Stupid Decisions By The Ivory Tower Elite - And Replies

  • Wednesday, February 14, 2007

Gov. Bredesen:

I felt that as a math teacher I had to respond to your address. Please come and talk to some teachers in the trenches.

I am an algebra teacher here to proclaim loudly that algebra is not for everyone. When will the out of touch face reality? A fourth math is NUTS.

It was totally crazy to ever require algebra - let alone the geometry all must now take. When will the out of touch realize that some are left brained and most are right brained?

You can say the the Gateway scores show success in algebra and I say bull. The Gateway is barely above pre-algebra level and much of it can be done on the calculator.

Here is an algebra problem that any Algebra I student will be taught. Factor 8Xsquared -95X -96 I will bet that very few of your staff or even the state school board could do it.

I do not know anyone who has ever factored anything outside of a classroom. Have you ever rationalized a denominator?

We need to teach students what they really need to know not what the elite think they should know.

Sorry for the informality of this email, but I am a very passionate and dedicated educator. I am very sick of the ivory tower elite making STUPID decisions about education that are pie in the sky not real.

Jim Ludwig
jimludwig@bellsouth.net

* * *

Maybe if Mr. Ludwig spent more time motivating his students and less time trying to figure out which side of their brains they use he could be more effective in teaching math.

Our oldest son decided early on that he was never going to use "all of that higher math" when he was in high school. On hearing this my husband made some phone calls and took him on a tour of several friends' shops. He saw how an air conditioning technician may have to use geometry to determine the most efficient route to run duct. He saw how a machinist has to use geometry every day to lay out a panel or other piece of material to be machined. He saw how electronic technicians, electricians, plumbers, draftsmen, engineers and all sorts of other craft or trade practitioners have to use algebra and geometry every day. At least they should know how to use it. When they came back and told where they had been and what they had done I wished I would have gone with them. Computerized CAD systems are great and wonderful, we use them in our business, but those who use them also have to understand the basic concepts.

My dad was a carpenter and he used geometry every day. He also complained about how hard it was to find employees who could figure the materials for a job and then not waste a lot of what was ordered for it.

I don't understand where Mr. Ludwig gets all this right brain left brain gobbledygook in respect to learning the math our children need to perform so many of the jobs they'll go on to do to earn a living as adults. Could it be that his personal prejudices and preconceptions are the cause of some of the difficulties his students have learning math skills? Math takes a lot of repetition and homework, and the concepts may have to be explained in several different ways like had to be done with me in school, but it isn't an impossible task.

Maybe if Mr. Ludwig put more of his passion into teaching math and less in how the human brain works and why this or that student shouldn't be required to learn the subject, his students would be more capable of going out to earn a living when they graduate from high school instead of employers having to teach some of them how to read when they reach the work place. Maybe that's the reason so many college students fail, and 70 plus percent of the scholarships funded by the Tennessee lottery are lost because the students are ill prepared for college.

If this is the attitude of teachers in Tennessee, I'm glad my children have already graduated from high school and college. I'm also glad we won't have to hire employees when we retire over there in a few years. Maybe that's also one of the reasons East Tennessee has such a difficult time attracting industries that pay well.

Ivory white towers? Who's looking out from an ivory white tower? Is it a self proclaimed "passionate educator" who is "here to proclaim loudly that algebra is not for everyone" or his "customers", the employers his students will eventually work for? Maybe some of those "teachers in the trenches" should go out and see what actually goes on in the rest of the world, the one that exists outside the walls of their schools. In my opinion it's awfully arrogant for a teacher to even imagine that he knows more what an employer needs than the employer does.

Barbara Fields
Stallings, N.C.
BF1217@bellsouth.net

* * *

Isn't the polynomial (8x^2-95x-96) prime? There are no number pair factors of -768 (the product of 8 and -96) that will add algebraically to -95.

With all due respect Mr. Ludwig, there certainly are those of us who must use math each and every day...relatively complex math. Not just the pluses and minuses but the timeses, gazintas, and more; powers, roots, functions, sets, transforms. And those funny little Greek thingies. Mathematics is the basic language of the universe, of thought. We use mathematics for triangulation, calculating roof geometries, calculating distances with only basic tools, phase relationships, vector forces, mapping coordinates, playing pool, music, writing, writing poetry, and timekeeping. Some of us even work with other than 1s and 0s, outside of the digital world.

