1.26.2005
Confessions of a Reluctant Mathematician
My natural strengths have always been reading and writing. From the moment I learned to read, I devoured books. The library was my sacred refuge. I could bring home several books from the school library and read them all before going to bed that night. On those nights I couldn’t sleep, I would often use a flashlight to keep on reading after I was supposed to be asleep. I was a troubled child growing up. I often got grounded or restricted to my room. No matter how much trouble I got into, my parents did one thing right: they never took away my books. It was the only thing I had going for me in the dark years of my youth and adolescence. In the 7th grade, we took aptitude tests in math and reading. My reading score was in the 98th percentile. My math was in the 28th percentile. I could read and comprehend better than 98 out of 100 students, whereas I could solve math problems better than only 28 out of 100 students. This disparity would follow me for many years to come. In 9th grade, my teacher noticed me squinting to see the notes on the blackboard. It turned out I was nearsighted, so to add to the discomfort of being an awkward teenager, I added glasses. Now I could see better, but it still didn’t cure my negative attitude towards anything math-related. I failed the first semester of Introduction to Algebra, and as a result, I was transferred into the lower Introduction to High School Math, where I just managed to scrape by. My negative attitude towards school in my freshman and sophomore years of high school would live to haunt me when I struggled my junior and senior years to improve my GPA. Despite getting nearly all A’s and B’s the last two years, my GPA at graduation was a dismal 1.8, placing me close to 345 out of a class of 500.
After graduation from high school, I enlisted in the Navy. My ASVAB (Armed Forces Vocational Aptitude Battery) scores indicated I was on the high-end of their scale. I was by no means a “super genius,” but I scored better than 80% of my contemporaries taking the test. An opening in Electronics school because someone else failed to graduate gave me an opportunity to get more education than I had thought. Of course, the pre-school for electronics school just happened to be known as B/EE, or Basic Electricity and Electronics School, and it was nearly all mathematics. At the time, I had no idea about the men who pioneered what I was studying. Later I would discover they were the life works of people like Georg Simon Ohm, Andre Ampere, , Michael Faraday, James Maxwell, Rudolf Clausius, James Joule, and many others. The most important thing I remember from this time was Ohm’s Law, which allowed one to determine resistance, voltage, or current in a series circuit if one had at least two of the values. As many of my peers discovered, the calculations fell into a nice pattern that was easily remembered as a triangle:
I
E R
I = current measured in Amps
V = Voltage, measured in Volts
R = Resistance measured in Ohms
To find the current, cover up the I, and you know it’s V multiplied by R. To find either the Resistance or the Voltage, cover up the desired item and it is I over its opposite. This worked great in simple circuits, but they didn’t stay simple for long. Soon I was knee deep into circuits with values that changed depending on the state of gates, semi-conductors, and diodes. It got pretty complicated and I was nearly out of my depth on more than one occasion. I managed to pass BE/E with a 73%.
Electronics school proved too much for my brain. Despite spending a lot of time in extra-study, I just couldn’t keep up and I failed. Because of my extra study hours, I was given the opportunity to be reclassified into another rate. After careful consideration of the choices, I ended up in electro-mechanical calibration and repair. This presented another whole aspect of math and physics I was ill-prepared for, but it also provided me with an opportunity to shine. The school spent an entire month teaching what I had learned at BE/E in 7 months. I didn’t really need to pay attention because they were not presenting anything new. In the months that followed, I was able to grasp the concepts of machines, pressure, torque, temperature, mechanical revolution, precision instrument measurement, and several others. I graduated from this school with a 92%.
Despite this early success, my thinking was not very clear, nor was my problem-solving skills very sharp. I would manage to pass promotion tests by a narrow margin, and I was able to perform most of the duties I was assigned to, but I was not the best technician in the world, mostly because I lacked the necessary patience, forethought, and discipline. As my Navy career winded down, I began to look at college. As a sailor, I was afforded an opportunity to take the SAT’s at no cost to me. I scored a 970. Again, this was my abilities as a reader and writer that allowed me to score high on the verbal, and rather dismal on the math. To nobody’s surprise I looked towards earning a degree in a Liberal Arts field.
My college entrance exams indicated I had the necessary skills in English, but lacked math skills. I was enrolled to take Introduction to College Algebra against my wishes. I did try hard, but my frustration, lack of patience, and lack of interest led me to drop the class and seek a degree program that had no math requirement for graduation. I had neatly side-stepped the problem for the time being. However, again and again, I would find myself in situations where math skills were crucial, and I would be unprepared.
