughout each engineer's professional career as he or she adapts to change and develops professional skills.

My greater concern is the pipeline of students into the profession. Electrical engineering, and especially the various disciplines of systems and control, require depth in mathematics. Unfortunately, and especially in the United States, few public or private schools are providing adequate training in mathematics, and the quality of mathematical training of entering university students is in decline. Over the holidays I spent a lot of time with my two children, Alex and Nicole. Alex is a senior at Georgia Tech, majoring in mechanical engineering. As he packed up to return to campus I thought about his past 16 years of schooling, and the threads we have wound to attain the best education possible. I also thought of students I've seen at the University of Tennessee and other universities over the past 25 years, and conclude that for most students the mathematical maturity they achieve from kindergarten through college is to a great extent a product of random events outside of their families' control. In the systems and control subspecialties of engineering, we tend to select students at the very top end of a wide distribution of mathematical abilities - or, perhaps more correctly, the random nature of the education process performs the selection - because people without a high level of mathematical maturity are at a substantial disadvantage in our field.

In the United States, recent reform efforts in mathematical education have focused on improving the performance of students at the low end of the distribution, and I believe the effect has been a compression of the distribution on both sides. I will give three examples of problems, as I see them. The National Science Foundation has funded and encouraged the development of "constructivist" mathematics curricula over the past 10-15 years. These curricula are frequently termed "new new" curricula to avoid confusion with the "new math" curricula developed with funding from NSF in the 1960's which, contrary to the current efforts, added rigor to junior high and high school mathematics programs and appeared to push the high end tail of the student capability distribution higher. Many of these constructivist programs of the 90's advocate a "self discovery" method of learning mathematics, and as all of my readers probably know, "discovery," as opposed to learning existing and well-developed methods, takes a lot of time. There are false starts and dead-ends, and even when one pursues the correct track and develops a workable approach, the first procedures or algorithms will invariably be greatly improved as more people work on the problem. When "self discovery" is applied to fundamental concepts such as multiplication, students who discover poor methods can be hampered for life. Probably more important, the only way to accommodate significant amounts of "discovery" in K-12 mathematics is to remove material from the curriculum - things that we take for granted, such as factoring and division of polynomials, concepts upon which both the transfer functions of classical control methods and the newest multivariable controller design methods are based.

My second example is pointed: calculators. One of the new NSF-sponsored curricula teaches that much of the mechanics traditionally taught in mathematics should no longer be covered, because everyone can use a calculator for these operations. I am reminded of a colleague's discussion with a student who had mis-calculated the volume of a small water tank. The student repeatedly asserted that his answer, a few thousand gallons, was correct, and demonstrated how he found the answer on his calculator. The tank was approximately the size of a US gallon milk jug, and, exasperated, the professor finally held up an empty milk jug and asked the student how much water it would hold. Many teachers and textbooks in US high schools exacerbate this problem. My daughter, who is a high school sophomore, recently had a problem set that taught mastery of a few keys on a calculator that allow one to manually search for solutions to a polynomial equation on a graph - definitely an important life skill, at least in this particular class. In another high school class, but fortunately not at my daughter's school, the teacher announced she would no longer teach logarithms because there is a "log" button on the calculator - as if the only reason to understand logarithms is to perform calculations. My point is that calculators, while excellent tools for many things, discourage thought.

My wife, who is also an engineering faculty member, has two habits that are endearing to some, myself included, but must be incredibly exasperating to her victims. She samples the mathematical knowledge of the general population at supermarket deli counters. Many times, she has asked the deli clerk for "0.4 pound" of a meat or cheese. The responses are both amusing and a severe indictment of the general level of mathematical literacy. Some examples: "My scale (which is digital) can't do that." Or, the clerk places one slice of meat on the scale at a time and watches my wife's face expectantly to see if she has brought out enough. My son tried this question once when he was about 10 years old. The clerk told him he must mean "one-fourth of a pound." When he protested, the person behind him in line told the clerk that my son was obviously confused and had to mean 1/4 pound. A recent example: The clerk (with a digital scale) said "you mean 2/5?" Only once, over the 15-20 years that my wife has done this, has she heard a correct response. The man at the deli counter simply measured out 0.4 pound of the product, wrapped it up, marked it, and handed it to her. My wife, astonished, asked him where he was from. His answer: "Europe."

You may ask what this has in common with engineering education. I claim: a lot. My wife's second habit is more germane; I will describe it first, and then explain the connection. Friends of our children who visit our home are usually, at some time or other, asked a question - more to the point, a math question. These questions usually originate with questions we have asked our children at some point in time. A favorite is the "cheesecake problem," which originated when our son was in junior high school. We were at a restaurant, and ordered the kids a slice of cheesecake for dessert. The slice was wedge, or "pie" shaped, and yes, that is important. My wife asked Alex to figure out how to divide the wedge so that Nicole would get exactly half of the slice, and specified that he had to cut it in a specific manner. Imagine the top face of the wedge is an isosceles triangle, with the base being the outer rim of the cake. He had to make a single cut parallel to the base. The problem is easy - if one steps back to think about the similarity and ratios of the two triangles that are involved, which many people forget to do. Alex struggled a little, but worked through the problem to get the answer. These types of problems illustrate the difference between "thought" and "computation." A calculator is useless here, unless of course you've brought your trusty ruler to the dinner table. There are many similar problems, which all see the light of day at some time or other, with one of our children's friends. Stories get around, and I suppose that a few people are a little worried about visiting our home, but most seem to enjoy the challenge, which in a sense speaks well of our children and their friends. Many, however, struggle with the problems, and I suspect this challenge is due to an emphasis on computation rather than thought in school.