Anyone who has designs upon a career doing more than flipping burgers at the local fast food joint will use more than pluses, minuses, times, and gazintas...gazintas being an actual program command in the old Hewlett-Packard programmable calculators as well as HP BASIC used in their control computers way back when. However, in the interest of full disclosure I've never flipped burgers so I'm not really certain that math beyond basic arithmetic isn't required to perform one's duties well in that capacity.

Having gone to high school in Southern California in the 60s, perhaps I was at an advantage over some. My second favorite math teacher taught geometry, Mr. Wolfe. The kid that sat next to me in class was a carpenter's apprentice in a work study program, and slept through class most of the time. One day Mr. Wolfe woke him and asked why he slept through his class. The response? "Man, I'm gonna be a carpenter. I don't need none of this geometry crap." We had several good lessons that day. One was that when we're teaching we need to be able to give real world examples. We learned how to calculate the length of boards to use for a roof with a specific slope with the least waste possible, waste being lost profit, by using the Theorem of Pythagoras...one of those Greek guys. We learned to calculate the surface area of a wall for paint, the number of cubic yards of concrete necessary to build a patio, the number of squares of shingles to do the roof, and how to use a carpenter's square to calculate the slope of a roof. During the World Series we also got lessons in baseball strategy between innings. And Reuben decided that geometry actually did have something for him to use in life, so he stayed awake in class from then on.

In college my first calculus instructor was the absolute best. She had all our attention when she showed us how to calculate instantaneous values along a curve and how to apply the process in real life to such things as population growth, magnetic fields, and fluid pressures at various depths at standard gravity and atmospheric pressures. She showed us how to calculate the pressure applied to the surface of a dam, hydrostatics. When she talked about discontinuous functions...whew, boy!

Billiards is nothing more than applied geometry, and physics. Orienteering and land navigation is geometry. How can our Marines travel 10 miles across broken terrain, back and forth in various directions, with nothing but a map and compass, and locate an ammo can buried under a rock without using geometry?

How did seamen navigate the oceans without geometry, back before the days of LORAN and GPS systems? And they didn't have computers, or calculators, or even a slip stick to help them with those calculations. How do they differentiate between friendly and unfriendly aircraft as they approach in current times?

How do engine designers and race car builders do their thing without geometry and trigonometry? How does one calculate a gear ratio without geometry and trig? The angle and shape of the lobes on a cam? How about the compression ratio? Firing angle? Torque generated at the drive wheels? Or the resonant frequency of various frame members? I'm an electronics guy and even I know these.

How does one program a computer or write a control program without math beyond basic arithmetic, even write a program for a computer game? Game theory is pretty serious mathematical stuff.

Mathematics by rote is truly a boring subject...and one that those forced to study in such a manner will never be able to imagine a use for. It's also a certainty that many a bright student will be totally discouraged and run off from the fields of science and math if they cannot develop an interest. A student who's taught mathematics by rote, by the book, with no practical examples from real life, is truly a disadvantaged student...because he isn't being taught how to think. Any math teacher worth his salt will also understand that mathematics is a foundational subject...each level must build upon the foundation of what's been taught before...we cannot jump right into ciphering Laplace Transforms when we don't know how to add and subtract.

Why would one want to know the phase angle between the voltage and current waves of the power delivered to our homes and businesses? We may not, but the power company certainly does...and its shareholders.

Why would we want to know that sound pressure is a square law function? Radio waves the same. Perhaps because it gives us a measure of the intensity of each at a given distance from the source? Why would we want to know how to calculate the resonance factors in an auditorium? Maybe for acoustic compensation to improve the sound of a concert? Resonant frequencies of mechanical members of a bridge? Perhaps to keep the bridge from self destructing in a wind? Why would we want to be able to calculate the affects of gravity on two objects? Maybe to calculate how high a satellite must be above the Earth in order to maintain a geostationary orbit? Or some orbital distance for a known ground speed? Or the orbits of the planets around our sun? However, imaginary numbers and smith charts are for those really weird guys...and they can keep them.

Why would anyone want to know how to use hyperbolic trig functions...sinh, cosh, and tanh? Maybe to calculate the length of a cable between two fixed points, like a power line, with minimum stretching and to minimize failures due to material fatigue? How about converting angular velocity to linear velocity? Maybe to determine how fast a roll of paper is being processed? Or how long a carpet fabric is in a drying oven for finishing by knowing the drive motor's rational velocity? Or how fast a pizza is traveling through an oven? Oops, that's fast food.