By this time, my affinity for all things computing had made itself evident. I had a “knack” for figuring out how to make them work, how to fix basic problems with them, and how to get the most out of them. As a result, I began looking into graduate coursework in computing, where, not surprisingly, I ran into math once more. My first programming class was in C programming . I worked very hard at this, but I never quite felt like I knew what I was doing. The people around me chattered in what seemed to me to be some sort of foreign “techno-babble.” The only reason I passed this class with a “B” was because I had help on my final exam. My program worked really well until it got to the very end when it was supposed to output the results of a mathematical problem. For whatever reason, I couldn’t resolve the error, but a friend of mine saw the issue in a moment and fixed the one or two lines of code needed to make the program work. If this hadn’t happened, I don’t know if I would have passed the class. At the time I was just so relieved to have gotten by this obstacle that I really didn’t consider the fact that no matter how one slices it, I cheated to pass a class. I am not prone to cheating in anything, but in a subject I desperately wanted to learn more about despite my perceived struggles and handicaps, I let it slide. Of course, my lack of understanding would have dire consequences on the next programming class I took.
The next class took C programming several steps further. We were looking at how to use the language to solve more “real world” problems, most of which were purely mathematical in nature. I withdrew from this class twice to avoid failing it outright and I never got a chance to take a programming class at this school again. I got a job teaching computers at a local high school and dropped out of graduate school all together.
My very first teaching job paid very little. My fiancée had been trying to get hired by any district in the area with little or no success, so we both applied to districts outside where we lived and landed interviews with the Clark County School District in Las Vegas Nevada. As luck would have it, both of us got hired, so we packed up and moved across the country to better paying teaching jobs in Nevada.
I taught for a year and found teaching was not what I thought it was going to be. I was not as well-prepared for a more “traditional” classroom as I had thought from a year teaching computers. The rules had changed and I didn’t adjust with them very well. Within a year I was politely told my contract would not be renewed. I was out of a job. I took refuge in the realm that I loved so much: computers. By the time the school year ended, I was on the phones doing technical support for Dell Computers.
My first tech job did not pay very well, but it did have regular bonuses for good call times and resolutions. I quickly gained a reputation for being able to help people with their problems and resolve calls efficiently. My monthly bonuses were among the top 10 for the six months I remained a phone technician. Then I was promoted. My career as a tech would take many unusual twists and turns, sometimes I was out in the field, sometimes I was on the phones, still other times, I was given very non-specific duties to support computing efficiency. All of these jobs were sub-contracting. All of them carried little in the way of benefits and stability. Most of them ended up with my contract being terminated after my services were no longer needed.
In an attempt to improve my chances of landing a more stable position, I decided to go back to school and pursue a Masters in computing. I ended up at the University of Phoenix in their Computer Information Systems Management degree program. Here I began to see what it takes to really run technology projects, how to understand the very uncertain nature of the business world’s take on computing. Technology projects are rarely cheap and more business-minded individuals have a hard time seeing what they call a “return on investment” from them. Technology projects often bolster the infrastructure of a business, but rarely do they have an immediate or direct impact on the bottom line, rather, their benefits are realized in very small increments over a much longer term. This has a tendency to make men and women who are responsible to shareholders nervous and reluctant to allocate funding and resources to IT departments.
As I am now coming to the end of my masters program, a new fire has begun to burn brightly within me. My field has many organizations, journals, conventions, and resources that I have become more aware of. As the industry changes at the speed of light, so must I continually keep up with it through research, reading, and communicating with my peers. As with so many others, my career field often “brushes up against” the fields of science, math, and engineering, so much so that I have become far more aware of the implications they have upon my future. As a result, I have come to read far more technically-oriented materials. I have successfully programmed computers using a variety of programming languages. I have come to see my lack of math skills as a detrimental flaw in my abilities. I have also begun to understand what I never understood before. My lack of understanding of math and science was just that, a lack of understanding. Now that I understand the underlying principles of both, I find myself drawn to the very problems and theories I used to repel from. I want to learn them. I want to be able to apply them. I want to know more. In essence, maturity and a new sense of myself have driven me full circle, and I am no longer afraid.
