I had gone to a local hardware supply store (for my father) with the intention of buying some lengths of material which would increase the traction on a flight of stairs. This abrasive material was to be applied in 24 inch sections to 12 stairs. The material was rated at $1.59 per foot, and I needed him to cut me twelve 24-inch strips.
After mentally computing this to be $3.18 per 2-feet, and the total to be well over $36, (it was actually a little over $38; tax included brought the total to $40.93) and telling the clerk what I had figured, the young man assisting me just gave me a blank stare!
I would suppose that my point is this: that it is perhaps all too sad that few people wish to use their minds anymore. Even for a simplistic computation such as this, the clerk checked the $1.59 at 2-feet. Sure enough, it was $3.18. I'm not a math wiz, but I was struck by how much of a dependancy some have on "conveniences" such as a pocket calculator for simple addition. I found this remarkable.
WRW: It must make you wonder. If the people who are working with money are so unsure of themselves with fairly simple arithmetic, then there must be others who have no clue at all. I work with numbers daily and when I perform the simplest of mental computations with some speed and dexterity I am looked at by many as if I possessed some prodigious talent. I do not gloat or let on because I know this is the performance of a well practiced skill and no demonstration of higher ability. Many very bright people appear to loath anything to do with numbers.
JW: Yes, I totally agree with your views about people being reticent to perform calculations in their heads. I do suppose it is a skill, but hadn't really thought about it as such.
For several years, when extremely bored, it has been a habit of mine to raise a number to a pretty extreme amount in my mind. It is fun to do this when the person you are listening to happens to be speaking in a monotone, and you wish to block the sleepiness induced by his or her words! To me, it is much easier if the two sets of numbers being added are the same, as it is easier to visualize. An example is: 2+2=4, 4+4=8, etc., until I can no longer control the visualization. I do this probably in the same way that you do, in that I work from left to right. If there are thousands, I will first add the thousands together, then the hundreds, being sure to carry over when necessary, on down the line until all numbers are added. I don't consider this to be too phenomenal. As you said, it just takes practice.
CLF: I hope that this, my first posting, gets to the list...
Anyway, Isaac Asimov wrote a short story about this problem. In the tale, an elderly and otherwise rather ordinary man was paraded before the public and even studied by research scientists due to his prodigious talent. His astounding ability was that, merely using a paper and pencil, he could add, subtract, multiply and divide. Society had long delegated such mundane arithmetic to computers; thus, almost no one could do basic math.
JCC: Thank you all for a lot of interesting and thoughtful posts on this subject. I can only feel that the magic and mystery of numbers, the beauty of mathematics... is something that one comes to love. Maybe our society "collectively" disdains it as something useless to the demands of a so-called service economy. Is it possible that the young man in the hardware store is the front-line cannon-fodder of the service economy, that the earning power of his wages would be a little lower in Mexico, China, or somewhere else. If he has a passion for something of the mind, and is indiscreet enough to show it, he may well be begging some work elsewhere.
Perhaps I'm a bit cynical in my dotage, but I doubt that the employer is seeking to cultivate budding mathematicians there. I fear that our society seeks technological improvements as a means of cutting labor costs and using people *as* machines. The net effect of thousands of economic decisions, from the hardware store to the dumping of tenured professors--- it's not good for the society as a whole. It's the system of things; I don't pretend to know a solution to promote the greatest good for the greatest number, but some little voice whispers "reward excellence!"
VWB: I doubt many companies care much about employing people who can do much more then just get by. I once went through the drive through of a local hamburger outlet. After handing the girl at the window some bills and change to get back a five and two quarters I found she could not do simple math in her head ( the register would not do it for her....broken I guess). She still handed me the wrong change back and then could not come up with the correct amout even after I explained it to her. She then called the manager who had to get a pencil and paper and still had trouble with this. It seems to me that most companies only want to hire people who can do very little so they can always have the threat of firing them since they will have a very hard time seeking employment somewhere else.
