My perspective concerning the situation in the public schools displays a measure of cynicism. The reasons for this are numerous, and run far deeper than budget cuts and limited teacher openings. School systems have for over 10 years complained of shortages of qualified math (and science) teachers. This phenomenon is in fact not the problem, but rather a symptom of the problems in today's public schools.
A mathematician such as myself, with a long family history of scholars and educators, may initially find the prospect of working in the public schools to be attractive. He expects that his innate mathematical talent will be appreciated by many of the students, and that the kids will respect his consistent enforcement of his behavioral standards in the classroom. Given that school systems complain of shortages of math teachers, he expects school principals will be highly motivated to support him as a teacher, and certainly will want to award him tenure at the end of his second or third year in the district. He naturally intends to grow as a teacher over the years, and- being tenured- will be able to provide for his family from that point on.
When he finally completes the credential program and enters the classroom, he faces the reality of today's public schools. Many students appreciate his mathematical knowledge and talent, but others would prefer not only to avoid learning, but also to disrupt the class and prevent all of the others from learning. The mathematician is initially patient, but soon needs to discipline the non-compliant students. Now the mathematician's personality becomes a liability. In most cases, the administrators do not support the mathematician's actions, but rather blame him for some of the students' disruptive behavior! It is not the kids' fault for misbehaving; rather, the teacher is responsible for not being able to relate well to these kids and- by establishing rapport with all of them- inspire them to not misbehave. The new student-centered learning environment requires the teacher to mould his expectations to the kids' wishes. Many kids are rude and discourteous, seeing nothing wrong in blatantly talking to classmates when the teacher is talking. Teachers who actually follow school policy prohibiting use of cell phones, headphones, and the like in class are considered "uncool" and overly strict by kids, who respond by being even more disruptive. Consequences for repeated disruption or even severe misbehaviors are usually light, and the kids are well aware of this. The inmates are now running the asylum! Only a master in the area of social interactions can manage these kids, and the mathematician- who as I indicated previously is typically deficient in this area- will find this a struggle. Even as he exerts his maximum available energy into running his classes, and several off-duty hours per day preparing for classes, grading, contacting parents, meeting parents, tutoring students and/or holding after-school detention, he finds his efforts are unappreciated by many students, their parents, and many administrators. He now knows the reason that 50% of teachers leave this stressful profession- often after such stress affects their health- within 5 years. (From personal experience, nearly everyone in the teaching credential program is initially energetic, altruistic, and optimistic as they prepare to enter the field of education). It is also evident why school districts face a shortage of qualified math teachers. Mathematicians and scientists are not desired in the classroom. Instead, administrators seek teachers who can relate well to and be accepted by their kids, including the difficult kids who have no desire to learn. Oh, by the way, we cannot use the term "bad kids"; rather, those who are a challenge are classified as "good kids who make bad choices." This follows even though the presidential and vice-presidential candidates in 2008 freely made reference to "bad teachers" who should not be in the classroom. What administrators seek are not masters of the subject matter, but rather masters of socialization and interaction with their students. Subject matter mastery is far less important, leading to mediocre quality of education. Future innovation in this country- which would greatly help our economy in the long term- is impeded, as both administrators and politicians are focused on the short-term at the expense of the long-term.
Wednesday, March 17, 2010
Tuesday, March 16, 2010
A Mathematician's Greatest Weakness
A very commonly asked interview question is, "What do you consider to be your greatest weakness?" The old school of thought was that an interviewee should cleverly answer this question and turn his weakness into an apparent strength. I shall not follow this approach, but rather shall honestly address this issue.
Stated quite simply, we mathematicians tend to have personalities which deviate significantly from the norm. In social settings especially, we tend to be quiet, introverted, and eccentric to varying degrees. I would thus describe my personality as my main weakness, one which has substantially impeded my career advancement over the years.
I can relate that in my own experiences in education, certain colleagues (who will remain nameless) have raised this issue with regard to myself. I shall make further reference to my experiences in the public schools on a future posting. For now, however, I shall point out that in teaching especially, a mathematician is likely to find his personality is a major liability.
From personal experience, personality has proved a obstacle in many settings. In an interview from several years ago, I recall a hiring manager informing me "You're quiet!" less than one minute into the interview. He made this observation- which was obviously intended negatively- based on my demeanor and social graces, before he had asked me any questions!