One day, I was reading what I thought was a fascinating article in Scientific American, where astonishing new theories concerning black holes were just coming to light. These new theories were causing scientists to look at the universe in a radical new way, as one big giant computer. It was once believed that nothing escaped the gravitational forces of a black hole, but brilliant astrophysicist Stephen Hawking, helped prove that some energy did escape from a black hole. Thus it was theoretically possible to input physical matter into a black hole and measure the output energy in a similar way to how one would enter data into a computer program and measure the output. This speculation does not answer whether or not the output would make sense in relation to the input, but the theory is none-the-less fascinating. The article also mentioned something called quantum information theory, which caused me to do a web search on that subject, and that led me to information theory, and a man named Claude Shannon.
In 1948, a mathematician working for Bell Labs named Claude Shannon proposed a mathematical theory for calculating the most efficient means of transmitting a message over a noisy channel. This theory was so revolutionary at the time that it led to breakthroughs in all aspects of communication, electronics, digital electronics, computing, and more. Shannon’s breakthrough paper, A Mathematical Theory of Communication, became the foundation upon which most of our Information Age would be built upon. Here is a man who more than likely died not knowing just how much impact his work would have upon the future. Here I was reading the paper and actually understanding the basic principles of it. Since then, I have ordered more books on this subject, and after that, I began ordering books on subjects such as discrete math, physics, Scientific math, and so on. I have joined the Institute of Electrical and Electronics Engineers, so I could get more access to the “bleeding edge” of technology today. I am looking towards finishing my masters and going on for a PhD. in Information Systems at Nova Southeastern University.
Along with all these developments, I began working as a junior Satellite Hub Technician for Hughes Network Systems, which again has required I learn the finer points of the engineering necessary to keep major satellite communications systems operating, troubleshooting remotely, and understanding the principles of electronic satellite communications. Once again, the marriage of science, math, and technology are demonstrating to me that I cannot hope to pursue a career in this field without all three of them. This time, I’m ready.
TANSTAAFL!
©2004, J.S.Brown
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1.20.2005
Done with Mirrors: The Impossible Paradox of Public Education
The Outside Looking In – Societal Perceptions
Public education for the majority of the Twentieth Century was modeled after the Industrial Age assembly line and behavioral psychology, which equated every student as merely a set of stimuli and responses, rather than as individual human beings with individual wants and needs. Students were “tracked” according to whether they were considered bound for further academic, general, or vocational training. Students who were unable to “fit” within these three areas were hidden away from view. Students were expected to behave, sit in rows, take notes, respond to teacher-led discussions, and come up with identical answers to problems. Deviation was not tolerated. Corporal punishment was permitted, as were other severe methods of forcing conformity. Students learned a much regimented curriculum that was considered to be more than adequate preparation for a male to spend a lifetime working in a factory, an office building, or further training at academic institutions. Exceptional males might become doctors, lawyers, or engineers. Female students were trained to be home-makers, secretaries, or teachers. The exceptional female might rise above these more common occupations as a nurse.
War changed many things. World War II in particular, saw women leaving the homes and the “traditional roles” to fill in for the men. Women got a taste of what it was like to earn a paycheck and do all the things that society normally proscribed for men. When the men returned home, women were again strongly encouraged to return to the home and leave “everything else” to the men. For a time at least, women seemed willing to reprise their previous roles, (but the times, they were a changing).
The “Baby Boom” that followed WWII would have a dramatic affect on public education. This dramatic increase in population would lead to the development of suburban housing tracts, which in turn encouraged the production of more roads, more cars, more home appliances, more babies, and of course, more schools. Everything about the Baby Boom would require the “assembly line” model of schools be rigidly enforced. There were simply too many kids for schools to cope, let alone experiment, with any other model. Besides, parents, teachers, politicians, and administrators were all of one mind when it came to education in this era. They worked together for the benefit of each student, so long as each student complied and conformed. Non-compliance and non-conformity was, by necessity, a punishable offense.
The evolution of public education from this very rigid model in the 1940’s and 1950’s would play an integral part in the social upheaval and backlash of the 1960’s. With the advent of the birth control pill, women were once and for all freed from their traditional roles. They could finally be as promiscuous as men without the constant fear of pregnancy. Women began to desire a larger role in society than that of the few professions open to them, and the one their wombs designated for them. This along with the anti-authoritarian backlash of the Vietnam War caused a major distrust of our government leaders and government institutions, of which public schools were. The new “liberated” parents of the younger generations would carry their distrust and disdain for authority to such an extent that it readily boiled down into their children, who became increasingly more unruly and undisciplined. The powers that were given to schools to enforce rigid conformity and discipline were taken away and replaced with no power at all. The Post Baby Boom generation, Generation “X” (my generation) would be passed the torch lit by the previous generation, and it would forever change public education.