CLF: Also, such people don't threaten the jobs of their immediate supervisors. Many bosses and companies like employees who are "just smart enough". Such workers will lack the intelligence to seriously challenge organizational policies/procedures or the authority and competency of their direct supervisors. On the other hand, they will not make their bosses and the company "look bad" by blundering excessively. In brief, the ideal employee is a robot with a narrow range of competancy.
Some exceptions include "start up" companies and companies which are undergoing extreme internal change to avoid extinction due to obsolescence or inefficiency. In the "start up" company, employees may number few and often resemble co-originators; because resources (including money for wages) are scarce and the company is struggling to survive, the valuable worker is then one who can improve efficiency and marketability, is creative, can troubleshoot well, etc..... Before they settle back into the complacency of a new bureaucracy, larger companies in upheaval often hire consultants to troubleshoot and improve "operations"; such "improvement" may include dismissing the managers of the "old order" and replacing them with supervisors of the "new order". All along, the nonmanagerial "peons" will be expected to function robotically; once the company has achieved a new sense of security/prosperity, it will expect its middle management as well to function as robots with a narrow range of interests and competancy.
Many people spend huge amounts of time doing work which, in reality, could be omitted - for example, attending numerous committee meetings where nothing is accomplished, filling out forms which are merely filed away or are redundant. Such people may work hard at doing nothing. However, their diligence and expenditure of time/energy create the illusion that "there's much work to be done" and that "people are working hard". Likewise, fewer people are unemployed (What would happen if, by some magical means, corporations overnight decided to "streamline" operation?). In addition, the "work ethic" (a "good" man is defined as a man who works hard) is satisfied; how would the nation, with many holding values tied to the work ethic, adjust to a society wherein the average person only worked three hours daily, instead of eight?
VWB: The other kind of people companies seem to be trying to hire would be people who are good at many things but they don't want to pay these type of any money. These people can then be trained to do any job in the factory for example. It does seem that there is no real reward for doing your best most of the time.
CLF: I'd agree.....unless one chooses to be somewhat entrepreneurial, as become a consultant, selling one's services to the needy highest bidder, but leaving when the project is completed.
Also, there are other reasons for the "standard" employee to not put forth his absolute best efforts. People rapidly acclimate to many things: The usual climate, the usual level of environmental noise....the usual standard of a worker's performance. They don't tend to think "It's usually sunny and warm here, climatically better than most places in the world"; instead, they tend to notice, and complain about, unpleasant deviations from a usually comfortable norm (thus loudly bemoaning the occasional storm). If illness or personal problems keep a usually diligent employee from putting forth "100%", if he then only "puts forth 75%", people will notice the decrement in performance; they will criticize his performance loudly, speculate about the reasons for the decline, even if he is still performing far above average. Phrases such as "seems lacking in motivation" or "allows personal problems to overly affect his performance" may appear in his evaluations, and later be used as legally permissible ammunition should the company have other reasons for dismissing him. If he'd only been "giving 50%" all along, he'd still have the energy to maintain his usual level of performance even when ill - and would thus avoid coming under such scrutiny.
VWB: Yes this is a sad but true state of thought in most workplaces I have been in. The other problem I have had is this is used to deny raises....even though producing more money for the company then any two other people in the department. The only time that doing my best was rewarded was as you say in smaller companies. In larger companies, even when I was very happy with the job I held, my boss or sometimes his/her boss would feel I was after their job( not true by the way). Also doing well on tests for training is sometimes bad as well....I was once told after doing well (99%) on a test to find people who could be trained for certain types of work.I was told yes I would be able to learn what was needed but they would not train me because they felt I would be bored and leave the company after they spent money and time to train me. Of course I just wanted to learn something new and would have stayed.....result?! I left and found more interesting work making the money I needed, so they lost me anyway. I wonder how many other people have been refused employment and/or training for such a foolish reason. Many of us value our time and are only looking to make decent money at interesting work without having to spend eighty-plus hours a week doing them.
JW: I have enjoyed the interjections provided by everyone participating, and have a little story of my own to relate.