On a number of interviews (none of which led to a job offer), the interviewer began the interview by asking me, "Did you find us okay?" My reaction to this question may have been my undoing. To a non-mathematician, this question is probably intended and received as a social ice-breaker. A mathematician's mind works differently, and processes the question as a logical absurdity. Our mind processes something like this: "Illogical!! I am sitting right in front of him, and he is asking me if I found them okay? This question does not compute! Is there an alternative meaning intended in this instance? Attempting to analyze... Illogical! Recommend answering in the affirmative..." This entire mode of thought takes place within 1-2 seconds, perhaps less. However, in that short time the interviewer has noted our look of perplexity, or perhaps sardonic amusement, and that mere facial expression- however brief- is sufficient to cost us a potential job offer.
We learn in modern economic theory that companies will take actions so as to maximize their profits. This same theory would include hiring and maintaining employees based entirely on their qualifications and ability to perform their jobs. History has shown this theory is not altogether accurate. Past racial discrimination is a clear example of this; better qualified people were often declined on the basis of their ethnic and/or religious identity. Nowadays, although racial discrimination has greatly decreased in this country, employers do often consider superficial factors such as personality, demeanor, and the like, and thereby pass up more qualified applicants in favor of less qualified ones because they are more extroverted, charismatic, or the like. Acquaintances in the past have advised me that I should present myself as more outgoing at interviews; in response, this advice is unhelpful as it incorrectly presupposes an ability to maintain this facade every working day.
I have now openly presented the main weakness of myself, and probably that of most mathematicians, as a potential employee. Having accepted this weakness, I now move forward....
Stated quite simply, we mathematicians tend to have personalities which deviate significantly from the norm. In social settings especially, we tend to be quiet, introverted, and eccentric to varying degrees. I would thus describe my personality as my main weakness, one which has substantially impeded my career advancement over the years.
I can relate that in my own experiences in education, certain colleagues (who will remain nameless) have raised this issue with regard to myself. I shall make further reference to my experiences in the public schools on a future posting. For now, however, I shall point out that in teaching especially, a mathematician is likely to find his personality is a major liability.
From personal experience, personality has proved a obstacle in many settings. In an interview from several years ago, I recall a hiring manager informing me "You're quiet!" less than one minute into the interview. He made this observation- which was obviously intended negatively- based on my demeanor and social graces, before he had asked me any questions!
On a number of interviews (none of which led to a job offer), the interviewer began the interview by asking me, "Did you find us okay?" My reaction to this question may have been my undoing. To a non-mathematician, this question is probably intended and received as a social ice-breaker. A mathematician's mind works differently, and processes the question as a logical absurdity. Our mind processes something like this: "Illogical!! I am sitting right in front of him, and he is asking me if I found them okay? This question does not compute! Is there an alternative meaning intended in this instance? Attempting to analyze... Illogical! Recommend answering in the affirmative..." This entire mode of thought takes place within 1-2 seconds, perhaps less. However, in that short time the interviewer has noted our look of perplexity, or perhaps sardonic amusement, and that mere facial expression- however brief- is sufficient to cost us a potential job offer.
We learn in modern economic theory that companies will take actions so as to maximize their profits. This same theory would include hiring and maintaining employees based entirely on their qualifications and ability to perform their jobs. History has shown this theory is not altogether accurate. Past racial discrimination is a clear example of this; better qualified people were often declined on the basis of their ethnic and/or religious identity. Nowadays, although racial discrimination has greatly decreased in this country, employers do often consider superficial factors such as personality, demeanor, and the like, and thereby pass up more qualified applicants in favor of less qualified ones because they are more extroverted, charismatic, or the like. Acquaintances in the past have advised me that I should present myself as more outgoing at interviews; in response, this advice is unhelpful as it incorrectly presupposes an ability to maintain this facade every working day.
I have now openly presented the main weakness of myself, and probably that of most mathematicians, as a potential employee. Having accepted this weakness, I now move forward....
Monday, March 15, 2010
Mathematics Applied to Civil Engineering
One additional career field- aside from those mentioned in my previous posts- requiring a strong mathematics background is civil engineering. "Estimators" (often with assistants) are needed to interpret engineers' plans of public projects and perform "takeoffs", mathematical calculations. In excavation, for example, estimators need to calculate the volume of dirt moved, as well as the amount by which to decrease or increase the altitude (cut or fill dirt, respectively) at any given location. This information is needed in the bidding process, when endeavoring to simultaneously compete with other excavation companies, as well as guiding the workers in the field when the actual excavation is completed.
