posted
I teach in an American High School (math and physics, as it happens), and I cannot for the life of me figure out what they're teaching in Elementary and Middle Schools...
It's true, however, that American High School education is being horribly twisted away from anything that is actually worth learning. In my opinion, the push for Standardized Testing as the ultimate measure of student and teacher accomplishment is one of the biggest factors behind this.
Don't get me wrong, I think that we need to have standards, because we need a way to measure that getting credit for "Geometry" at High School A means that the student has gained mastery over the same concepts and to the same level as a student who got credit for "Geometry" from High School B. Obviously, some means of measuring this is necessary. If every student in the state or nation is to be given the same test at the same time and the results assessed in a timely and cost-efficient manner, a computer-scorable, multiple choice test on a representative sample of problems makes sense... of a sort.
Unfortunately, this solution raises as many problems as it solves. As they currently exist, standardized tests are designed more to show the comparative achievement of students and schools rather than an absolute scale. Another way of saying that is that the test results tell you how many students you did better than, but not how well you did overall. If the test focused only on the basics of each discipline that all schools teach well, you would get everyone scoring pretty much the same and the results wouldn't be very helpful in sorting out the "good" schools from the "bad" schools. As a result, test questions have been shifting away from the basic principles that are actually worth knowing and useful (at least in math and science) and toward more esoteric, abstract concepts that are not foundational to the discipline. Schools are pressured to focus on the "fringe" of a given discipline, which concepts cannot be fully understood in context without a solid grounding in the basics, which are being rushed through. The only way to teach these concepts is rote memorization that involves knowledge of algorithms and mnemonics removed from any meaningful context.
Although my experience is in math and science, my colleagues assure me that the same pressure is at play in the humanities as well. What kind of meaningful learning in the humanities is measurable by multiple choice tests? What level of literature can be read, analyzed, and understood in the context of a 45 minute test covering five reading selections from different genres?
There are a lot of problems with the American educational system. Fatal problems that are killing education and our kids. Something does need to be done, but the current mania for more and more testing isn't part of the solution, it's just making the problem worse.
Posts: 99 | Registered: Jan 2001
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I live in Ontario, and the government has just decided to drop Calculus from the high school curriculum. Starting next year, students will NOT be able to take calculus (not even as an option!) until they reach university.
What is your opinion on this? (especially you, Mateo, as a high school math teacher?) What sort of long-term concequences will we see?
Personally, as an avid calculus student, I think we just shot ourselves in the foot.
Posts: 32 | Registered: Jan 2006
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posted
That's terrible Wench. We thankfully have a lot of options at our school, but with having so many options comes the fact that you don't have time to take most of those options.
The school curriculum is seriously messed up. Did you know that the only MI state requirements for high school are 1 semester of Civics, and 1 semester of Econ (And starting for freshmen next year, either 1 or 2 semesters of World History). That is ALL that is required by state. No English, Math, Science, or Language or anything- Of course, individual districts set more rigorous requirements. I just find that whole idea sort of weird though.
Also Sergeant mentioned earlier that he was an avid reader in high school, and I was just thinking, I don't really have time to read AT ALL anymore. Throughout middle and elementary school, reading was stressed up the wazoo and I would do it willingly, I love reading. But now I'm in high school, I realize I don't have time to read and that just really GETS to me. Because I know that one of the reasons I do so well in school is from a long history of avid reading, and I can't fit that in anymore. Actually, it's not even that I can't really fit it in, I have the free time for it, it is just that my free time is limited enough so that I always feel like I should be doing something else besides reading that I never have time to do, like hang out with friends, or play a video game or something. I'm always in the mood to read at night, and I do, but I normally end up reading a page or two before drifting to sleep. And whenever I DO try to read during the day, I also end up falling asleep very fast because I'm worn out from school and my lack of sleep from the night before.
I started reading The Dispossessed about 2 months ago, and I'm barely 80 pages in. More time needs to be allotted to take part in cool activities like reading.
Posts: 879 | Registered: Apr 2005
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quote:Originally posted by King of Men: Which is actually a rather interesting subject, in its own right, but does tend to require mathematical notation which the forum just doesn't support. However, waving my hands a bit, you will see people on board the train living in extreme slow motion, and they will see you living in extreme slow motion, since from their point of view, you're the one going at lightspeed.
