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Kirian

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Re: Education
« Reply #25 on: February 12, 2013, 09:56:22 am »
+1

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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Re: Education
« Reply #26 on: February 12, 2013, 10:02:46 am »
0

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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Re: Education
« Reply #27 on: February 12, 2013, 10:08:44 am »
0

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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Kirian

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Re: Education
« Reply #28 on: February 12, 2013, 10:10:45 am »
+1

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 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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Kirian

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Re: Education
« Reply #29 on: February 12, 2013, 10:16:32 am »
0

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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Re: Education
« Reply #30 on: February 12, 2013, 10:18:44 am »
0

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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Re: Education
« Reply #31 on: February 12, 2013, 10:21:14 am »
+1

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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Re: Education
« Reply #32 on: February 12, 2013, 10:29:34 am »
+1

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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Re: Education
« Reply #33 on: February 12, 2013, 10:30:25 am »
0

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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SirPeebles

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Re: Education
« Reply #34 on: February 12, 2013, 10:44:45 am »
+1

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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Re: Education
« Reply #35 on: February 12, 2013, 10:46:03 am »
+1

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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Re: Education
« Reply #36 on: February 12, 2013, 10:48:03 am »
+1

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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Kirian

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Re: Education
« Reply #37 on: February 12, 2013, 10:55:39 am »
0

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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Tables

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Re: Education
« Reply #38 on: February 12, 2013, 11:14:58 am »
0

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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Re: Education
« Reply #39 on: February 12, 2013, 11:19:38 am »
+1

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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Re: Education
« Reply #40 on: February 12, 2013, 11:21:28 am »
0

Tests can be something different than multiple choice though.
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theory

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Re: Education
« Reply #41 on: February 12, 2013, 11:41:07 am »
0

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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Brando Commando

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Re: Education
« Reply #42 on: February 12, 2013, 04:10:19 pm »
0

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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Kirian

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Re: Education
« Reply #43 on: February 12, 2013, 04:53:31 pm »
0

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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Re: Education
« Reply #44 on: February 12, 2013, 06:00:12 pm »
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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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Re: Education
« Reply #45 on: February 12, 2013, 06:06:16 pm »
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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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Re: Education
« Reply #46 on: February 12, 2013, 06:20:28 pm »
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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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Re: Education
« Reply #47 on: February 12, 2013, 06:35:43 pm »
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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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Re: Education
« Reply #48 on: February 12, 2013, 06:50:46 pm »
0

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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Kirian

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Re: Education
« Reply #49 on: February 12, 2013, 10:30:12 pm »
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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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