Dominion Strategy Forum
Miscellaneous => General Discussion => Topic started by: Kirian on February 11, 2013, 03:33:16 pm
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EDIT: Is this not a concept that is taught in middle school anymore? I run into this a lot these days.
Don't you know, we only teach reading and math in schools now. At least in the US.
I'm only half joking.
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EDIT: Is this not a concept that is taught in middle school anymore? I run into this a lot these days.
Don't you know, we only teach reading and math in schools now. At least in the US.
I'm only half joking.
Looking at my 11 year old's curriculum:
Math (year round, good)
Reading (year round, good)
Social Studies (year round, ugh)
Choir (year round, WTF?)
Science (1/2 year, WTF?)
Gym (1/2 year, good)
With as subjective and political as Social Studies is, I would much rather see Science take a half of that year. Or maybe add in History as the objective counter part to Social Studies.
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The fact I'm learning programming right now in a public school in the US proves you wrong. I also have Choir as a possibility.
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The fact I'm learning programming right now in a public school in the US proves you wrong. I also have Choir as a possibility.
I had programming as an option in HS. I wish I had been interested in it then. I think my kids middle school program is crap though. On a side note, I had his choir teacher way back when for choir too.
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The fact I'm learning programming right now in a public school in the US proves you wrong. I also have Choir as a possibility.
Like I said, half joking. There was a reason I chose middle school, though it applies more to elementary schools than middle schools. Obviously high school students branch out, but they're woefully underprepared for most science courses thanks to the "teach to the test" mentality they dealt with in lower grades. And that mentality is pretty rampant, especially in inner-city schools. I have a friend, a first-grade teacher, who literally has been told she can't teach anything other than reading and math due to her school's performance.
Students coming into my ninth-grade science classroom had low math skills and mediocre reading skills. Learning science was worse than simply difficult for them; not only had their previous science experiences been useless, their math and reading skills were low, both thanks to the teaching to the test mentality. It's a vicious cycle, and it now stretches all the way into college classes, where my freshmen also have started coming in unprepared.
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Interesting. Where I am learning we don't seem to have that problem. There are those that struggle with either math or reading, but mostly the problem is with math. (Personally, I don't struggle at all with either. I'm just that kid that learns almost everything pretty well but can't get himself to do his HW at home T.T)
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Interesting. Where I am learning we don't seem to have that problem. There are those that struggle with either math or reading, but mostly the problem is with math. (Personally, I don't struggle at all with either. I'm just that kid that learns almost everything pretty well but can't get himself to do his HW at home T.T)
Don't worry, I was that kid too. I just did my Calc homework during Physics and my Physics homework during Calc. And of course there are differences between different school districts, depending on the affluence of the community.
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Like I said, half joking. There was a reason I chose middle school, though it applies more to elementary schools than middle schools. Obviously high school students branch out, but they're woefully underprepared for most science courses thanks to the "teach to the test" mentality they dealt with in lower grades. And that mentality is pretty rampant, especially in inner-city schools. I have a friend, a first-grade teacher, who literally has been told she can't teach anything other than reading and math due to her school's performance.
Students coming into my ninth-grade science classroom had low math skills and mediocre reading skills. Learning science was worse than simply difficult for them; not only had their previous science experiences been useless, their math and reading skills were low, both thanks to the teaching to the test mentality. It's a vicious cycle, and it now stretches all the way into college classes, where my freshmen also have started coming in unprepared.
I am really just quoting this because I am pleased the topic shifted.
It always seems to me that lower grades are really just about daycare and learning social skills. My kids aren't quite in the system yet though.
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Like I said, half joking. There was a reason I chose middle school, though it applies more to elementary schools than middle schools. Obviously high school students branch out, but they're woefully underprepared for most science courses thanks to the "teach to the test" mentality they dealt with in lower grades. And that mentality is pretty rampant, especially in inner-city schools. I have a friend, a first-grade teacher, who literally has been told she can't teach anything other than reading and math due to her school's performance.
Students coming into my ninth-grade science classroom had low math skills and mediocre reading skills. Learning science was worse than simply difficult for them; not only had their previous science experiences been useless, their math and reading skills were low, both thanks to the teaching to the test mentality. It's a vicious cycle, and it now stretches all the way into college classes, where my freshmen also have started coming in unprepared.
I am really just quoting this because I am pleased the topic shifted.
It always seems to me that lower grades are really just about daycare and learning social skills. My kids aren't quite in the system yet though.
Relevant - I wrote this:
https://docs.google.com/document/d/11AA0-Vwd_ufhcghfgA8tBUaAsDUvCUDUTtkMkBkNfy0/edit (https://docs.google.com/document/d/11AA0-Vwd_ufhcghfgA8tBUaAsDUvCUDUTtkMkBkNfy0/edit)
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Like I said, half joking. There was a reason I chose middle school, though it applies more to elementary schools than middle schools. Obviously high school students branch out, but they're woefully underprepared for most science courses thanks to the "teach to the test" mentality they dealt with in lower grades. And that mentality is pretty rampant, especially in inner-city schools. I have a friend, a first-grade teacher, who literally has been told she can't teach anything other than reading and math due to her school's performance.
Students coming into my ninth-grade science classroom had low math skills and mediocre reading skills. Learning science was worse than simply difficult for them; not only had their previous science experiences been useless, their math and reading skills were low, both thanks to the teaching to the test mentality. It's a vicious cycle, and it now stretches all the way into college classes, where my freshmen also have started coming in unprepared.
I am really just quoting this because I am pleased the topic shifted.
It always seems to me that lower grades are really just about daycare and learning social skills. My kids aren't quite in the system yet though.
Alas, in days gone by, which is to say before the mid-1990s, elementary students did all sorts of things other than just spelling, math, and day care. I'm sure you remember this, of course. :) I hope that your kids end up in a better-than-average school system.
Relevant - I wrote this:
https://docs.google.com/document/d/11AA0-Vwd_ufhcghfgA8tBUaAsDUvCUDUTtkMkBkNfy0/edit (https://docs.google.com/document/d/11AA0-Vwd_ufhcghfgA8tBUaAsDUvCUDUTtkMkBkNfy0/edit)
"Only the most advanced high school students take calculus and physics, and that during their final year."
"We need to push math forward to the point where calculus will be taught across the board in at least the sophomore year of high school, though freshman year would be better."
"The second year of physics would cover nuclear physics, quantum mechanics and relativity."
.... um. So. Um. Yeah. Where to begin?
I'm thrilled at your idealism. Really. And I hope you go on to become a physicist/EE/programmer/what-have-you. But I can tell you haven't considered developmental psychology as a career.
It's an understatement to say that most students are not equipped to handle calculus at 15 years old, or nuclear physics and QM at 17. These are classes that only about--respectively--10% and 0.1% of college students take. Those are, again, people who are already in college. (For reference, my second year of college physics, i.e., QM, atomic and nuclear mechanics, had 12 students at a school of 20000.)
To make this less of an understatement: I hate to say it, but most people aren't equipped to handle calculus at any age. And most people won't need to, ever. (Hell, after four semesters of calculus and differential equations, I haven't used most of it since undergrad, and all my jobs have been scientific or academic in nature.)
One doesn't need to understand QM to program a computer, nor does one need to know how to program a computer in order to use a computer. One need not understand general relativity to use GPS. In fact, I know academics for whom GPS and computer analysis is a vital part of their work who, nonetheless, could likely not explain to you why GPS satellites have to account for relativity, nor how QM makes modern computers possible (or even explain how a transistor works), nor program their own computer software. I'll leave it to you to figure out what academic and practical disciplines this applies to; I can think of three from the top of my head, I'm sure there's more.
When Newton and Galileo were working, those who did science were able to know everything there was to know in the scientific literature. That's how little we knew. This is no longer the case; we now teach top high school students about the same body of knowledge that Galileo would have had. College students, obviously, go beyond that. But the average high school student doesn't need all of it.
What they do need--what we need to be teaching to all high school students, and no longer do--is critical thinking. Now, this can be introduced in the form of problems related to the disciplines we spend so much time teaching them, and that's good, but it doesn't go far enough.