KoM, changing the subject slightly, this comment made me think of a question. It's my perception that relativity holds that there is no absolute inertial reference frame, i.e., it is just as legitimate to say that the train is still and that the universe is sweeping around it at 0.99c (or whatever hefty fraction of c we want to use). The question of which is moving and which is stationary is a relative one, dependent on the observer, right? This seems consistent with what you said above.
Yet, even though each group (those on the train and those outside it) perceives the other as living in extreme slow motion, 'time dilation' as I understand it says that one party will experience little passage of time while the other grows old and dies (e.g., Ender is still around when 3,000 years have passed back on Earth). So, in the absence of any absolute inertial reference frame, what determines which group gets old and which one stays young? Why doesn't Ender, having been left behind in his arbitrarily 'stationary' position on the spaceship, grow old and die while Peter lives on, speeding away (with the rest of the solar system) at nearly the speed of light?
Obviously I have too simplistic an understanding of one part or another, I just don't know which.
Posts: 326 | Registered: Aug 2005
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posted
personal confession: I can't use chopsticks properly. Dunno where that tangential thought came from, and it won't do much to contribute to this thread. But, here I thought I was pretty adept with the sticks in moving food from my plate to my gullet, only to learn that it wasn't necessarily so. Alas! While my technique is efficient and would put most American's to shame, I came to learn that I'm quite crude and inelegant. For shame, for shame.
Even if I could move my chopsticks at lightspeed (far surpassing any fly-catching antics), I'd still be behind, relativistically speaking.
Posts: 351 | Registered: Jan 2006
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posted
Indeed, this is a classic question, referred to as the Twin Paradox. (It is a common misconception that this just refers to one twin being biologically younger than the other; that would be an interesting effect, but hardly a paradox. The paradox is that both twins should be younger than the other, for precisely the reasons you give : They both see the other as moving at near lightspeed.)
Let me reformulate the question in the classical way : We have two twins, Traveller and Stay-at-home. Traveller uses a spaceship to travel to Alpha Centauri and back at something very close to the speed of light. Stay-at-home, meanwhile, does exactly what his name suggests. When Traveller gets back, he is essentially the same age as when he lefts; Stay-at-home is eight years older. "No fair!" cries Stay-at-home. "I was going at lightspeed too!"
The answer is that Traveller has not, in fact, been sitting in an inertial frame of reference. At some point, his spaceship accelerated. That takes us right away into the domain of general, not special, relativity. While accelerating, all bets are off; the spaceship loses any claim to be an inertial reference frame.
You might ask, then, why we could not just as well consider the spaceship to be at rest, and the Earth to be accelerating. But here we can distinguish between the two frames : If you drop an object in a spaceship that is accelerating at, say, 600G, it will fall to the floor at 5880 meters per second per second. That won't happen on Earth. It is not unreasonable to say that all the differential aging is taking place in those few seconds of acceleration.
Now, of course, if you drop something on Earth, it will fall to the floor at 9.8 meters per second per second. So the Earth is also an accelerated reference frame, and in consequence, time goes slightly more slowly for us than it would in free space. (This indistinguishability of gravity and other acceleration, incidentally, is the major postulate of general relativity.) It is this effect that is being measured when people send atomic clocks into orbit; it needs to be taken into account when doing the math for GPS satellites. This is one of the major tests for general relativity, in fact.
You'll note that the Twin Paradox only arises if the twins meet up later and can compare life histories. Since they start out in different reference frames, presumably moving quite fast relative to one another, this means that one or both must accelerate. If they remain in their state of relative motion, then it is indeed perfectly valid to consider either one as being the old one - but the question never arises, because they cannot meet up and compare notes.
Posts: 10645 | Registered: Jul 2004
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posted
Sorry for not responding earlier, IB_wench, I hope the intervening posts haven't irretrievably lost us the thread of your question (though as a physics teacher I thoroughly enjoy the diversion!).
No calculus at all? Hmmmm. Off the top of my head, I'd say that while requiring all students to take calculus is wildly inappropriate, it seems similarly inappropriate to deny the option to anyone. Of course, the option is still there, it just isn't available until University-level studies.
I think that there are obviously students who are ready to study calculus at a level beyond memorizing tricks and algorithms to allow them to pass the AP (Advanced Placement) test. In some ways, calculus is one of the most useful branches of mathematics, as it provides a way to understand and predict natural phenomena as well as give us the tools to venture where we haven't been able to go before.