A mathematician working in this field can appreciate the application of numerical analysis and modern computer technology to greatly reduce the time required for excavation takeoffs. Prior to the computer age, a civil engineer was compelled to make use of a planimeter, a useful device which computes the area of a figure it is rolled around. By rolling it around contour lines at various intervals, for both the natural (untouched) and final (excavated) grades, civil engineers used this device to compute volume, estimated as the sum of the volumes of figures with base defined by the contour line traced and height determined by the interval at which the contour lines are traced. Modern-day computer software packages perform this calculation much more quickly. Civil engineers can now use software packages allowing them to digitize contour lines, add grade breaks along altitude gradients, and direct the computer to perform this calculation (within a few minutes, at that point). Takeoffs are still quite time-consuming, but much less so than prior to the availability of computer technology.
A mathematician working in this field can appreciate the application of numerical analysis and modern computer technology to greatly reduce the time required for excavation takeoffs. Prior to the computer age, a civil engineer was compelled to make use of a planimeter, a useful device which computes the area of a figure it is rolled around. By rolling it around contour lines at various intervals, for both the natural (untouched) and final (excavated) grades, civil engineers used this device to compute volume, estimated as the sum of the volumes of figures with base defined by the contour line traced and height determined by the interval at which the contour lines are traced. Modern-day computer software packages perform this calculation much more quickly. Civil engineers can now use software packages allowing them to digitize contour lines, add grade breaks along altitude gradients, and direct the computer to perform this calculation (within a few minutes, at that point). Takeoffs are still quite time-consuming, but much less so than prior to the availability of computer technology.
Saturday, March 13, 2010
The Engineer and the Mathematician (a joke)
I could not resist including this joke, widely told among mathematicians. Besides, life is incomplete without a sufficient dose of humor...
An engineer is asked the following question:
"You are in a modern kitchen, with an empty pot, and need to produce 2 quarts of boiling water. How would you do this?"
Replied the engineer, "Fill the pot with at least 2 quarts of water from the tap, put the pot on the stove, turn on the stove, and wait for the water to heat up to the boiling point."
A mathematician is asked the same question, to which he replies, precisely in the words of the engineer, "Fill the pot with at least 2 quarts of water from the tap, put the pot on the stove, turn on the stove, and wait for the water to heat up to the boiling point."
The questioner now returns to the engineer, and asks the follow-up question:
"Now imagine you are in the same kitchen, but the pot is already filled with at least 2 quarts of water. How would you produce 2 quarts of boiling water."
Replied the engineer, "The task is simpler! Put the pot of water on the stove, turn on the stove, and wait for the water to heat up to the boiling point."
The mathematician is asked the same follow-up question, to which he replies:
"Take the pot of water, pour it into the sink- down the drain- and put the empty pot down on the counter. Now it reduces to the previous case!"
An engineer is asked the following question:
"You are in a modern kitchen, with an empty pot, and need to produce 2 quarts of boiling water. How would you do this?"
Replied the engineer, "Fill the pot with at least 2 quarts of water from the tap, put the pot on the stove, turn on the stove, and wait for the water to heat up to the boiling point."
A mathematician is asked the same question, to which he replies, precisely in the words of the engineer, "Fill the pot with at least 2 quarts of water from the tap, put the pot on the stove, turn on the stove, and wait for the water to heat up to the boiling point."
The questioner now returns to the engineer, and asks the follow-up question:
"Now imagine you are in the same kitchen, but the pot is already filled with at least 2 quarts of water. How would you produce 2 quarts of boiling water."
Replied the engineer, "The task is simpler! Put the pot of water on the stove, turn on the stove, and wait for the water to heat up to the boiling point."
The mathematician is asked the same follow-up question, to which he replies:
"Take the pot of water, pour it into the sink- down the drain- and put the empty pot down on the counter. Now it reduces to the previous case!"