But at the high school level, the students I was teaching were expected to be able to demonstrate knowledge X, Y, and Z on a standardized multiple-choice exam. There was no time to spend two months developing critical thinking skills because we focused on the very lowest levels of Bloom's taxonomy. That is the travesty of education in the US. Not that we don't teach enough [science|history|math|literature], but that we teach too much at the knowledge and comprehension levels and very little at even the application level, much less higher levels. Teachers are expected to make sure the students can regurgitate information onto a standardized test, when what's important for society is not whether a student knows (as an example) the quantum mechanical properties of the hydrogen atom, but whether a student, given the bulk physical and chemical properties of hydrogen, can explain what happened to the LZ Hindenburg.
And now I've gone off on another rant about education. Back to work, I have a three-hour lecture on gas laws to give on Thursday.
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Just curious, as I am a high school student, is there anything you feel that a high school student can do to improve their critical thinking skills? As I am strongly considering programming as a possible career(Taking an AP class in C next year after finishing this year!), I would love to be able to improve my critical thinking skills.
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There was no time to spend two months developing critical thinking skills because we focused on the very lowest levels of Bloom's taxonomy. That is the travesty of education in the US. Not that we don't teach enough [science|history|math|literature], but that we teach too much at the knowledge and comprehension levels and very little at even the application level, much less higher levels.
Plus one for this.
But while it's easy to rant about standardized testing, there is no denying that it won't go away -- it's cheap, easy, and effective monitoring of progress. Even for elementary grades. In some cases the problem is that the tests don't test what we want them to test and school curriculum is not what we really want to teach ("trivia" versus thinking/creativity). But standardized tests do shine lights on schools which are atrocious but no one wants to admit exist and students who have fallen behind but whom we push through the system anyway. We say how bad teaching to the test is, but what does it say about teachers and schools that "teach to the test" all year yet have most of their third grade students fail on questions like:
Which has the same product as 3 X 4?
A) 2 X 6
B) 7 X 2
C) 4 X 6
D) 3 X 5
What counting number comes right after 539?
A) 530
B) 538
C) 540
D) 541
(These are actual representative sample questions from a 3rd grade test required by No Child Left Behind).
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Just curious, as I am a high school student, is there anything you feel that a high school student can do to improve their critical thinking skills? As I am strongly considering programming as a possible career(Taking an AP class in C next year after finishing this year!), I would love to be able to improve my critical thinking skills.
Here's my best bit of advice: Read with a pencil in hand (annotated reading/active reading). Thinking critically requires constant questioning (Why does the author/do I think this is true? Is he/Am I right? How could he/I be wrong here? What assumptions is he/am I making and are they correct? Are there other explanations that may be better? ...).
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I never really understood the "teach to the test" criticism. What is the alternative to "teaching to the test"? Teaching a subject in such a way that students can't demonstrate proficiency?
A well-designed test (SAT Math is a good example) makes it so that teaching to the test is equivalent to teaching the subject. You cannot do well on the SAT Math without actually being good at math. In this respect NCLB gets it right -- you shouldn't be able to mask your terrible teaching with unstandardized, unrigorous, and arbitrarily graded tests of your own design. If your students can't demonstrate basic proficiency you are doing something wrong.
From a Bayesian perspective, if your students fail standardized tests, it's a lot more likely that you're a crap teacher, rather than you're some genius teacher who somehow still can't get his kids to demonstrate basic proficiency.
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Just curious, as I am a high school student, is there anything you feel that a high school student can do to improve their critical thinking skills? As I am strongly considering programming as a possible career(Taking an AP class in C next year after finishing this year!), I would love to be able to improve my critical thinking skills.
Here's my best bit of advice: Read with a pencil in hand (annotated reading/active reading). Thinking critically requires constant questioning (Why does the author/do I think this is true? Is he/Am I right? How could he/I be wrong here? What assumptions is he/am I making and are they correct? Are there other explanations that may be better? ...).
To expand on this subject -- near and dear to lawyers' hearts -- you should develop a habit of skepticism. I don't mean skepticism as in, become a 9/11 truther: I mean skepticism in thinking about the motivations of your speaker, the likelihood of competing scenarios, and what you should believe. Try to see both sides of the issue -- there almost always is one, and it's not just "xxx is evil and greedy".
Here's an example: http://www.nydailynews.com/new-york/new-yorkers-outraged-bureaucrats-order-city-change-lettering-single-street-sign-article-1.443695
If you read the first few paragraphs, you might get your pitchforks ready. WTF, stupid bureaucrats, why are they forcing NY to pay $27M to change the font on signs? How dumb, this is a sign of how dysfunctional BigGov is.
Exercise your critical thinking skills. Is this what is really happening? What's the actual likelihood that the DOT would arbitrarily decide that NYC has to change all its street signs all of a sudden? Wouldn't the more logical thing be to just say, "When you replace these signs anyway, because of wear and tear, use these new ones instead of those old ones."
And as you read on, you realize that buried deep in the article, this is the actual plan, and the article concedes that there is no actual cost to NYC to doing this.
Another example: http://newyork.cbslocal.com/2012/03/19/bloomberg-strikes-again-nyc-bans-food-donations-to-the-homeless/
See if you can figure out for yourself why this is a stupidly sensationalistic article. Note, for example, how the links provided don't back up the assertions at all, and how you have to do your own research to see that the article's thesis (that Bloomberg is banning food donations to the homeless because they can't assess their nutritional content) is something made up by the author, when the real reason (because it's goddamn unsafe to just dump unsanitary leftovers at a homeless shelter) goes entirely unmentioned. Note the tone that the author takes, to deliberately try to goad you into outrage, and don't fall for it.
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There was no time to spend two months developing critical thinking skills because we focused on the very lowest levels of Bloom's taxonomy. That is the travesty of education in the US. Not that we don't teach enough [science|history|math|literature], but that we teach too much at the knowledge and comprehension levels and very little at even the application level, much less higher levels.
Plus one for this.
But while it's easy to rant about standardized testing, there is no denying that it won't go away -- it's cheap, easy, and effective monitoring of progress. Even for elementary grades. In some cases the problem is that the tests don't test what we want them to test and school curriculum is not what we really want to teach ("trivia" versus thinking/creativity). But standardized tests do shine lights on schools which are atrocious but no one wants to admit exist and students who have fallen behind but whom we push through the system anyway. We say how bad teaching to the test is, but what does it say about teachers and schools that "teach to the test" all year yet have most of their third grade students fail on questions like:
Which has the same product as 3 X 4?
A) 2 X 6
B) 7 X 2
C) 4 X 6
D) 3 X 5
What counting number comes right after 539?
A) 530
B) 538
C) 540
D) 541
(These are actual representative sample questions from a 3rd grade test required by No Child Left Behind).
OK, so the first one might require kids to multiply five pairs of numbers, and that might be daunting to some. But how do kids get the second one wrong? Is there some arcane definition of "counting number"? The answer is 540, right? Isn't it obvious, or is there some trick I'm missing? ???
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OK, so the first one might require kids to multiply five pairs of numbers, and that might be daunting to some. But how do kids get the second one wrong? Is there some arcane definition of "counting number"? The answer is 540, right? Isn't it obvious, or is there some trick I'm missing? ???
Depends on your definition of "right" ;)
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OK, so the first one might require kids to multiply five pairs of numbers, and that might be daunting to some. But how do kids get the second one wrong? Is there some arcane definition of "counting number"? The answer is 540, right? Isn't it obvious, or is there some trick I'm missing? ???
Depends on your definition of "right" ;)
...do most grade 3 kids have trouble counting with 3 digits?
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I never really understood the "teach to the test" criticism. What is the alternative to "teaching to the test"? Teaching a subject in such a way that students can't demonstrate proficiency?
Focusing on the subject matter rather than the method of evaluation.
Fundamentally, it's because "how easy is this to evaluate" is NOT a useful metric for deciding whether something should be taught. The stuff that goes on standardized tests is dictated as much by the format as it is by the curriculuim. Take your own example of the SAT math. It gives a bit over a minute per question. So that means all skills that are difficult to evaluate in a minute of a student's time simply get discarded. Since they're not going to be tested, they're not going to be taught.