By the time I was of school age, television was no longer a curiosity, but an influence to be reckoned with. New technologies were emerging that would bring motion picture special effects to never-before viewed levels. We were on the edge of the computer explosion, and the seeds of the Internet were already being sewn. By the time I was in sixth grade, (1981) cable television was becoming the norm (those who could not get cable had satellite dishes). The rotary telephone was rapidly being replaced with the touch tone. Answering machines were starting to be seen, and the first generation of affordable personal computers was flying off the shelves. VCRs, microwave ovens, and Compact Discs would soon follow, as the promise of the emerging Information Age began to gather steam.
Nobody could have predicted how far we would come from a technological standpoint, but this was one “Pandora’s box” that nobody wanted to close, and no institution would feel the brunt of this dramatic change more than public education. At the time, there were very few teaching jobs to be had. Teachers were often not well-paid, but they had good benefits, plus they had excellent vacation time. Most teachers taught their classes based upon the classical training given them using methods that were valid in previous Industrial Age era classrooms, but these methods were no longer valid in Information Age classrooms. The knowledge gap between teachers and students was no longer the same. Most teachers knew more about their content area than students, but they lacked the added dimension that technology could have offered them; students began to have an ever-widening edge that left most teachers behind. This phenomenon has continued to the present day in many ways. The older generations do not, as a rule, truly understand or comprehend technology, and have been intimidated by it, whereas the younger generations have grown up immersed and inundated by it. The Information Age has caused us to view “literacy” in a whole new light. Once this meant merely the ability to read, now literacy is applied to a much broader spectrum of abilities and understandings.
The New Student is not as challenged by the ideas of the past, not when they have the ideas of the future all around them all the time. They cannot relate to the written word the way previous generations did, for them, the written word is something one does only when one cannot use some other means of communication; and then usually it is truncated for use in text messaging over cell phones or the internet. Young people are constantly entertained by high technology means to the point that they find any other means of entertainment dull by comparison. Getting their attention and keeping it, takes far more effort than most teachers are capable of providing. It is not just that we are in an Information Age anymore, but that we are in a Digital Information Age that continues to elude educators and administrators alike. For young people who can not imagine a time before 100+ channels on TV, VCR’s, DVD’s, Cell Phones, Personal Computers, and so on, how can it be that we’re still using essentially the same methods of teaching and learning that haven’t been valid for more than 50 years?
We have a large amount of schools spread out over a large area. Not only do these schools have to contend with the fact that they are outdated in a period of rapid technological and social upheaval, but they have their own regional issues to deal with. Nearly all public schools have fluctuating student populations, and many face the lack of adequate resources to contend with this. Many formerly industrialized regions have seen those industries dry up and blow away (along with the funding these organizations provided). Severe poverty in these regions results in low teacher pay and even higher teacher expectations. Schools are seen as the “only way out” for many young people. Involvement in scholastic athletics is for many, their only way to afford a college education. For the relatively few who are talented enough to go beyond collegiate sports, there is the allure and dream of professional sports. Academics thus become a second-class citizen in this lofty pursuit; seen only as a means to an end, rather than the end in itself. The “heroes” of the school become the stereotypical male athletes and their cheerleader girlfriends. Hierarchy is determined not by who is the smartest, but by shallow concepts of popularity and vanity. The smart kids, who might someday actually have something to contribute to the world, add very little to the reputations of the schools, are given extra “brain teasers” to work on. Academics are devalued in our society. Intellectuals are considered “radical liberals” and “socialists” by adults, so why should young people view them as valuable? Smart people are viewed with distrust and distaste. They are given labels such as “geek” and “nerd.” They are often viewed as social outcasts because they aren’t a part of “the norm.”