I think that most calculus taught in the US (I don't know about Canada) is designed to allow a student to do well on the AP exam and get college credit. I think that the number of high school students who are prepared by an American public school education to actually study calculus from a conceptual viewpoint and not just know how to solve problems but understand what they're doing is pretty low. I also think that learning calculus any other way is in many ways a waste of time...
I guess my answer would be that if you're going to teach calculus in high school and make it a course that's worth taking, you need to teach math differently for the previous 10 years to train students to expect math to make sense and be useful.
What do you think?
Posts: 99 | Registered: Jan 2001
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posted
...and if a train moved at the speed of light, it would have infinite mass. Reducing its speed would release infinite energy, which would destroy not only you, but the universe.
This is why we have speed limits.
Posts: 1877 | Registered: Apr 2005
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posted
Thanks for responding, Mateo! As one of the calculus students who loves to go beyond memorization tricks and algorithms, I definitely agree with you. Not only is calculus the branch of mathematics with the most real-world application, but the logic and the types of thinking required are useful - even necessary - for many other disciplines as well! Unfortunately, while we don't have AP exams in most high schools, thorough understanding continues to be bypassed in favour of an "easier" curriculum.
Part of the problem stems from the decision to eliminate grade 13, thus compacting 5 years worth of curriculum into 4 years of high school. Many students couldn't handle the more intense workload, and as a result the curriculum continues to be watered down further and further.
Of course, the obvious solution would be to move some of the curriculum down to a younger grade level, distributing it more equally and lessening the burden on the students once they reach high school. (As it is, grade 9 Canadian students are about 2 years behind grade 9 students from elsewhere in the world.) But instead of bringing the students up to the level where they can meet the standard, we simply lower the standard. Aaargh, frustrating!
I'm really lucky in that I take IB math (which covers many concepts that are not included in regular Calculus, including trig functions and antiderivatives) and I have an enthusiastic teacher who loves to show us HOW and WHY the math works rather than just listing formuae. But it's too bad so many other students won't get the same chance to find out how interesting calculus really is...
Posts: 32 | Registered: Jan 2006
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quote:Originally posted by Will B: ...and if a train moved at the speed of light, it would have infinite mass. Reducing its speed would release infinite energy, which would destroy not only you, but the universe.
This is why we have speed limits.
This isn't strictly possible either as it would take an infinite amount of energy to slow it down.
Posts: 92 | Registered: Jul 2005
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posted
So if what Dale says is true then your body would be instantly vaporixed and you'd be nothing more than a splatter on the side of the train. Please note that the train would not be traveling continuously it would make super fast trips from place to place.
Posts: 110 | Registered: Jan 2006
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posted
As a recent graduate of the American High School educational system, I can honestly say I got what I wanted to get out of my classes. And that I probably got more than most people. Most classes were taught with obvious contempt to the way the government is currently being run. And our textbooks were some of the most biased material I've read.
But I did, in my opinion, gain enough of an education that I was somewhat prepared to entire college life.
I learned several years ago, not to bother with what I would be tested on, because that's what is stressed so much. I came to the conclusion anything I wanted to learn I would have to get on my own. So instead of asking questions in class that had relevance to the current topic. I asked questions that fulfilled my curiosity.
As I learn of what my younger siblings are being taught, I come to realize why schools are starting to fail so miserably. When I was younger we were taught things at a pace which accomodated students who did not understand the material as quickly as others. Nowdays it seems as though those students are just out of luck. They rush through basics to get to the 'important'- high level- information. But since students do not get a full understanding of the basics it becomes difficult for them to grasp anything else.
Posts: 31 | Registered: Jul 2005
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posted
I'm an American high school student, and I have to say that I'm extremely disappointed in the way that our curriculum is headed.
I'm very academically accelerated, and grasp concepts much more quickly than other students. Our school does not offer "AP" classes, but because we are very small (300 students total, grades 9-12), if you wish you just take a higher level course. For example, as a sophomore, I'm in Algebra II, Chemistry, and Short Story/Novel, all three of which are typically junior level courses.
In Chemistry one day, we were doing electron configurations of elements in the F-orbitals (lanthanides & actinides). I noticed that the teacher had forgotten something, so as he gave us a break to work on our homework for the chapter, I told him that he had forgotten to include the electron from the d orbital. He told me that he skipped that part because people would get more confused and not understand it. I was astounded! How could he 'make up' material just because everyone else can't understand the reality? (We've since worked this out, by the way.)