Are you really saying that there are no math skills worth teaching to high school students that can't be boiled down to a one-minute multiple choice question?
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...do most grade 3 kids have trouble counting with 3 digits?
I write my numbers right to left, so 540 is actually the number left after 539.
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...do most grade 3 kids have trouble counting with 3 digits?
I write my numbers right to left, so 540 is actually the number left after 539.
I get your joke but I am still looking for a serious answer. :P
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It's an understatement to say that most students are not equipped to handle calculus at 15 years old, or nuclear physics and QM at 17. These are classes that only about--respectively--10% and 0.1% of college students take. Those are, again, people who are already in college.
I was quite surprised about this. In Finland all high school students study calculus, somewhere between age 15-17. One can choose either "short" or "long" maths curriculum and the former only goes as far as differential calculus, but nevertheless everyone at least touches the subject and more than half choose the long curriculum. And that's for a country that to my knowledge has a bit less focus on maths compared to many other European countries, though admittedly for one that seems to shine in international comparisons (http://www.guardian.co.uk/news/datablog/2010/dec/07/world-education-rankings-maths-science-reading) for education in general (despite actually having the kids spend less time on studies).
US students seem to fail particularly in maths.
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Looking at my 11 year old's curriculum:
Math (year round, good)
Reading (year round, good)
Social Studies (year round, ugh)
Choir (year round, WTF?)
Science (1/2 year, WTF?)
Gym (1/2 year, good)
"Science"? There's actually a school subject called "science"? :o I thought it was used to refer to various subjects.
Here, 11-year-old kids learn subjects such as mother tongue & literature, English, math, history, biology, geography, physics, chemistry, handcraft, music, visual arts, gym and either religion or ethics (parents' choice). Additionally, most schools offer some optional subjects such as French, German, electronic data processing, optional music, optional visual arts, optional gym, etc. and usually it is required to choose some, but not all of these.
Sorry for off-topic, I was so shocked that I couldn't resist posting.
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"Math" and "Social studies" each refer to vast arrays of subjects. Such a broadly named course would be an overview, which is what one might expect for an 11 year old. A little bit of of geology about plate tectonics or how rocks form, then a little bit of ecology or talking about the cell theory of life, then maybe a unit on the sun, moon, and planets.
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...do most grade 3 kids have trouble counting with 3 digits?
No. Most third graders don't have problems multiplying, either. The issue is that the problems tend to be localized and concentrated in certain schools and districts. Problems compound over the course of students' careers and these easy questions are actually hard enough to identify problem schools. Standardized tests in the US are designed to identify under-performers, not high achieving students.
US students seem to fail particularly in maths.
Much of the problem is high variance and clustering leading to very bad outcomes on the low end. For instance, on the most recent TIMMS, average 8th grade US math scores are right behind Finland (http://nces.ed.gov/timss/table11_3.asp). Also, it's usually bad to compare the US as a whole to an individual European country. Education in the US is highly localized (mostly state-level and district-level curriculum and funding) and many states are about the same geographic and population size as a European country. Some state breakdowns are at the bottom of the table. Massachusetts is on par with Japan, while Alabama is on par with Armenia, for instance. There is also significant racial differences which makes the discussion very difficult. Using the data trends tool on the TIMMS site, Asian Americans score 549, White Americans score 533, Hispanic Americans score 475 and Black Americans score 457 (you can look at the linked table for comparisons). This is less variance than in the past which is both good and bad because reforms and emphasis on testing has reduced scores at the upper end as well as increased them at the lower end. In 1992, dividing the US into four "countries" by race, Asian Americans were top in the world, White Americans 6th, Hispanic Americans third from the bottom and Black Americans worst in the world (of countries tested).
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Ay yi yi, so many questions to consider. I'll probably be answering various of these piecemeal over the course of the day, so apologies in advance for filling up the thread with multiple replies.
I never really understood the "teach to the test" criticism. What is the alternative to "teaching to the test"? Teaching a subject in such a way that students can't demonstrate proficiency?
A well-designed test (SAT Math is a good example) makes it so that teaching to the test is equivalent to teaching the subject. You cannot do well on the SAT Math without actually being good at math. In this respect NCLB gets it right -- you shouldn't be able to mask your terrible teaching with unstandardized, unrigorous, and arbitrarily graded tests of your own design. If your students can't demonstrate basic proficiency you are doing something wrong.
From a Bayesian perspective, if your students fail standardized tests, it's a lot more likely that you're a crap teacher, rather than you're some genius teacher who somehow still can't get his kids to demonstrate basic proficiency.
FTL partly covered this, but I'll give a slightly different wording at least. There two major assumptions in what you've said. The first is that any given standardized test is a good metric of what students know. This is demonstrably untrue in many, though not all, cases. The second is that any given standardized test is a good metric of what students should know. While this delves into more philosophical problems about what we should be teaching students (and some of my opinions are outlined above), you'll find a lot of agreement among teachers, especially science teachers, that many state standardized tests don't do a great job with this either.
As I said, the failing is in testing knowledge rather than application or analysis. Mathematics tests usually get around this problem because they are, inherently, application tests; there is very little to "know" about math. (Once you know what positive integers are, and what the four basic operations are, everything further is an application of those to more complex situations.) Yet even at that, the students are not often required to show their work; instead, we leave it as a multiple-choice question. Standardized science tests are often little more than knowledge tests, however, and this is a huge failing. Consider which of the following two questions more usefully demonstrates mastery of physics:
(1) Determine the kinetic energy of a baseball with a mass of 95 g travelling at a velocity of 35 m/s.
(2) A baseball is pitched, hit by the batter, and becomes a pop-fly [insert graphic showing the path for someone not familiar with the sport]. Describe the energy changes that happen to the baseball as it moves along this path from pitcher to batter to fielder. Where is energy gained, and where does it come from? Where is energy lost, and where does it go?
Now, which of those is going to show up on a standardized test?
The "teaching to the test" criticism isn't so much that the tests exist, though countries with better education systems often don't have the same kinds of standardized tests (Finland, for instance, which was mentioned above). The problem is that the tests suck, and the nature of the testing system means they will continue to suck. And the result is that the curriculum... well, sucks.
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there is very little to "know" about math. (Once you know what positive integers are, and what the four basic operations are, everything further is an application of those to more complex situations.)
Whoa Dr. Kronecker, easy. I am sure Peebles can put a rebuttal in better words, but this seems like a very terse description of math to me. Had you said "there are axioms , and there are proof techniques, everything further is an application", you may have a point, in a warped kind of way (as much as a point can be warped).
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Ay yi yi, so many questions to consider. I'll probably be answering various of these piecemeal over the course of the day, so apologies in advance for filling up the thread with multiple replies.
I never really understood the "teach to the test" criticism. What is the alternative to "teaching to the test"? Teaching a subject in such a way that students can't demonstrate proficiency?
A well-designed test (SAT Math is a good example) makes it so that teaching to the test is equivalent to teaching the subject. You cannot do well on the SAT Math without actually being good at math. In this respect NCLB gets it right -- you shouldn't be able to mask your terrible teaching with unstandardized, unrigorous, and arbitrarily graded tests of your own design. If your students can't demonstrate basic proficiency you are doing something wrong.
From a Bayesian perspective, if your students fail standardized tests, it's a lot more likely that you're a crap teacher, rather than you're some genius teacher who somehow still can't get his kids to demonstrate basic proficiency.
-snip-
I agree, Kirian. Recently I had to take the Physics GRE 3 different times. The GRE is a standardized test similar to the SAT that you take to get into graduate school. The Physics subject GRE entails 100 multiple choice questions. Because it's multiple choice, the test has to test purely mathematical problems or simple concepts, like "Which of the following happens when an electron passes a charged nucleus" followed by five different terms, or "Susie's going half the speed of light, what's her Lorentz contraction" followed by five different numbers. This sort of test does not show your knowledge of physics - it shows how well you you practiced with flash cards showing simple formulae. I spent four years in college studying Physics, and I'd like to think I have a good grasp on the fundamental concepts, which are what I'm actually going to need when I'm in graduate school. However, I didn't bother to memorize most of the formulae because, hey, in an actual Physics job (such as my current internship) you don't need to have those memorized, because you can always look them up. What's more important is understanding the concept - not having the formula memorized. The GRE tests if you've memorized the formula, not if you understand the concept. So in order to prepare students for the GRE, physics profs would have to drill these formulae into their students' heads, rather than actually teaching them the fundamental concepts of physics. Science is more than just formulae.