Recently, I went back to school and completed a two-year degree with a well-known technical school. The reason for my participation, besides wishing to have a viable career to fall back on, was the promise by this organization of a "95%" placement rate. Of course, this wondrous dream of the ages was all dependant upon my successful completion of the degree program. Supposedly, after meeting all the requirements, there would be the proverbial "pot of gold at the end of the rainbow." I would have the American dream-employers would be begging me to work for them. "Oh what tangled webs we weave, when we practice to deceive," or something of that nature!
CLF: Oh yes....the school wants to make money, and exaggerates to attract students - just another advertising ploy, this time, with graduates falling victim to the deceit.
JW: Needless to say, I have met many a stone wall since my graduation date. Many a resume has proceeded forward; propelled from that tangled abyss of desperate hopes that all opportunistic possess, such as myself. Alas, it has come to naught so far. And this, at the last, is the point I have been leading up to: at times, there is a Catch-22 type of situation.
CLF: That old "experience" line: "We only hire people who have experience"; Yes, but how do people get that experience, if the inexperienced are denied that opportunity?
And then, the "You're too experienced" line - so, of course, we know that you won't need us sufficiently, that you'll be tempted to abandon us disloyally when offered better positions elsewhere". How much experience is just enough?
JW: Prospective employers either want
A: a graduate with a higher degree than what I have obtained;
B: a graduate which has somehow gained the experience
that the particular employer desires, in combination with a degree; {or}
C: a person that has several years experience
gaining the viable skills the potential empoyer wishes.
This person usually does not have to have a degree, but can stand
alone on his or her job experience. And also, the criteria can
be different from the ones I have stated. Yes, at least to me,
this is all very frustrating!
CLF: It's been my observation that many people
are over-educated for the jobs that they perform, that companies
often cite requirements far beyond what is needed to do the work
competently. At times, companies use (unnecessary) high
standards, and cite the educational attainments of key
personnel, as a buffer against law suits; they think "Well, if
we're hauled into court by some careless, money-hungry @*&$@, the
credentials may help to influence a jury in our favor". At
times, the over-education is an outgrowth of outmoded traditions:
For example, I know that pharmacists spend about 8 years in
college and graduate school, learning the esoteric intricacies of
biochemistry and physiology; they graduate as "scientists".
However, what do many of them actually do? They folow the
instructions on a prescription by reading labels correctly, and
correctly counting out thirty or sixty pills; when they log the purchase
into the computer, a program warns them of potential problems
with the prescription and prints out a list of side effects which
they then hand to the patient. In essence, they act mainly as
administrators or clerk; the extensive education relates to
1) historical tradition, wherein pharmacists really did need to
custom-make medicines and thus needed to know chemistry and
2) people's extreme caution/fear when dealing with issues of health,
pain, etc. ...
And sometimes, a company may not even intend to hire anyone when it calls you for a job interview, sends out recruiters or sends out an application packet. The people in personelle have to justify the continuation of their own jobs - and heaps of forms related to interested applicants, superficial evidence of being busy, help convince others that these employees should stay. Also, companies sometimes "feel out" the market by interviewing people: When an interviewer asks you to describe your most recent projects in detail, he may be gathering information for his boss about what "the competitor" is doing, may be probing for new ideas to give his own organization an "edge", etc.... In addition, through constantly interviewing job-hunters, personnel people can hone their skills in assessing others' character quickly, practice and improve their ability to read people - so that such skills will be sharp when they are needed. They can also keep abreast of market trends pertaining to a given specialty, and are thus less likely to fall into the trap of offering too much to the candidate who does come at a time of (company) need.
JW: Where do the ones such as myself interconnect within the clockwork of the working force-the field of interest I had chosen, lest someone provides an opportunity to gain the experience that is all too pertinent to most employers? To me, this is the riddle of the ages.
CLF: Well, what have the "successful" graduates done to land a position? Did they work part-time jobs at a company while going to school, then join that company full time after graduation (hired due to their contacts at the company)? Did they move to geographically less desirable areas, work there for a few years until they had enough "experience", then relocate to a preferred region? I guess I'd ask any graduates who are still in your area, and any professors who merely teach part-time while also holding jobs in the field but outside of academia. Also, search the web for any mailing lists or news groups which might be pertinent - lots of junk posted on some of these, but you might also get some honest, practical advice (people won't view you, a faceless and merely "virtual" entity, as a competitor).