I would be nowhere near the level I'm at today if I had not studied on my own over the years. I probably have more textbooks in my room than some of the teachers do! (In the online world, Wikipedia is my savior when it comes to research. So many students resort to frantic Google searching that they get everything mixed up.)
Standardized testing is the (if I may twist the idiom) straw that will break the camel's back eventually. Instead of teaching until everyone grasps the concept, we teach what will be on the test, and must fit everything in before the test. Even in math class, where I see this problem the least, it is evident that lessons are rushed through. If teachers in areas like math weren't afraid to (pardon the pun) go off on a tangent once in a while and explain the history of something, or tie into another subject, maybe students could generalize their learning, and begin to see connections. This is the only way I can stand to learn things in school.
I'm especially concerned with extracurricular downfalls, because I'm involved in so many activities. I've found that I'm running out of time to take classes I want to take (like Band and Yearbook) because of the classes I'm required to take (like PE and foreign langauge). I was excited earlier today when I read in the newspaper about the possible integration of a government-sponsored online "public school". In essence, students would be able to take online classes for high school credit. The article wasn't clear if you could be dually enrolled in an actual school or not, but did mention the possibility of participating in the activities (band, etc) in your local school district. The installation of this program could be my lifesaver, because I desperately need the time for 'required' classes. (On a related note, I wish PE credit was given for sports...it has been in the past but is no longer done, at least at my school...it makes sense!)
Posts: 206 | Registered: Jun 2005
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quote:I'm especially concerned with extracurricular downfalls, because I'm involved in so many activities. I've found that I'm running out of time to take classes I want to take (like Band and Yearbook) because of the classes I'm required to take (like PE and foreign langauge). I was excited earlier today when I read in the newspaper about the possible integration of a government-sponsored online "public school". In essence, students would be able to take online classes for high school credit. The article wasn't clear if you could be dually enrolled in an actual school or not, but did mention the possibility of participating in the activities (band, etc) in your local school district. The installation of this program could be my lifesaver, because I desperately need the time for 'required' classes. (On a related note, I wish PE credit was given for sports...it has been in the past but is no longer done, at least at my school...it makes sense!)
Can you not take 0 and 7th period classes, and get required courses like history, math, P.E. out of the way during the summer? That's what everyone in my HS did.
Posts: 21182 | Registered: Sep 2004
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posted
My school offers 7 classes per day, required. There are no classes offered before 1st period or after 7th.
I have explored the option of taking summer school classes for some credit, however not many higher-level courses are offered (assuming that the students coming to summer school are not the ones needing high-level courses, I guess). Also, I only receive half a credit for a six-week course, which would only be good in PE for me, really. I'd me much more willing to attend 'night classes' or correspondence courses for credit.
Which is why I'm kind of excited about this new online prospect, although I'm nervous that I can't be dually enrolled.
Posts: 206 | Registered: Jun 2005
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posted
I'm taking a VHS (virtual High School) class in which a group of students from around the country takes the same class and everything is done online. It's not the same as a regular class education wise, in that you're only going to learn if you want to. however it's a nice alternative if your school doesn't offer many classes or they are full.
Posts: 959 | Registered: Oct 2005
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posted
I recently taught high school chemistry in an urban school. (I'm now looking for an alternate career track, to put it mildly.) As bad as many teachers may be, I have to have some admiration for their ability to take the abuse students can dish out, though much more so for those that can abely correct and improve behavior.
Standard test were certainly a problem, although I don't know if they would have been if I'd had 30 students like foresicgeek and genius. Basically, I was repeating the most basic concepts of a chapter for a month, then giving a test that everyone flunked, then moving on despite the fact that no one had the foundation needed, because we had to learn x y & z before the test that was stupidly six weeks before the end of the year, and if our test results didn't improve, blah blah blah.
(That was when I wasn't breaking up fights or begging kids to take out a pencil, or sending them out for refusing to mess up their hair with goggles, or taking away electronic devices, or trying to make sure every student had a textbook before we were auditied, or trying to find chairs for the extra 20 students that would only be their until classes were 'balanced' in late october, etc.)
It was my first year full-time teaching, but I wasn't the only one, the other teachers who had non-AP/IB students told me the same stories. I would have quit sooner, rather than the end of the year, but the other teacher who did had a long succession of short-lived subs fill in, and that would have served the students slightly less than my frustrated attempts.
I'm not sure what can or should be done about it all, I just think, "God, I don't want to send kids of mine into that mess."
Posts: 105 | Registered: Dec 2005
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