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I was quite surprised about this. In Finland all high school students study calculus, somewhere between age 15-17. One can choose either "short" or "long" maths curriculum and the former only goes as far as differential calculus, but nevertheless everyone at least touches the subject and more than half choose the long curriculum. And that's for a country that to my knowledge has a bit less focus on maths compared to many other European countries, though admittedly for one that seems to shine in international comparisons (http://www.guardian.co.uk/news/datablog/2010/dec/07/world-education-rankings-maths-science-reading) for education in general (despite actually having the kids spend less time on studies).
Note that Finland, unlike the US, has a split secondary education. About half of students in Finland don't go to what the US would call "high school," instead going to a vocational school. Frankly, it's something the US could use more of--part of our problem is the push that everyone should go to college.
Of those in Finland that do go to what we'd call high school, apparently about 20% take the harder math curriculum--I'm grabbing this number from WP, which links to a source that is, alas, in Finnish, so I can't read it. If you can, I'll link it.
So 50% of Finns don't do upper-level math, 40% get through what we'd call Pre-Calc in the US (higher trig and basic differentiation), and 10% do Calculus around age 16-17. That's not too unreasonable; higher than the US, which is unsurprising. About 7% of my high school classmates had Calc in HS, though the average is going to be lower in some places and higher in more affluent communities.
The Finns also have a government that cares about education at the national level. In the US control is at the state and local level, and not nearly enough money goes into education, leading to affluent students having more opportunity and better education, which of course acts as a vicious cycle for those of low socioeconomic status and OK, I won't go farther on that or I'll have to take it to the Politics forum.
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there is very little to "know" about math. (Once you know what positive integers are, and what the four basic operations are, everything further is an application of those to more complex situations.)
Whoa Dr. Kronecker, easy. I am sure Peebles can put a rebuttal in better words, but this seems like a very terse description of math to me. Had you said "there are axioms , and there are proof techniques, everything further is an application", you may have a point, in a warped kind of way (as much as a point can be warped).
Perhaps I was unclear. When I said "know" up there, I was speaking from Bloom's taxonomy. Mathematics inherently sits at a higher level in Bloom's taxonomy, because it is the application of lower-level ideas. Yes, OK, you can memorize formulae, and certainly some standardized tests go that direction, but most (in the US) will give you the formulae and expect you to use and manipulate them.
In other words, we teach math at a higher level than we teach science. This is a good thing for math teachers. Not so hot for science teachers.
But yes, at its most fundamental, there are axioms and then everything that comes from those axioms. Sure, we're not teaching 8-year-olds ZFC, but their understanding of multiplication comes straight from addition, and leads straight to exponentiation, then to functions, and thereon to calculus, with some odd excursions into practical geometry.
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there is very little to "know" about math. (Once you know what positive integers are, and what the four basic operations are, everything further is an application of those to more complex situations.)
Whoa Dr. Kronecker, easy. I am sure Peebles can put a rebuttal in better words, but this seems like a very terse description of math to me. Had you said "there are axioms , and there are proof techniques, everything further is an application", you may have a point, in a warped kind of way (as much as a point can be warped).
I agree, this description of maths apllies to what people in school think is maths at best.
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As a math educator, I'm a bit skeptical of the pedestal on which calculus is placed in secondary education. Proability and statistics is considerably more practical and useful, as is linear algebra. Calculus is great, don't get me wrong. Absolutely vital if you are going to be further studying physical science or engineering. But everyone should be familiar with a decent amount of probability and statistics.
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As for further discussion on whether there is more to know about math beyond the four arithmetic operations, I'll have to get back to you. I'm currently attending at a math conference at UC Berkeley and need to get going or else I'll miss the first talk. I'll ask them about the question. Although as most of us work on rings, I'm not convinced they'll consider even the fourth operation of division to be of much use :P
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It's not that easy to proceed to probs and stats without some knowledge of calculus. While I'd concur that calculating variance estimates by second derivatives is something to be reserved for after high school, it is not that easy to get the relation between density and cumulative distribution function without knowing what an integral is, or survival function and hazard.
That being said, calculus and analytical geometry got too much attention when I went to school, at the expense of probs and stats (which we did a bit) and discrete methods such as graph theory (which we omitted).
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It's not that easy to proceed to probs and stats without some knowledge of calculus. While I'd concur that calculating variance estimates by second derivatives is something to be reserved for after high school, it is not that easy to get the relation between density and cumulative distribution function without knowing what an integral is, or survival function and hazard.
That being said, calculus and analytical geometry got too much attention when I went to school, at the expense of probs and stats (which we did a bit) and discrete methods such as graph theory (which we omitted).
You can say this about any subject. Things are interconnected. But you can teach someone a hell of a lot of useful probability and statistics without ever mentioning cumulative probability distributions.
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I never really understood the "teach to the test" criticism. What is the alternative to "teaching to the test"? Teaching a subject in such a way that students can't demonstrate proficiency?
Focusing on the subject matter rather than the method of evaluation.
Fundamentally, it's because "how easy is this to evaluate" is NOT a useful metric for deciding whether something should be taught. The stuff that goes on standardized tests is dictated as much by the format as it is by the curriculuim. Take your own example of the SAT math. It gives a bit over a minute per question. So that means all skills that are difficult to evaluate in a minute of a student's time simply get discarded. Since they're not going to be tested, they're not going to be taught.
Are you really saying that there are no math skills worth teaching to high school students that can't be boiled down to a one-minute multiple choice question?
What would you replace it with, though?
I'm saying, success on a standardized test is more correlated with mastery / understanding than any other alternative. It would be wonderful if we had a magic committee that could individually interview every student fairly every year. But we don't have that, and the alternative to a standardized test is essentially no oversight at all. There are enormously strong institutional pressures at the local level to pass students no matter what. I would think, then, that if you care about reforming schools the very first thing to do would be to hold them all accountable, and the only fair way to do that is with standardized testing.
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The Finns also have a government that cares about education at the national level. In the US control is at the state and local level, and not nearly enough money goes into education, leading to affluent students having more opportunity and better education, which of course acts as a vicious cycle for those of low socioeconomic status and OK, I won't go farther on that or I'll have to take it to the Politics forum.
Local control is not necessarily a bad thing. Local is relative, you know. For example, the entire population of Finland is a little over half the population of the greater Chicago area. Illinois has much greater income per capita. Why can't Chicago schools or the state of Illinois implement good education policy on their own? They can implement exactly what Finland has if they want it without needing DC. (In fact, what Illinois does is not so bad.) Policies that utilize standardized testing like NCLB are needed only so that states don't delude themselves into thinking they are doing better than they are and make comparisons across states easier, like TIMMS makes comparisons across countries easier.
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As a math educator, I'm a bit skeptical of the pedestal on which calculus is placed in secondary education. Proability and statistics is considerably more practical and useful, as is linear algebra. Calculus is great, don't get me wrong. Absolutely vital if you are going to be further studying physical science or engineering. But everyone should be familiar with a decent amount of probability and statistics.
Absolutely agreed. Basic stats and probability are incredibly useful to the general populace, and not taught to the depth they should be.
As for further discussion on whether there is more to know about math beyond the four arithmetic operations, I'll have to get back to you. I'm currently attending at a math conference at UC Berkeley and need to get going or else I'll miss the first talk. I'll ask them about the question. Although as most of us work on rings, I'm not convinced they'll consider even the fourth operation of division to be of much use :P
Yeah, yeah, all right, I've oversimplified. :P
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I never really understood the "teach to the test" criticism. What is the alternative to "teaching to the test"? Teaching a subject in such a way that students can't demonstrate proficiency?
Focusing on the subject matter rather than the method of evaluation.
Fundamentally, it's because "how easy is this to evaluate" is NOT a useful metric for deciding whether something should be taught. The stuff that goes on standardized tests is dictated as much by the format as it is by the curriculuim. Take your own example of the SAT math. It gives a bit over a minute per question. So that means all skills that are difficult to evaluate in a minute of a student's time simply get discarded. Since they're not going to be tested, they're not going to be taught.