WRW: Would "dumbing down" on an interview help? Some conversation I have seen here concerns the insecurities of supervisors and managers. Maybe they feel threatened by you in the interview process. I know it goes against your convictions, but getting your foot in the door first is what counts. As Julia mentioned earlier, our service economy demands less than excellence.
JW: You bring an intriguing thought to mind. Perhaps it is time to use strategy? It is true that I can be a tad "over-articulate" on occasion, but hadn't considered the "dumbing down" aspect of which you had mentioned.
Your ideas definitely deserve some thought, and I very much appreciate the input you have given. I suppose that "whatever it takes to get my foot in the door" would be the appropriate course of action at this point! I will not being paid to philosophize, (as far as I know) but to do a regimental series of actions, anyway.
CLF: And, if you're like many Americans, you may just end up working in an area unrelated to your training! Friend or family member with some influence hears of a job opening in an unrelated field, mentions your name personally to the big boss; you're called in for the interview (merely to ascertain that you're not a bellowing cyclops, as the Big Boss has already decided to hire you based on your relative's glowing praises). In desparation, you accept the job, learn that you can do it well and that the place "isn't all that bad"......and voila, the guy who was trained as a CAD drafter ends up managing a book store for the next 5 years!
JW: Thank you for all the excellent ideas provided me in the last post. I have contacted several of my classmates, and it is my understanding that very few have received employment as a direct result of attending this school. Most of the ones working now, had empIoyment prior to, and during their studies. I know that many bright individuals are still attempting to be employed , as I am.
Well, forgive my venting. Thank you all for your input.
KB: ... Many here must have had similar experiences in earlier life, say school, that has made them guarded; thin-skinned ...
WHK: I remember an incident in elementary school class (perhaps 5th Grade) when the map of the world was pulled down. It occurred to me, and I blurted it out as a Eureka experience, that the West coast of Europe and Africa "fit" into the East coast of the Americas, if you just nudged them together. I was severely chastised for even thinking anything so stupid! - and furthermore, disrupting the rest of the class. Basically, "sit down and shut up!" {sigh!} Took the wind out of my sails for quite a while. Something is just plain wrong when teachers don't foster this type of exploratory thinking, but instead stifle it. I've felt a lot of suppression of creativity, particularly in my early education. Would have been nice to have a truly caring mentor; unfortunately, that was never the case.
CW: There was a segment on PrimeTime Live about how Japanese and American schools differed in how they taught math and science. In Japan it is the norm to let the class figure out the problem without giving them any way to solve it. The opposite in the US. Who do you think gets higher math and science scores?
LDL: In algebra class I had a similar incident ... fiddling around with math I discovered that multiplying the middle of a sequence of numbers times the end is equal to the sum and I jotted down a algebraic formula for it, even modified it to include sequences beginning with any number. Essentially the formula is repeated twice with the first part subtracted from the second part. Elementary stuff, right?
Still, in high school, I was pretty proud of it and showed my teacher. She was brilliant herself, but couldn't teach shoe-tying if she had been provided with diagrams, let alone algebra. In study hall before class the kids would gather round me (I was her only A student) while I explained the lessons. She knew I was doing this and maybe that explains why she called me a liar concerning my formula, claiming I had skipped ahead in the book. I felt hurt and betrayed and refused to take advanced algebra and geometry from her the following year. Fortunately there was another teacher ... he was a great teacher.
I played games with his head for awhile. Sat in class pretending to ignore what he scribbled on the board. Looked out the window, day dreamt, and if he asked me a question about a problem in the book or on the blackboard I would rattle off the answer and was prepared to demonstrate the proof. This went on for about a week and he asked me to stay after class one day. He presented me with a challenge ... I could continue my little mind game with his blessing so long as my answers were always correct, but if he ever caught me with a wrong answer I was to sit up and pay attention the rest of the semester. I agreed! The old fox! Two weeks later he had put a problem on the board and I was, as always, only paying it half attention. He called out my name and I snapped out the answer and then I heard a word I hated to hear ... "Wrong!" I turned around and looked at the board and saw my mistake immediately, he had a nested negative. I sat up in my seat, folded my hands in front of me, and he looked at me, smiled, and nodded ever so slightly. I nodded ever so slightly in return. He had recaptured the respect I had for teachers, the respect that had been demolished the previous year.