Another group outside the norm is the “rebels,” who are often very smart, but use that intelligence to rail against rigid authority. Many of them come from broken homes, where they experienced firsthand the imperfections of the most important adult authority figures in their lives. Without being able to trust their own parents to be consistent and make them feel secure, it is no wonder why so many young people have an intense distrust and dislike for all authority figures. These are the ones who spend an inordinate amount of time in detention, in suspension, or waiting for more punishment to be meted out just outside the principal’s office. Their emasculated (and often split) parents just shrug and throw their hands up, not knowing what to do to correct the many problems their children encounter. Parents who can barely own up to their own irresponsible behaviors are unable to force their children to face them. The parents are victims of poor choices, and it is their children that ultimately suffer for them. This is too much for most parents to accept, so they want someone else to blame. Send in the teachers.
Public education in America has suffered through a social and technological crisis that is difficult to understand. It has its roots in the anti-authoritarian movement of the 1960’s which led people to see anything that had ties to the government as “the enemy.” Young people then became the parents of a generation of kids who were not subject to the same rigid discipline at home, and thus did not behave as such when they entered school. The children of the 1970’s also had an advantage over their predecessors, thanks to television shows such as Sesame Street and Mr. Rogers; they came to school with what were considered advanced skills and knowledge at the time. Schools had to adjust their curriculum to deal with a generation of kids who learned more and more from visual media rather than the written or spoken word. Schools did not adjust well. Many of them tried very radical changes that inevitably failed and the response was to force them to go back to what had worked before, but which couldn’t possibly work on a generation of students that lacked the same set of social and academic backgrounds as the students before them.
The Inside Looking Out – Teacher Perceptions
The law of averages seems to indicate that a given classroom of kids will spread out over a bell shaped curve that describes their grade level, skills, and abilities, but cannot assess potential. The highest number of children in the class will fall into an "average," whereas a minority of them will appear in the "low-end" and "high-end" portions of the curve. Because of the large numbers of young people there are in the public school system, it becomes a "numbers game," in which the most popular strategy is to "...teach to the middle" and hope that the "low-end" students can somehow keep up and the "high-end" students can somehow occupy themselves.
Then we use “one size fits all” standardized testing to score the performance of a school. These tests lack any incentives for the students to take them seriously, (and many of them do not) but are taken seriously in the assessment of the performance of the school. In our score-driven society, public schools are being tried, judged, convicted, and condemned, all based upon faulty criteria which seeks to vindicate parents and politicians of any wrongdoing in the matter, thus leaving the blame on the schools, (which eventually filters down to the teachers). This, of course, is only the academic portion of the story.
From a behavioral point of view, we have students with all sorts of issues and problems, many of which have nothing to do with school. The vast majority of them are likely due to issues with their family, and a good portion of them are the result of physiological, psychological, and neurological abnormalities that range from minor to severe. It used to be that those who demonstrated a severe threat, whether behavioral or academic, to the progress of the class as a whole were segregated from the "normal" classroom. This led to an outpouring of parental complaint that has now created the "multicultural" or "inclusive" classroom environment. By law child must now be placed in the least restrictive environment in which he or she can achieve according to whatever limitations they may have.
The problem with this concept is that the classroom teacher is not adequately trained, nor prepared to handle children with everything from minor to severe developmental delays, lack of ability or skills, behavioral abnormalities, and the various accommodations these children may require. Some children with these sorts of problems are "shadowed" by a special education facilitator, but this sort of assistance is generally hard to come by.
What we have is a veritable pressure-cooker of problems being compounded by political, economic, and social pressures which make heavy demands upon an institution without providing it with the necessary tools and resources to properly enact them. We then have the same political and social pressures blaming the institution for its inability to carry out the impossible tasks for which the pressure was brought to bear in the first place. In the vicious cycle of events, everyone blames the other, nothing ever gets done, and the students are the ones who ultimately get short-changed, by receiving a mediocre education at best.
The result of these two dissimilar images is one of anger, frustration, confusion, and disillusionment. Both are no more than reflections in a mirror; the perceptions of the people who are looking into them for the truth, and seeing only what they want to see. The current negative perceptions of teachers will eventually reach a point where there won’t be enough of them to go around. While this may benefit the current crop of teachers, it is certain to have a negative outcome on the student population. It is up to every part of the educational process to recognize their roles and responsibilities if we are to cure what ails public education. Only when parents, teachers, administrators, politicians, and students throw away their mirrors and start working with one another will things improve. As long as everyone remains locked in a constant battle to deflect the blame, there is no way the false images can be changed.
TANSTAAFL!
©2005, J.S.Brown
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