Ph.D. Program in Mathematics
For mathematicians who are admitted to a Ph.D. program, some (like myself) are treated to a strong dose of humility. The universities' math departments quickly proceed to screen their Ph.D. students in such a way that- within a few years- about 1/2 of them ultimately drop out of the program. The method of screening such students is the qualifying exams, which the graduate students dreadingly refer to as "the quals." Students must pass courses, but professors usually pass most of the students in their courses; "the quals" are the main obstacle students must overcome. Most of the problems on the quals are of the form "Prove that..." or "Show that ...." Preparation for the quals requires incredible memory capacity- memorizing all of the proofs that might potentially be covered, and incredible devotion to spending sufficient hours studying them. Ph.D. students are usually offered 4 years of "funding", which consists of a small salary (about $13,000 back in 1997) and free tuition as payment for TAing undergraduate math courses. TAing involves leading about 4 discussion sections per week, holding 2-4 office hours per week, and grading tests and quizzes. I remember TAing as the most enjoyable part of the program. However, "funding" is contingent on following the timeline for passing "quals"; once a student falls behind (which happens to most), they are subject to losing funding, being bumped down to the master's program, and ultimately removed from the program. The Ph.D. program is described in the universities' catalogs as a 4-year program, of which the first 2 years are spent passing qualifying exams, and the last 2 years focus on completing the dissertation. Very few (if any) of the Ph.D. students- even the successful ones- ultimately follow this timeline. Most of those who complete the program require 3 to 4 years to pass all of the quals. Only then are they allowed to begin work on the dissertation, which takes another 2 to 3 years. Those who ultimately complete the program typically do so in 5 to 7 years; thus, they are lucky to be done with school by the age of 28 or 29.
Whereas college allows for a healthy balance between studying and participating in the social and cultural life on campus, successful completion of the Ph.D. program requires intense immersion in mathematics and self-isolation that is excessive to some of us (like myself). Here is where I must diverge from those who completed the program and will ultimately become leading researchers in mathematics. This blog is for mathematicians who- like myself- left or chose not to enter the "ivory tower" so to speak, and realize they must function in the "real world."
Whereas college allows for a healthy balance between studying and participating in the social and cultural life on campus, successful completion of the Ph.D. program requires intense immersion in mathematics and self-isolation that is excessive to some of us (like myself). Here is where I must diverge from those who completed the program and will ultimately become leading researchers in mathematics. This blog is for mathematicians who- like myself- left or chose not to enter the "ivory tower" so to speak, and realize they must function in the "real world."
Friday, March 12, 2010
Military Career
For a young mathematician, entering the military as an officer may be a viable career option. The U.S. military recognizes the mathematician as a valuable long-term asset to the country, and will provide the necessary job training. Lack of prior technical experience is thus not an issue. Our military naturally possesses cutting-edge technology, and thus the opportunity to participate in research and development not found in the corporate setting. In the Air Force, for example, mathematicians can potentially work in space and missile operations. For the science fiction enthusiast like myself (and probably many of you), this path is reminiscent of the Star Trek universe. While at UCLA's graduate program in math, a small panel of young mathematicians from the Air Force gave a presentation in which they described- very positively- their experiences as officers. Before entering the military, they had unsuccessfully endeavored to begin their careers in industry (during the 1990s, when the economy was booming). They described their huge collection of rejection letters, to which many of us can relate. Later in this blog, I shall consider the issue of why we mathematicians tend to amass large collections of such letters. However, in the Air Force- with the logical structure and merit-based system in which we mathematicians thrive- these gentlemen had found their niche. I can certainly relate to the appeal of following the military path, and- to relate my personal experiences- very nearly did so myself. After passing the required written tests and interview process, applicants to the officer training program are required to pass a very rigorous and thorough medical exam. In my case, severe myopia (nearsightedness) was sufficient to disqualify me. If you are nearsighted or have any medical issues whatsoever, be prepared for this possibility. In addition, before pursuing this career you should realize that while the military recognizes families as such, you can expect to be transferred between bases frequently, and perhaps endure periods of being separated from your family for temporary duty assignments. If you are single at the moment, please consider that your perspective in this regard may well change once you are married.
Thursday, March 11, 2010
College Guide for the Gifted Mathematician
As a mathematically gifted young adult, you enter college with a sense that the tremendous forward momentum in your mathematical development will proceed - and perhaps accelerate- for many years, perhaps decades, to come. I speak from personal experience. If your teenage years resembled mine, you are accustomed to the terms "mathematical genius" and "genius" describing yourself. You may have memories of winning prizes at numerous local math competitions. You were a kid frequently called in to the principal's office, but for positive recognition rather than punishment. At the current moment, you probably perceive that your mathematical talent will inevitably be regarded as an asset to potential employers. You might dismiss the possibility of facing future unemployment or encountering difficulty finding a job after graduation. With your math degree- especially a graduate degree- you might not even have to apply for jobs; rather, companies will come after you. Right???
