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My sentence is still being carried out and, as such, I am still gathering much damning evidence on the topic. Hopefully I will be able to compose a meaningful -- perhaps even persuasive -- critique of the system. There is quite a bit of bureaucracy and conformity to overcome.
The education system is profoundly skewed and this is the second time I have experienced its most significant problem: placement and grading. Most educators place too much value on inflexible systems for identifying proper places for students and estimate their comprehension of the material; there are many factors that may aid or hinder a student's performance on such tests. Yet, even excusing poor test score(s) is not my main intention.
Throughout most of my education I felt extreme boredom and "excelled" at all "academic studies" (as ill-defined as they were), which made me rather excited about the prospect of going to college early. I thought the MASMC, focusing on (personal) and academic challenges, should provide the extra stimulation and opportunity to let me "soar." I have come to understand the harsher conformity of lower level courses.
In highschool I had precalculus (which actually ended with limits!) and chemistry, and I considered my entrance to calculus and (advanced/secondary) chemistry in college almost guaranteed. I found out about placement tests the night before actually taking them (the best I can remember) but still felt confident after having completed them. I found out little before actually going to the academy that I would be placed back in precalculus and chemistry one. After talking with a few "authorities" I discovered there was one other test I could take. Without even looking at the C I received on the first precalculus (mostly algebra and some trig) test, I took another one. Again, I received a C and felt rather bad.
I talked with Dr. Malm to figure out what I did wrong. After looking over the test, I felt somewhat worse: the errors I made were not due to a real lack of understanding, rather they were "stupid errors" from lack of attention, sleepiness, and some misinterpretation. I was assured that the college precalculus course would "fill the holes" of my precalculus education. I doubted it, and was correct: I learned, effectively, nothing in precalculus while spending hours (and taxpayers' money) listening to the same material and doing homework (unnecessary -- I didn't last year and by not doing homework I did not hurt my placement test score).
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Here, finally, is the reason for this "essay": I just got back from looking over my calculus placement test. I technically could have taken a D in calculus and moved on to a course where I would learn something (we are going over limits again; an hour of boredom in college [REQUIRED] is becoming hard to stomach alongside programming [more on that later]) but, for the sake of my GPA, I decided to abandon efficient education.
The obvious question raised by my situation is, if I didn't score well on the tests, don't I belong in the classes? Not necessarily, I would respond. That was why I looked over the test and why I was somewhat upset to discover that my problems were trivial in my mind (although also somewhat relieved that I did/do know about the course). Placement tests are "one shot" opportunities, like most tests. I completely disagree with that, even though I understand the difficulties of creating a new yet equally investigatory test for every new attempt. I learned something (places to especially check my work) from testing, and others may learn more (actual material from the test).
For more detail, here are examples of things I did wrong:
Confused Mean Value Theorem and Rolle's Theorem: I was to show the Mean Value Theorem correct when f(a)=f(b); that _IS_ Rolle's Theorem (so I proved that f'(c) = 0 rather than = (f(b)-f(a) / b-a)) = 0).
Eyes skipped: two problems had similar equations (one had an x squared, the other didn't) but asked for different things; my eyes jumped and they looked identical (every time) so I used the same equation as above (which I had worked with already). Also, I simply forgot a few details: x^2 - 2 = 0 when x = sqr(2) not when x = 2. Perhaps they should send me back to Algebra with the sixth -- no, in Liberty 8th! -- graders.
Too quick: I didn't use product rule on xcos(x) as I was speeding through (and didn't notice it any time in re-checking...). The derivative should have been cos(x)-xsin(x) instead of just -sin(x). On another problem I forgot to bring down the "2" in a squared variable when differentiating. Etc.
Minor: I mistated the FTC to requiring the interval (a,b) to be differentiable (this is not necessary). There goes a couple more points.
Deserved (?): On a word problem I probably deserved to miss it if, for no other reason, the inordinately long time I took in figuring out how to set it all up and what to do. Had I practiced (done some problems in the first place) I would have zipped through it. Maybe next time...
The system will probably not change as each professor has (near) complete reign over grading and they all seem to be conforming to nazipointism (a 90 and 99 matter none while a 90 and 89 do: every point counts far too much; there should be some subjectivity as humans can estimate each other's understanding [oral quizzes as a practical example] more easily than any contrived grade); most professors won't buy into this.
The best consolation would be to change the system.