Are you really saying that there are no math skills worth teaching to high school students that can't be boiled down to a one-minute multiple choice question?
What would you replace it with, though?
I'm saying, success on a standardized test is more correlated with mastery / understanding than any other alternative. It would be wonderful if we had a magic committee that could individually interview every student fairly every year. But we don't have that, and the alternative to a standardized test is essentially no oversight at all. There are enormously strong institutional pressures at the local level to pass students no matter what. I would think, then, that if you care about reforming schools the very first thing to do would be to hold them all accountable, and the only fair way to do that is with standardized testing.
In my first year of uni, one of our lecturers in the first lecture of the course said something along the lines of: "The exam will make up 85% of the mark. It isn't great, because we can't truly test what you know on the exam, so if anyone has a better suggestion let me know" *Cue laughter from the lecture theater* "No, seriously, I really want a better alternative. Please try and think of something."
Needless to say, we didn't. Tests aren't great, but as long as we need a standardised way of measuring approximately how good people are at something, they're the best we can do in terms of the balance between cost, time and accuracy. Interviews are probably better, but they're a lot more subjective in general. So ultimately, the issue comes down to, how well is this test examining what we want it to? A well written test does a good job.
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It would be wonderful if we had a magic committee that could individually interview every student fairly every year.
Tests have time and again shown to have a better reliability than committees. Maybe because they didn't have magical ones in their sample.
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Tests can be something different than multiple choice though.
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Tests can be something different than multiple choice though.
Free-response questions are much, much worse. They are impossible to grade fairly, as any teacher will tell you. You can of course do "free-response" the way the SAT does (i.e., bubble in a numerical answer), but subjective grading undermines the purpose of a standardized test.
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I never really understood the "teach to the test" criticism. What is the alternative to "teaching to the test"? Teaching a subject in such a way that students can't demonstrate proficiency?
Focusing on the subject matter rather than the method of evaluation.
Fundamentally, it's because "how easy is this to evaluate" is NOT a useful metric for deciding whether something should be taught. The stuff that goes on standardized tests is dictated as much by the format as it is by the curriculuim. Take your own example of the SAT math. It gives a bit over a minute per question. So that means all skills that are difficult to evaluate in a minute of a student's time simply get discarded. Since they're not going to be tested, they're not going to be taught.
Are you really saying that there are no math skills worth teaching to high school students that can't be boiled down to a one-minute multiple choice question?
What would you replace it with, though?
I'm saying, success on a standardized test is more correlated with mastery / understanding than any other alternative. It would be wonderful if we had a magic committee that could individually interview every student fairly every year. But we don't have that, and the alternative to a standardized test is essentially no oversight at all. There are enormously strong institutional pressures at the local level to pass students no matter what. I would think, then, that if you care about reforming schools the very first thing to do would be to hold them all accountable, and the only fair way to do that is with standardized testing.
I agree. I feel as though what's really happening in America is that we're trying to figure out a way to pass the buck on underfunding education (I feel like we're using the cross-your-fingers strategy with a lot of kids), and I'm hoping that maybe testing could counter that by putting school failures in concrete terms.
I like the idea of teaching critical thinking as much as the next guy, but I find that a lot of schools -- even the good ones I was lucky enough to go to -- didn't have much of a solid plan for teaching it anyway, even in an era when "teaching to the test" wasn't much of a thing. (I graduated high school in '98.) So if they weren't going to teach me something intangible, why not teach me something tangible?
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Tests can be something different than multiple choice though.
Free-response questions are much, much worse. They are impossible to grade fairly, as any teacher will tell you. You can of course do "free-response" the way the SAT does (i.e., bubble in a numerical answer), but subjective grading undermines the purpose of a standardized test.
No teacher who understands testing will try to convince you that free response questions cannot be graded fairly. A well-written free response question with a well-written rubric can be fairly graded by a different teacher. I mean... what you have said here is just false.
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It can be true though. For example, once in my eigth grade class, we were given the chance for the whole class to grade eachothers essay. Our teacher used a projector to project each essay on the board and using a rubric, we had to give our grades. We didn't know who's essay was who's of course, and when we were done, we folded them up and gave them to the teacher. She then tallied them up. It was amazing how conflicting some of the views were. Some essays being rated much tougher than others. Also, when asking students why they rated an essay a certain way, some responded with something very subjective. It was interesting to find just how subjective graders can be with written short answer, essays, etc.
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Teachers can be trained at grading in a way that comes close to being fair. Also, there are questions where you can objectively say wether something is true or false, for example a mathematical proof.
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Teachers can be trained at grading in a way that comes close to being fair. Also, there are questions where you can objectively say wether something is true or false, for example a mathematical proof.
Ha! If I objectively graded proofs as either true or false I doubt a single student I've ever had would pass one of my classes. Maybe some small handful of them would have, but well under 1%
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Teachers can be trained at grading in a way that comes close to being fair. Also, there are questions where you can objectively say wether something is true or false, for example a mathematical proof.
Ha! If I objectively graded proofs as either true or false I doubt a single student I've ever had would pass one of my classes. Maybe some small handful of them would have, but well under 1%
I had a math professor in undergrad who graded homework this way (for abstract algebra). My heart dropped the first time I got a proof back I had spent 3 hours on and got a zero! I asked why, since I had followed the line of the suggested proof halfway through before making an error and going off track, and the professor responded, "Is the proof correct?" I said no, and that was that. I have never been so happy for a curve in a class since.
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Tests can be something different than multiple choice though.
Free-response questions are much, much worse. They are impossible to grade fairly, as any teacher will tell you. You can of course do "free-response" the way the SAT does (i.e., bubble in a numerical answer), but subjective grading undermines the purpose of a standardized test.
No teacher who understands testing will try to convince you that free response questions cannot be graded fairly. A well-written free response question with a well-written rubric can be fairly graded by a different teacher. I mean... what you have said here is just false.
I daresay that a free response question with a mechanical rubric or checklist is not really superior to a multiple choice question. The advantage of free response is also its failing, namely, that you introduce some subjectivity into the grading. Does he "really" get it despite a poorly written answer? Does she get to the right answer for the wrong reason? Does this answer that meet all the rubric requirements fail because the student clearly just regurgitated as much as possible and doesn't really understand the concept? But that undermines the purpose of standardized testing.
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Tests can be something different than multiple choice though.
Free-response questions are much, much worse. They are impossible to grade fairly, as any teacher will tell you. You can of course do "free-response" the way the SAT does (i.e., bubble in a numerical answer), but subjective grading undermines the purpose of a standardized test.
No teacher who understands testing will try to convince you that free response questions cannot be graded fairly. A well-written free response question with a well-written rubric can be fairly graded by a different teacher. I mean... what you have said here is just false.
I daresay that a free response question with a mechanical rubric or checklist is not really superior to a multiple choice question. The advantage of free response is also its failing, namely, that you introduce some subjectivity into the grading. Does he "really" get it despite a poorly written answer? Does she get to the right answer for the wrong reason? Does this answer that meet all the rubric requirements fail because the student clearly just regurgitated as much as possible and doesn't really understand the concept? But that undermines the purpose of standardized testing.
Listen. I know this seems like a common sense thing to many people, probably because we've all been in school and therefore believe we all know about testing. But this is the sort of thing that can be researched, measured, and quantified; there are entire academic disciplines devoted to studying these things.
Reading a non-educator try to make these incorrect points probably feels much like what it would feel to you if I were to try to explain an esoteric point of international law to you, a lawyer. Based on my extensive experience watching Law and Order, and having recently been called for jury duty.
The difference is that for some reason people think that teachers, I don't know, just go by instinct? As opposed to being trained, like we actually are.
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Note that Finland, unlike the US, has a split secondary education. About half of students in Finland don't go to what the US would call "high school," instead going to a vocational school.
Good point, I did not think of that since I did not know that US does not have such a split. Also, Polk5440's point on not treating US as a big chunk is very valid one, though his post also indicated some alarmingly high degree of variance across different states or populations.
