My introduction to the American education system was only at the graduate school level. That still exposed me to some of the systems in place for undergraduate education, and the university system in general, and I marveled at the choices and sheer flexibility that the students had during their education. So, even though I had no exposure to the school system here, I made the assumption that the school system would be as flexible and innovative and accommodating as the university system. I thought a school student here in the US would have as many choices, options and variety that a college student had.
It turns out though that while the university system here remains the envy of the rest of the world, the school system is a far cry from the university system. It is as bureaucratic, static, dogmatic, rigid, uninspiring or banal as any other system anywhere else. This is a story I recently heard from an acquaintance I run with. She studied in one of the (better) public schools in the Dallas area. Now, my friend was a pretty good student, and what is quite atypical is that she really liked math. She wasn’t exceptional at it or anything. She just liked it. It was her favorite subject. Usually, in most schools (especially in the US) it isn’t cool to actually like math or science. She did, and so did another friend of hers.
Anyway, somewhere in 7th or 8th grade, they had to take some tests, which would determine if they took some more advanced math classes, which would then introduce them to calculus and high school AP math. Both she and her friend did only modestly in that test, and were marginally below the required score to be allowed to progress to AP math in high school. But they both liked math so much that they wanted to take those advanced courses over the next few years, including AP math.
They actually wanted to take those courses.
So it seems perfectly reasonable (to me) that they should have been encouraged to take those courses, or at least been given some option to retake that 7th or 8th grade test (to see if they could qualify for AP math later on). Usually, students are forced to learn something. Here they wanted to learn something themselves. Anyway, her then math teacher flatly told the two of them that since they hadn’t made the required grade in that standardized test (which they had missed by a whisker), they would not be allowed to go on and take calculus in high school. These two begged and pleaded, and even had their parents write to request that they be allowed to take those math courses and study more, or at least be retested in order to see if they could qualify for those courses.
Close, but no cigar. The teacher stuck to her guns (and rules) and declared that they would not be allowed to take those math courses in high school, since that is what the rules said. So finally the two of them had to go sleepwalk through “simpler” high school math curriculum without calculus, which were too boring and too easy for them, and did not challenge or inspire them in anyway.
Finally, when this girl ended up in college, she thought she’d try to take more advanced math courses. Because she hadn’t taken AP math and science, she didn’t get into her first choice colleges, and had to settle for a “lesser” state university (which was a good one though, in my opinion). But still, she thought she could now take some more interesting math courses. She registered for a few, only to find that the college curricula assumed substantial prior knowledge of lots of math that she’d never had (and not for lack of interest). She also found that most of the other students in that course had taken AP math/calculus in high school. So she spent a frantic semester trying to work twice as hard to learn things that the rest of them found quite basic. In the end, it turned out to be too hard to catch up. She didn’t want to take a big hit on her GPA. So instead of finally majoring in chemistry/biochemistry with a math minor (what she wanted to do, and which required quite a bit of math and calculus), she ended up with a developmental biology major. The story of her friend from school is a little different. He also struggled with some math courses in college, but he was more resolute (and loved math more), so stuck it through some very tough courses. After a few tough semesters, he finally became good at it, and eventually majored in mathematics. He loved math so much that he even went on to get a masters in math, and now works as an analyst for some company.
So the decision of a bureaucratic, uninspired teacher from 7th or 8th grade possibly changed the entire career of this girl, who now feels bitter at being denied the opportunity to learn and do what she wanted to and liked to do. Had she just been encouraged to retake a test in 7th or 8th grade, or had been allowed to take calculus in high school, it is quite possible that she would have gone on to a college of her choice, or at least majored in the subjects she wanted to, and liked the most. One single decision not made by her potentially changed her life.
And while this is a story of one particular teacher, it apparently is quite reflective of a lot of the school system here. An excessively bureaucratic, rule-obsessed system, with a huge amount of pressure on teachers to make sure the maximum number of students go through high school and get their diplomas, even if they do not learn as much. What this is doing though is two things. (i) It produces a number of students who go on to college (and are interested in college), but are ill equipped to handle a lot of college courses (which they might be interested in) and (ii) it also potentially produces an even larger number of students who, thanks to diluted educational standards, will never be able to go through college at all.
It is a shame though that a university system that is exceptional overall has to be fed by a school system that really leaves so much to be desired. The university system (particularly advanced or graduate education) is therefore partly forced to rely too much on imported foreign students (the school system alone isn’t responsible for so many foreign students, but I believe it does play a big part in it). Secondly, it isn’t fair to burden the university system (which by definition should strive for excellence) with teaching students basic subject concepts that should have been handled in high school or earlier.
And if we flash to the current presidential election, both candidates have only given lip-service to the educational system, and promoting “science and math”. Look deeper, and both of them have no ideas or real desire to really try to fix anything (or perhaps Barak does, but then focuses too much of his plan on hiring more teachers, and very little on educational standards and educational choices themselves).
How difficult would it have been for this girl to have studied calculus at home, while she was "sleepwalking" through the simpler high school math curriculum? She could have bought a few textbooks on calculus and taught herself, saving herself a lot of trouble later on.
Calculus has defined rules and is quite easy to learn too..especially if you love math.
I agree the system is flawed, but I can also see that your friend does not acknowledge her role in this fiasco :(
"How difficult would it have been for this girl to have studied calculus at home, while she was "sleepwalking" through the simpler high school math curriculum?"
I don't think that's really the point. Sure, if the girl was dedicated and/or good enough, she would have learnt calculus anyway. (Actually, Sunil does mention that the girl was doing modest in maths and just had a liking for it.) But the question of depriving students of exposure to a variety of skills due to unsound reasons still remains. It should not happen at that stage of a student's career. Too early.
Loving math is different from learning it. Calculus as a concept is difficult to understand to someone who is primarily versed with conventional arithmetic and algebra. Teaching the right concepts in the right way at the right time can go a long way in molding the student's thinking abilities.
Lekhni....i think it would have been *very* difficult. I don't know about you, but for most kids in the 7th/8th grade, self-motivated learning isn't that easy. If she was in college, perhaps...but college places enough requirements and stresses on you. My friend never said she was a genius.....she just felt that she was unfairly denied an opportunity, and that the system really stinks if it can go out of the way to prevent someone from learning.
The bigger point here is the state of the school system....which is what feeds the university system. The feeder to a superb system (the university) is seriously broken, and it doesn't matter how good the top is, if the foundation is crumbling, the top is bound to get hurt.
I agree with you about calculus-- it is hard to "understand" it at that stage without help. I personally often feel that it is hard to make systems that create that kind of atmosphere, it is usually the individual teachers-- one of my high school teachers helped me think algebraically about geometry.
There are schools in the US for gifted children- whether they teach students to think mathematically or physically or not, I am not sure.
Somewhat facetiously, I think that your post comes about 35 yrs too soon in our lives- we should all get together to start such a school post-retirement.
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