Without math there is almost no science. With no science there is no progress. With no teachers who can teach math and science with applications, there will be no interest in learning to think or to invent new gizmos to make life easier. To be sure, there would still be invention but every invention would be a new work from the ground up and the lessons learned would not be able to be used on new inventions at a later time...and the concepts could not be generalized for use in ever newer applications. Part of being a good teacher is helping to instill a sense of interest and curiosity in the subject material...and how to think, not just regurgitate numbers.

But even a good teacher must have the support of the system administration to keep the behavior problems out of the way of those who want to learn. If those determining the curriculum don't know the subject matter, that's a problem too.

Just the opinion of a lowly engineer...an engineer who doesn't know much about all those gazintas and stuff...

Royce E. Burrage, Jr.
RBurrage@bellsouth.net

* * *

The quadratic formula shows Mr. Ludwig's math problem (8Xsquared -95X -96) to be unresolvable using whole numbers - I assume that he intends the whole formula to be set so that the given equation equals 0. The correct answer is ultimately along the lines of x = 12.81165 and x = -0.93665. The factoring would look something like (8x-102.493) (x+0.937). If this is indeed a baseline Algebra I problem, then math education in the U.S. has come a long way indeed.

I may be mistaken but believe Mr. Ludwig intended the problem to read (8xsquared - 88x - 96), which resolves neatly to (x+1)(8x-96) where x = 12 and -1 - a much more suitable problem for Algebra I.

I have a master's degree in creative writing (poetry) and extensive training in Philosophy, Ethics, and Literary Theory. My current career relies largely on my ability to plan and implement communications on large scales, and yet...

I am very glad and grateful for the outstanding math (and science) education I received from the 5th grade of elementary school through to my senior year of high school. For one thing, I am not left cowering in the shadows when a math teacher lobs a quadratic equation my way.

Thus I do not have to accept authority when teachers/administrators decide, as they might very well attempt, that I am (or my child is) too incompetent or otherwise unworthy to be allowed to learn this discipline of thought.

I spent a large part of my academic life deliberately learning skills that would lead to the career I thought I was destined for - being a professor of English or creative writing at a university. In mid-life, when it became plain that I did not want to continue along that path, it was sheer dumb luck that in the course of preparing myself for one career I was also learning skills that could transfer to a different one. I am moderately certain that I'm not the only person to have had this experience. So...

I would rather we be in an environment where a few people incapable of grasping Algebra are thrust involuntarily into it; than be in an environment where some who are capable are bypassed - even those (perhaps especially those) who believe in the full bloom of adolescence that they will never need it.

It may be worth adding that while many students may never use their Algebra skills in adult life, I daresay that many would benefit from sustained exposure to the idea that problem solving is an important life skill, and can often be approached creatively, methodically, and rationally with success. Factoring quadratics is particularly relevant to this because there are multiple proven tools, multiple routes to take in trying to arrive at the right answer. Success often entails a fair amount of trial and error along with a good dash of intelligent resourcefulness and persistance.

(PS I stand by my argument even if I got the Algebra question wrong! And if I have, I hope Mr. Ludwig will be so kind as to re-educate me briefly in these pages.)

Kip Soteres
Signal Mountain

* * *

After reading Mr. Ludwig's Stupid Decisions article, I was disappointed in his assessment of Algebra for all in our schools. As an Algebra I teacher in an urban middle school, this is not my belief.

Research from the Education Trust and the College Board shows that students who have early success in Algebra I are more likely to enroll in college. Also, a study conducted by the U.S. Department of Education concludes that the highest level of mathematics one studies in secondary school has the strongest continuing influence on a bachelor's degree completion.

With that challenge in mind, why would we try to deny this opportunity for all of our students? Algebra is much more than factoring horrific polynomials as suggested by Mr. Ludwig. Have you ever bought paint for your house and had to calculate how much to buy based on the coverage per square foot? Ever bought carpet? Ever had to purchase fencing for your yard? Ever conducted a little comparison shopping as to the best buy per unit in the grocery store? Ever needed to compare stocks and make predictions before making your investments? If so, you've used Algebra.

Algebra I is one of the first math courses where problem solving comes into play - Algebra is not just symbol manipulation anymore - factoring can now be done with a calculator - technology has changed all of the rules and it is imperative for all of our students to have this gateway to college opportunity. Our challenge as teachers is to find ways to help all students achieve success in Algebra I. Adding a fourth year for our seniors can only help better prepare them for their college experience.

Buddy Sullivan
Algebra I teacher
sullivan_ulyses@hcde.org


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