Of those in Finland that do go to what we'd call high school, apparently about 20% take the harder math curriculum--I'm grabbing this number from WP, which links to a source that is, alas, in Finnish, so I can't read it. If you can, I'll link it.
Please do give the link -- I was actually looking for the percentage when writing my reply, but could not find a reliable source so chose to go with my subjective personal memories that are a bit dated and probably also biased because of the high school I went to back in the nineties. If the percentage indeed is as low as 20%, then we are indeed looking at only 10% of the total population studying integral calculus.
The Finns also have a government that cares about education at the national level.
Certainly. Besides focusing on elementary education, they also offer completely free university education (and in fact, pay notable monthly allowance for all bachelor and master's students).
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The difference is that for some reason people think that teachers, I don't know, just go by instinct? As opposed to being trained, like we actually are.
I'm pretty sure the point is that teachers are still people, and people make subjective decisions (even if they are well trained not to).
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The difference is that for some reason people think that teachers, I don't know, just go by instinct? As opposed to being trained, like we actually are.
I'm pretty sure the point is that teachers are still people, and people make subjective decisions (even if they are well trained not to).
So do judges, lawyers, doctors, nurses, engineers, and architects. But I'm not talking about subjective decisions; I'm talking about non-educators who believe they know all about teaching because they went to school. Rarely do those other professions have to deal with non-professionals telling them how their profession works. We all deal with people telling us how our profession ought to work, but people who say "I think doctors should treat cancer with honey" are treated as nutjobs, while people who say "You can't objectively grade a free response question" are given serious consideration. Which is why we end up forced to make students prepare for a standardized multiple-choice exam as opposed to teaching them how to think.
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The difference is that for some reason people think that teachers, I don't know, just go by instinct? As opposed to being trained, like we actually are.
I'm pretty sure the point is that teachers are still people, and people make subjective decisions (even if they are well trained not to).
So do judges, lawyers, doctors, nurses, engineers, and architects. But I'm not talking about subjective decisions; I'm talking about non-educators who believe they know all about teaching because they went to school. Rarely do those other professions have to deal with non-professionals telling them how their profession works. We all deal with people telling us how our profession ought to work, but people who say "I think doctors should treat cancer with honey" are treated as nutjobs, while people who say "You can't objectively grade a free response question" are given serious consideration. Which is why we end up forced to make students prepare for a standardized multiple-choice exam as opposed to teaching them how to think.
You're being overly dramatic. My wife has a master's in education and is my go-to source. I freely admit you have more personal experience than I, but the original point was that you could make standardized tests out of free response questions, which is still baffling to me. They exist in some standardized tests (SAT II Writing, AP History) but are notoriously subjectively graded.
The dichotomy between "forced to prepare for a standardized multiple choice exam" and "teaching them how to think" is overstated in this country. They don't align perfectly, but neither does literally any other form of evaluation. Is it a coincidence that SAT scores correlate strongly with college GPA (as strongly as HSGPA)? What would you replace it with?
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So do judges, lawyers, doctors, nurses, engineers, and architects. But I'm not talking about subjective decisions; I'm talking about non-educators who believe they know all about teaching because they went to school.
No, you were talking about what theory was talking about, and I was talking about what theory was talking about. If you weren't, that is a non sequitur.
Man, that sentence was hard to write.
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the original point was that you could make standardized tests out of free response questions, which is still baffling to me. They exist in some standardized tests (SAT II Writing, AP History) but are notoriously subjectively graded.
I'll again drop in with some examples from abroad. In Finland we have no standardized tests with multiple choice questions, but we do have ones with free response questions, though only at the very end of the high school; here's a randomly googled US-centric rough overview of our system (http://www.educationnation.com/index.cfm?objectid=344AE6BA-FB34-11E0-B00E000C296BA163).
The matriculation exam has one test for each subject (though you only need to do some subset of those), and the tests are purely free response with the exception of some parts of the language tests. For maths, physics, history, biology etc you simply have a set of 10-13 free response questions, out of which you have to answer 6-8, depending on the subject. For languages you even have essays of 4-5 handwritten pages, graded between 0-60. The questions are fairly complex; even though you only answer 6-8 questions the exam lasts for 6 hours.
Some effort indeed goes to the grading. The tests are graded by the local teachers based on guidelines given by a nation-level board, but after that the exams are sent to the same board that re-checks all of the exams. They can change the grades and they also do so, though not terribly often (maybe a few percent of the grades change notably). For the essays there can be even extreme swings, from the highest grade to fail or vise versa in case of controversial cases. Finally, you can file in a formal complaint for the final grade, though my understanding is that this does not happen often.
As you can imagine, the system is somewhat heavy and expensive and there have always been discussions on major re-design or even getting rid of the matriculation exams, but nevertheless the system has stayed fairly intact for decades; the exams and grading for my parents in mid sixties were virtually identical to the tests used still a few years ago. Also, the results are generally considered reliable, to the extent that almost all universities use the results of those exams as part of their entrance exams and some even grant entrance solely based on the exam results.
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The International Bacalaureate (IB) program might also be worth noting. It does not rely on mc and includes short answer, long answer and even essay questions for evaluating students (for English and Social Studies, multiple essays!).
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Students in the UK generally take GCSEs (at 16) and A Levels (at 18). I had to check that the term didn't mean something that couldn't be guessed from the two words, but it seems like these should count as standardised tests. Out of exams for about 15 different qualifications, perhaps one included any element of multiple choice. We certainly don't have anything like the US SATs, taken by everyone in the country and giving you a percentile rank.
I'd be interested in a summary of the US school system from anyone who's been through it. When do you move schools? When do you take various qualifications, and who awards them? What do you get taught each year? It seems to differ in lots of subtle ways from anything I'm familiar with, and I don't understand it as well as I'd like to, despite numerous attempts to figure it out.
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I'd be interested in a summary of the US school system from anyone who's been through it. When do you move schools? When do you take various qualifications, and who awards them? What do you get taught each year? It seems to differ in lots of subtle ways from anything I'm familiar with, and I don't understand it as well as I'd like to, despite numerous attempts to figure it out.
Super basic overview, from someone who graduated public High School in 2006:
12 grades, from age 6-7 to age 17-18. Also Kindergarten before first grade, sometimes. Also Pre-School before Kindergarten, but that's not really a part of the school system so much as it is day-care with learning.
Elementary School is K-5, Middle School is 6-8, High School is 9-12.
Elementary school, you have one teacher for 20-30 kids, who teaches major subjects -- math, language, "social studies" (history and geography), science. Ancilliary classes are taught by specialists throughout the day (your class has Music at 1pm on Wednesday and Friday, mine has Music on Monday and Tuesday at 10am) by specialist teachers. Your class walks together to the classroom for the specialized subject. Standardized tests are determined primarily at the state level and vary greatly from state to state. Generally speaking, you might have one test at the end of the year that covers all major subjects they expect you should understand for that year, but this test would not determine whether you continue to the next grade.
Middle School, all teachers are specialized, and students move from classroom to classroom throughout the day with autonomy. Lockers. School sports teams, after-school activities and clubs. Testing is
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Where I am in Canada, elementary is K-6, middle school is "Jr. High" and is 7-9, and Sr. High is 10-12. I believe some places in Canada have the 6-8 middle school split described by Drab, and some places in the US are like here with the 7-9 middle school.
Elementary here is the same as described by Drab. I remember doing English (basic reading and writing), math, social, some science. There was a music class. We also had gym and art, and very briefly some computers.
In Jr. High we actually got Options! I ended up taking French (in which I am terrible) and computers.
In Sr. High there were also Options, but I had less of them because I was in a full IB program. Notable about our Sr. High program is that you can now take Bio, Chem and Physics separately. There is still a unified Science course though, for those who prefer that for whatever reason.
Provincial testing is done at grades 3, 6, 9 and 12. And we did have some essay writing in grade 12... and I think 9 too? Maybe even creative writing, it's hard to remember.
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Students in the UK generally take GCSEs (at 16) and A Levels (at 18). I had to check that the term didn't mean something that couldn't be guessed from the two words, but it seems like these should count as standardised tests. Out of exams for about 15 different qualifications, perhaps one included any element of multiple choice. We certainly don't have anything like the US SATs, taken by everyone in the country and giving you a percentile rank.