My third example strikes close to our universities, and, I believe, will make clear the connections I have pursued in this column. In the United States, students who are exceptionally good in mathematics are often encouraged to take AP (for "advanced placement") calculus while in high school. On the surface, this would appear to be a good policy: It gives the students a substantial head start in their college programs. In practice, it takes the very best high school students and often exposes them to substandard teaching and a calculus curriculum that I will characterize as "cookbook." First, who teaches these courses? No matter what high school or how good the specific teacher, he or she is a person whom we hope has at least two years of mathematical training in college, through, very occasionally, bachelor's level or post-graduate mathematics training. Unlike a college mathematics professor, the teacher has probably never performed any research in mathematics, and in most cases has probably not been exposed to more than a rudimentary knowledge of rigorous (theorem and proof) mathematics. Put bluntly, the best high school students are quite likely to be subjected to a calculus course comparable to the worst types of calculus courses taught in college.

In contrast, suppose a comparably bright student were to forego AP calculus in high school. Put aside for the moment that this decision might place him or her at a disadvantage in competition for college admissions. Since I know my own university best, I will discuss the path available to a student at the University of Tennessee. Our mathematics department offers honors first- and second-year calculus sequences. These sequences are taught by some of the top faculty members in the department, and the material is developed in a rigorous manner using theorems and proofs. Students who take these courses are prepared to take, and master, additional theoretical mathematics courses, including senior-level courses in analysis and algebra that lead into the graduate courses. In short, these highly capable students are taught to "think about" rather than to simply "perform" mathematics. I have heard the arguments that "engineering," rather than "theory" mathematics courses are better for engineering students, and I don't buy them. People who can "think about" mathematics are perfectly capable of performing computations, and have the distinct advantage of knowing where the formulae originate. I claim that these students are exactly the ones that our field needs in order to continue to thrive. Unfortunately, present United States educational policies cause many of the most capable students to take calculus courses in high schools that leave them ill-prepared for additional mathematics training and poorly prepared for fields such as systems and control, where a high degree of mathematical sophistication is needed. Even more sadly, the situation in the United States is deteriorating. The "new new" mathematics curricula that have been developed, and are being adopted, will further thin the ranks of mathematically talented young people, even before they are eligible to enter a high school calculus class.

Fortunately, the mathematical and scientific communities have been bringing pressure on both the United States Department of Education and state and local school boards to bring mathematical thought and rigor back into the K-12 classrooms. See, for example, http://www.mathematicallycorrect.com/ for both information on these new curricula and the efforts throughout the United States by parents and professional mathematicians, scientists, and engineers to encourage schools to adopt rigorous programs. Many children are born with good to excellent abilities to learn mathematics, engineering, and the sciences, but the random courses of choices and opportunities allow only a few students to emerge into quality educational environments and excel. Sound mathematical and scientific thought processes are not developed in four years of college study; rather, they are developed upon good foundations learned throughout all years of a child's education and maturation.

Over the years, I've heard a fair share of griping by fellow faculty members about the declining population of mathematically well-prepared college students. I encourage everyone to be proactive and address these problems at their root causes whenever they are able, for example, through textbook review and adoption committees, local school boards, participation as guest experts in school classrooms and at parents' meetings, and through national forums and funding agencies. There are many factors that contribute to the decline - our culture's emphasis on entertainment, the huge number of organized activities our children participate in, a tacit assumption by many, both in education and outside its domain, that there are predefined roles for women, or for particular subgroups of our populations, the decline of intact families, drug and alcohol abuse, and many other distractions from educational goals - but educational agendas and programs that sacrifice the mathematical and scientific maturity of the most qualified children can be extraordinarily harmful to our civilization's capabilities in the sciences and engineering, and should be opposed wherever possible. I encourage all of the members of our society to become involved.

I am most familiar with educational practices in the United States, but I am certain that many of these issues are surfacing in other countries and cultures. In one sense, civilization is experiencing the impacts of "regression to the mean," as much of the drive to provide quality mathematical educational programs to children originated with the aerospace programs and the cold war. I understand from talking with friends in the countries that made up the former USSR that the quality of mathematical education programs in these countries, which used to be very high, has also declined. I have also observed evidence of a decline in my students from Asian countries. As affluence has improved throughout the world, there are more distractions from educational priorities, and parents, especially, have a difficult time competing with music, video, organized sports, and all the other activities in which our children become involved.

The need to monitor and continually improve education throughout all societies can best be met by the people most familiar with the consequences of not having adequate mathematical and scientific backgrounds, and IEEE members can help lead these efforts. I am well aware of how over-committed the time of all engineers is, but I hope each of you can make the time for public service and involvement to ensure that our field continues to have an adequate supply of well-prepared talent. Systems and control issues exist throughout essentially all application domains, and by encouraging talented individuals to enter the field and aggressively expanding the application of the field, we ensure our chosen profession's continued vitality. d.birdwell@ieee.org.

-- J. Douglas Birdwell
President, Control Systems Society