WRW: I had a similiar experience in math when i was in high school. I can't remember the exact thereom, I think it was one of Eulers'. I read that as a student he was asked, along with his classmates, to come up with a method to determine the sum of any consecutive series of numbers. I myself tried and came up with a commonsense method that has never failed. My teacher agreed with my method but said it had not been proven and therefore could not be considered correct.
My method went as follows: When summing consecutive numbers always go to the number just after the last one in the series (if you are summing one...fifty, then go to fifty one.) Take one half of that number ( in this case 25.5) and multiply it by the last number in the series (25.5times fifty equals 1275).
More simply take one through five. You can add this in you head to come with fifteen. Now take the next number in the series (6) half it (3) and take that number by the last in the series (5). You get fifteen.
EM: In 1943, when I was a high school freshman, our class had a monthly assignment of vocabulary testing based on words found in the Scholastic magazine. The tests were assigned, based on grade level. I think they were then graded to the 15.5 grade level max. I completed the test to the highest level in a few minutes, in that I did not have to refer back to the text, I then went back to reading a comic book. In a few moments I was called to the desk of the teacher, Miss Frances Rowe. She was a nice maiden lady of pitifully ordinary intelligence. She demanded that I produce the answer sheet that I had pilfered. I told her I had no need of the answer sheet. I was sent to the principals' office for insubordination, and suspended. It was already known, though not to me, that I had made the then highest recorded i.q. test in that school. This was clearly held against me as another example of my perversity and deviltry. It never occurred to anyone that a really bright pupil might know many more words than the average. Last year I attended the 50th class reunion of that school. I was happily informed that Miss Rowe was still alive, and undoubtedly would be delighted to see me. I have reached an age and stage of life where I do not have to suffer fools gladly or otherwise, and I made no least effort to meet the woman again.
JPr: ... Educational experiences are some of the worst for kids who are bright, aren't they? Even the teachers barb! (educator for 25 years)
KB: Absolutly correct. In sixth grade I received the paddle approximatly thirty times! (educator for five years)
JPr: Oooooh! That's dreadful. If you are only an educator for five years, you can't be too old, so this happened fairly recently. Bad news. Yet, you still decided to become an educator...good, let's see if we can change it!
CW: It is basically the same structure as prison (ie the 'two-tier' social structure). I think, because of Oprah etc, the atmosphere could become less inimical to individuality.
JPr: Well, that's pretty much how all the deaf kids at the school I run see it
CW: I had very many great teachers. One really went out on a limb for me and decided that I could handle 3 years of high school math in 1 year. That was one of the best years I ever had in school. I had at least 2 other teachers like that. I'm sorry that I had such a confusing family life that I couldn't take greater advantage of the terrific education I was getting from them.
KB: Twenty-eight years on this blue orb. I came from an extremely rural village where everyone knew each other and their actions. I made the mistake of being hyperactive. Home-town interpretation: little jerk.
I was quite bored, hyper, and bright. I recall asking the gifted teacher what the requisites were for gifted classes. Karen replied that the requirements were taken from the composite score on the SRA test, then given annually. I can't remember the score, but I do remember they were the highest in the class of approximately sixty (two classes). I produced my copy inquiring if my score counted. "Blah, blah. Yes, how did we ever overlook? ... blah, blah..." I decided not to partake ... the result of being the offspring of a sixties activist.
Special ed. classes in my school consisted of the classroom the furthest from any humanity. Where the "students" colored, ate cake, and listen to music (LD students!). I believe Einstein said, "When you teach you learn twice." I teach because I love learning. And who better, IMHO, than the under-dogs?
** Colloquy began 6 Jan 98 as the online discussion group open to individuals placing above the 99.5 percentile on measures of intelligence.