Ultimately, reality will set in. I can offer advice to you as I would if I had a time machine, and could travel back in time 15 years to counsel myself. If you are a declared math major, or leaning in this direction, it may be advisable to contemplate your long-term goals to guide your current course of study. A major in mathematics is well suited to the field of education- at the secondary or college/university level, or if you intend to pursue a Ph.D. in math. A math major may serve you well if you are considering applying to enter the military as an officer. In recent years (from personal experience), companies posting finance-related positions with the word "analyst", such as "data analyst", "financial analyst", "demand planning analyst", etc. are generally seeking math majors. If you are seeking an analyst position and can reconcile yourself to a finance-based position, a major in math or applied math- ideally with an economics minor- might be the ideal path for you. I would recommend the same if you are considering becoming an actuary or accountant, careers often associated with a math background; these do, however, require additional study after college. Accountant positions typically require an CPA (2 years in duration). Companies hiring actuaries tend to want evidence of commitment to the profession demonstrated by passing at least the first 2 exams given by the SOA (Society of Actuaries). As a mathematician, you could "easily" order the books to study for these exams, and register to take these exams. You would need to invest the time and money to prepare adequately for these exams (especially the 2nd). As I understand, the first exam is essentially math; subsequent exams become increasingly specialized and difficult.
If you are seeking a more technical position- such as working for aerospace, a computer company, or with engineers- changing your course of study at least slightly is probably advisable. In the past decade, there were countless positions posted that were described as "software engineer", "systems engineer", "C++ programmer" or the like. While these positions usually listed a Bachelor's degree in math as a sufficient educational background, they demanded technical experience which a mathematician finishing college (or perhaps even graduate school) would generally not have. Even an "entry level software engineer" applicant was often expected to have 2 or more years experience programming in C++ and/or Java and/or Visual Basic. If you seek work of this nature, I would recommend you consider changing your major to computer science or engineering. Perhaps your university offers a major combining 2 of these departments- math/computer science, or math/engineering. This might be the ideal choice for you. I make this advice tentatively, as it is difficult to predict the demand/supply of labor in the future.
Perhaps you are planning on pursuing your master's or Ph.D. in math. As I shall describe in subsequent blogs, and from personal experience, the doctoral program is more grueling and demanding than you may realize at present. About 1/2 of doctoral students end up washing out of the program. Bear in mind that practically all who are accepted into the program are "mathematical geniuses."
Ultimately, reality will set in. I can offer advice to you as I would if I had a time machine, and could travel back in time 15 years to counsel myself. If you are a declared math major, or leaning in this direction, it may be advisable to contemplate your long-term goals to guide your current course of study. A major in mathematics is well suited to the field of education- at the secondary or college/university level, or if you intend to pursue a Ph.D. in math. A math major may serve you well if you are considering applying to enter the military as an officer. In recent years (from personal experience), companies posting finance-related positions with the word "analyst", such as "data analyst", "financial analyst", "demand planning analyst", etc. are generally seeking math majors. If you are seeking an analyst position and can reconcile yourself to a finance-based position, a major in math or applied math- ideally with an economics minor- might be the ideal path for you. I would recommend the same if you are considering becoming an actuary or accountant, careers often associated with a math background; these do, however, require additional study after college. Accountant positions typically require an CPA (2 years in duration). Companies hiring actuaries tend to want evidence of commitment to the profession demonstrated by passing at least the first 2 exams given by the SOA (Society of Actuaries). As a mathematician, you could "easily" order the books to study for these exams, and register to take these exams. You would need to invest the time and money to prepare adequately for these exams (especially the 2nd). As I understand, the first exam is essentially math; subsequent exams become increasingly specialized and difficult.
If you are seeking a more technical position- such as working for aerospace, a computer company, or with engineers- changing your course of study at least slightly is probably advisable. In the past decade, there were countless positions posted that were described as "software engineer", "systems engineer", "C++ programmer" or the like. While these positions usually listed a Bachelor's degree in math as a sufficient educational background, they demanded technical experience which a mathematician finishing college (or perhaps even graduate school) would generally not have. Even an "entry level software engineer" applicant was often expected to have 2 or more years experience programming in C++ and/or Java and/or Visual Basic. If you seek work of this nature, I would recommend you consider changing your major to computer science or engineering. Perhaps your university offers a major combining 2 of these departments- math/computer science, or math/engineering. This might be the ideal choice for you. I make this advice tentatively, as it is difficult to predict the demand/supply of labor in the future.
Perhaps you are planning on pursuing your master's or Ph.D. in math. As I shall describe in subsequent blogs, and from personal experience, the doctoral program is more grueling and demanding than you may realize at present. About 1/2 of doctoral students end up washing out of the program. Bear in mind that practically all who are accepted into the program are "mathematical geniuses."
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