I'd be interested in a summary of the US school system from anyone who's been through it. When do you move schools? When do you take various qualifications, and who awards them? What do you get taught each year? It seems to differ in lots of subtle ways from anything I'm familiar with, and I don't understand it as well as I'd like to, despite numerous attempts to figure it out.
In most areas of the US, you essentially have the following progression:
Preschool (3-5)
Elementary School (5-12, labeled grades K-6)
Middle School or Junior High School (12-15 depending on school, grades 7-8 or 6-9)
High School (14-18, usually grades 9-12)
Graduation from High School is a prerequisite for college. Schooling through 16 years or 12th grade, whichever comes first, is compulsory, though most will stay in school until age 18.
In Ohio, standardized tests are given in grades 3, 4, 5, 6, 7, 8, and 10. About 80% of the questions are multiple choice. However, the 3-8 tests are meaningless to the students themselves; they won't be held back if they fail the tests. The school may lose its funding, though, or be forced into various interventions, if too few students pass.
Note the first problem here: the school can lose funding for failing students, but they don't get the chance to remediate the students. In fact, the junior high school they go to in 7th grade still must accept a student who has failed the 3rd through 6th grade tests. In addition, the test results are not based on "did this student do better this year than last year," but "did the student do everything this year that s/he was supposed to."
The 10th grade tests are high-stakes tests; students must pass them all in order to graduate. They first take them the second half of their 10th grade year; any that they don't pass get retaken in the first half of 11th grade, then again every following semester. If they've failed more than one, they generally get put into a special remedial class whose only purpose is to get them to pass the test, and they'll take this class until they pass every test. If they did poorly on their 8th grade tests, they'll often be put into this class in 10th grade automatically. That means this classroom is composed of 10th through 12th graders, some of whom are in it for 3 years in a row... and after late March, when the tests are given, the class is useless, and therefore becomes chaotic.
All of this testing varies from state to state, as if the US were composed of fifty different small countries; nonetheless, the basic mandate comes from the federal government.
In addition, actual funding for the schools comes mainly from property taxes at the local level. Only about 5% comes from federal money and 30-50% from the state. However, the local money is not distributed among different localities to equalize things. The property taxes are based on home values, which means neighboring districts can have vastly different budgets per pupil. Rural districts often far the worst.
In addition, the amount of property tax given to the schools is determined by the voters in most localities. Even a $10 a year hike in property taxes must be approved by 50% of voters. Shockingly, it's easier to get such tax levies passed in more affluent communities, where it's more affordable. In the less affluent communities, it's not uncommon for there to be bake sales and the like to get money to pay for advertising to convince voters. This means that budgets can vary significantly from one year to the next, meaning teaching jobs and therefore class sizes fluctuate.
Now, back to what gets taught. In Ohio, to graduate, a high school student must pass 4 years of English, 3 years of math, science, and social studies, a year of phys ed, and various amounts of other things. Especially for English and math, this means a lot of students end up in summer school--one reason the US will likely never go to year-round schooling. There is no foreign language requirement in Ohio, though there used to be. Again, all of this varies from state to state, and individual districts can require more.
From elementary to junior high school, curricula are pretty regimented (with different standards by state). Palindrome mentions class sizes; 25-35 per teacher is really closer for elementary school, with 20 being very low. Classes in high schools are about the same size, depending on subject. A high school teacher might teach six classes a day, and have 150 or more total students. (Why are so many high school students given mainly multiple choice tests? Because a good open-response test, which might take as much as 10 minutes to grade, means 25 hours of grading, where a test that can be put through a scanner and graded takes about 15 minutes total to grade, at about 10 scans per minute.)
I think that's probably enough to give you an idea how messed up our system is.
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I would have said everything Kirian said, and then I noticed he was describing Ohio, which is where I've done all my schooling (and living, thus far)...
The school system I was in was K-6 for elementary, 7-9 jr high, 10-12 high school.
1 High School
3 Jr High Schools
9 Elementary Schools
(along with numerous private and Christian schools)
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in almost of the public schools in Rhode Island, the system is:
elementary school: K-4
middle school: 5-8
high school: 9-12
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in almost of the public schools in Rhode Island, the system is:
elementary school: K-4
middle school: 5-8
high school: 9-12
I went a middle school in Rhode Island, and it was definitely graded 6-8
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I'd be interested in a summary of the US school system from anyone who's been through it.
How curious are you? Since Kirian brought up Ohio and I am familiar with the system there having both gone through it and studied it in economics classes in college, I would like to point out the Ohio Department of Education (http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDefaultPage.aspx?page=1) has one of the best sites describing the system, standard requirements, and testing. It has all the facts and aggregate data you could ever need, such as report cards to compare outcomes across districts (http://education.ohio.gov/GD/Templates/Pages/ODE/ODEPrimary.aspx?Page=2&TopicID=222&TopicRelationID=115), data on tests (http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?page=3&TopicRelationID=285&ContentID=9479&Content=137332), practice tests (http://education.ohio.gov/GD/Templates/Pages/ODE/ODEPrimary.aspx?Page=2&TopicID=216&TopicRelationID=240), and per pupil funding by district (http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?page=3&TopicRelationID=1214&ContentID=708&Content=140420).
...test results are not based on "did this student do better this year than last year," but "did the student do everything this year that s/he was supposed to."
I should mention that districts in Ohio are being pushed to consider "value add (http://education.ohio.gov/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicID=130&TopicRelationID=117)" seriously in terms of teacher compensation ("merit pay") and how they view student progress. This is generally met with resistance from teachers which is why progress is slow on this front both in terms in legislation and implementation.
Now, back to what gets taught. In Ohio, to graduate, a high school student must pass 4 years of English, 3 years of math, science, and social studies, a year of phys ed, and various amounts of other things.
See here for the details (http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRelationID=1696). Note the curriculum standards part of the requirement are updated every few years and the high school requirements are designed so that students can achieve them by the time they take the high stakes graduation test (OGT) in 10th grade, as Kirian describes above. Thus, while the standards don't mention calculus as a graduation requirement, students can complete calculus by their senior year if they take 4 years of math in high school (the "3 years of math" requirement Kirian notes above is increasing to 4 years soon); earlier if students select advanced tracks.
Also, on the college prep side, if you choose to be college bound, in 11th or 12th grade you take college readiness exams (either the SAT or ACT) which are used in college admissions decisions. Sometimes SAT subject tests (like physics or US history) are required, as well. If you take college prep courses in high school, there are AP or IB exams, as well. Passing these usually gives some kind of college credit.
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Graduation from High School is a prerequisite for college.
Except that you can take a test instead! That was true in my day and my skimpy research indicates that it still is.
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Man, how many Ohioans are there here?
Graduation from High School is a prerequisite for college.
Except that you can take a test instead! That was true in my day and my skimpy research indicates that it still is.
You know, I totally hadn't thought about that. I've never actually seen the test; I wonder what it's like.
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in almost of the public schools in Rhode Island, the system is:
elementary school: K-4
middle school: 5-8
high school: 9-12
I went a middle school in Rhode Island, and it was definitely graded 6-8
hence the word almost :P
what middle school did you go to? i grew up in portsmouth
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Is that an age system?
In Holland it's something like:
Age 3/4-11/12: Basic school
Age 11/12-17/18: Middle school
Age 17/18-?: University
All ages are rough estimates and depend on student aptitude and when in the year they're born.
I was what was called an "early" student (born in August prior to the school year) and I skipped 1 class, so I started university at 16.
Our basic school has 8 grades, middle school has 4 to 6. Some middle schools are more focused on physical jobs like wood- and metalworking and they have less years, but you can start another school after that. My grammar school had 6 years.
University depends on how lazy you are and how much you can borrow, I was very lazy. :)
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In addition, actual funding for the schools comes mainly from property taxes at the local level. Only about 5% comes from federal money and 30-50% from the state. However, the local money is not distributed among different localities to equalize things. The property taxes are based on home values, which means neighboring districts can have vastly different budgets per pupil. Rural districts often far the worst.
In addition, the amount of property tax given to the schools is determined by the voters in most localities. Even a $10 a year hike in property taxes must be approved by 50% of voters. Shockingly, it's easier to get such tax levies passed in more affluent communities, where it's more affordable. In the less affluent communities, it's not uncommon for there to be bake sales and the like to get money to pay for advertising to convince voters. This means that budgets can vary significantly from one year to the next, meaning teaching jobs and therefore class sizes fluctuate.
To give you an idea of how much things can differ from state-to-state, I teach high school math in the state of Washington (not to be confused with Washington D.C.).
The state of Washington has in its state constitution that "ample funding" for "basic education" by the state is the state's "paramount duty". Because of this, the state has taken it upon themselves to try to do the majority of the funding for the schools within the state. While Kirian cites that approximately 30-50% of the money comes from the state, in Washington State, that number approaches 75%.
Many parts of what individual local districts can do is limited by this state regulation. For instance, local districts can raise funds, but the state has explicitly limited how much can be raised by local levy, as well as what can be done with it. Since the state's current functional definition of basic education includes just five classes per day at the high school level, local levies often end up paying for the district's ability to offer a sixth class per day, and in some cases (but not many), a seventh.
Also, because the state considers it their duty to provide for basic education, salaries are set at the state level. Because local levy money is limited in terms of the total dollars that can be raised and since most of it is used for providing additional classes per day (and accordingly, hiring the extra staff required to offer these classes), local levy dollars often don't significantly add to this total. Local levy dollars are only allowed to be added to teacher salaries for TRI pay, where TRI is comprised of Time (you were required to spend more time, perhaps at trainings), Responsibility (you took on added responsibilities), and Incentive. The Incentive dollars are light, because the districts don't have the funds to offer them, by and large.
While Kirian describes a system where the most affluent districts are best off financially, the reverse tends to happen to some degree in Washington state: because the cost-of-living in or near affluent districts is so high, but school districts in those areas can't offer a proportionally comparable salary, affluent districts often become training grounds for newer and younger teachers before folks move on to districts closer to home. I teach in one of the more affluent districts in the state, live 45 minutes away in good traffic, and make 10% more than I would working for the high school five minutes from my house. This is my 11th year teaching in that district, and at age 35, I have been the most senior member of the math department in my particular high school for six consecutive years now.
Kirian mentioned class sizes, and mine operates at an average of 34 students per class, where I teach five classes per day. The more advanced classes tend to be larger so that we can focus more individual attention on the struggling students. That seems to be more of a district-level decision than a state-level decision.
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In addition, actual funding for the schools comes mainly from property taxes at the local level. Only about 5% comes from federal money and 30-50% from the state. However, the local money is not distributed among different localities to equalize things. The property taxes are based on home values, which means neighboring districts can have vastly different budgets per pupil. Rural districts often far the worst.
In addition, the amount of property tax given to the schools is determined by the voters in most localities. Even a $10 a year hike in property taxes must be approved by 50% of voters. Shockingly, it's easier to get such tax levies passed in more affluent communities, where it's more affordable. In the less affluent communities, it's not uncommon for there to be bake sales and the like to get money to pay for advertising to convince voters. This means that budgets can vary significantly from one year to the next, meaning teaching jobs and therefore class sizes fluctuate.
To give you an idea of how much things can differ from state-to-state, I teach high school math in the state of Washington (not to be confused with Washington D.C.).
The state of Washington has in its state constitution that "ample funding" for "basic education" by the state is the state's "paramount duty". Because of this, the state has taken it upon themselves to try to do the majority of the funding for the schools within the state. While Kirian cites that approximately 30-50% of the money comes from the state, in Washington State, that number approaches 75%.
Many parts of what individual local districts can do is limited by this state regulation. For instance, local districts can raise funds, but the state has explicitly limited how much can be raised by local levy, as well as what can be done with it. Since the state's current functional definition of basic education includes just five classes per day at the high school level, local levies often end up paying for the district's ability to offer a sixth class per day, and in some cases (but not many), a seventh.
Also, because the state considers it their duty to provide for basic education, salaries are set at the state level. Because local levy money is limited in terms of the total dollars that can be raised and since most of it is used for providing additional classes per day (and accordingly, hiring the extra staff required to offer these classes), local levy dollars often don't significantly add to this total. Local levy dollars are only allowed to be added to teacher salaries for TRI pay, where TRI is comprised of Time (you were required to spend more time, perhaps at trainings), Responsibility (you took on added responsibilities), and Incentive. The Incentive dollars are light, because the districts don't have the funds to offer them, by and large.
While Kirian describes a system where the most affluent districts are best off financially, the reverse tends to happen to some degree in Washington state: because the cost-of-living in or near affluent districts is so high, but school districts in those areas can't offer a proportionally comparable salary, affluent districts often become training grounds for newer and younger teachers before folks move on to districts closer to home. I teach in one of the more affluent districts in the state, live 45 minutes away in good traffic, and make 10% more than I would working for the high school five minutes from my house. This is my 11th year teaching in that district, and at age 35, I have been the most senior member of the math department in my particular high school for six consecutive years now.
Kirian mentioned class sizes, and mine operates at an average of 34 students per class, where I teach five classes per day. The more advanced classes tend to be larger so that we can focus more individual attention on the struggling students. That seems to be more of a district-level decision than a state-level decision.
OMG I want to come teach in WA.
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Just curious, as I am a high school student, is there anything you feel that a high school student can do to improve their critical thinking skills? As I am strongly considering programming as a possible career(Taking an AP class in C next year after finishing this year!), I would love to be able to improve my critical thinking skills.
Here's my best bit of advice: Read with a pencil in hand (annotated reading/active reading). Thinking critically requires constant questioning (Why does the author/do I think this is true? Is he/Am I right? How could he/I be wrong here? What assumptions is he/am I making and are they correct? Are there other explanations that may be better? ...).
To expand on this subject -- near and dear to lawyers' hearts -- you should develop a habit of skepticism. I don't mean skepticism as in, become a 9/11 truther: I mean skepticism in thinking about the motivations of your speaker, the likelihood of competing scenarios, and what you should believe. Try to see both sides of the issue -- there almost always is one, and it's not just "xxx is evil and greedy".
Here's an example: http://www.nydailynews.com/new-york/new-yorkers-outraged-bureaucrats-order-city-change-lettering-single-street-sign-article-1.443695
If you read the first few paragraphs, you might get your pitchforks ready. WTF, stupid bureaucrats, why are they forcing NY to pay $27M to change the font on signs? How dumb, this is a sign of how dysfunctional BigGov is.
Exercise your critical thinking skills. Is this what is really happening? What's the actual likelihood that the DOT would arbitrarily decide that NYC has to change all its street signs all of a sudden? Wouldn't the more logical thing be to just say, "When you replace these signs anyway, because of wear and tear, use these new ones instead of those old ones."
And as you read on, you realize that buried deep in the article, this is the actual plan, and the article concedes that there is no actual cost to NYC to doing this.
Another example: http://newyork.cbslocal.com/2012/03/19/bloomberg-strikes-again-nyc-bans-food-donations-to-the-homeless/
See if you can figure out for yourself why this is a stupidly sensationalistic article. Note, for example, how the links provided don't back up the assertions at all, and how you have to do your own research to see that the article's thesis (that Bloomberg is banning food donations to the homeless because they can't assess their nutritional content) is something made up by the author, when the real reason (because it's goddamn unsafe to just dump unsanitary leftovers at a homeless shelter) goes entirely unmentioned. Note the tone that the author takes, to deliberately try to goad you into outrage, and don't fall for it.
Relevant: http://www.cracked.com/blog/5-easy-ways-to-spot-b.s.-news-story-internet/
Any Time You See a Headline Like ...
"Vaccinated Children Five Times More Prone to Disease Than Unvaccinated Children" -NaturalNews.com
Or
"Studies Show That Online Gaming Can Add Years to Your Life" -i-Newswire
You Should Read It As ...
"Vaccinated Children Five Times More Prone to Disease Than Unvaccinated Children AND ALSO WI-FI IS CAUSING WORMS TO GROW IN YOUR BRAIN" -Hobo talking to his pet rat on the subway