Standardized Tests: Have we gone too far?

[SteamKing]

I think there's something wrong if we start taking public policy advice from comedians and hosts of fake news shows.

Obviously, there is no standardized test one can take to become a certified comedian. Anything they know at all about testing probably comes from when they were in school.

Are standardized tests being overused now? Probably.

Education as practiced in recent years, especially in the primary and secondary grades, is more driven by administrators and politicians signing up for the latest fads than deciding, based on results, what material students should learn and how best for them to show that they've learned the material. Standardized testing is a no-brainer for most people supervising public education because there's a company or two with a readily-available test which they can market to an interested school district.

 

[WWGD]

It would be interesting to see how well graduates of the Finnish system do farther along in their lives by some measures, e.g, number of patents, published papers, etc.

 

[stevendaryl]

Here's my ideal system: Instead of having a single, high-stakes test, you have lots of low-stakes assessments. The meaning of a low-stakes assessment is purely to decide how well a student understands a subject. The point of such an assessment would not be to decide someone's future destiny--Harvard or automechanics--it's simply to find out what the student still has trouble with, and what the student has mastered. The assessments would determine what happens next, as far as whether the student goes on to an advanced topic, or is given more help with the current topic.

This might not be universally the case, but it seems to me that for a student to get much out of a course, that student has to be at the right stage of academic development. If the course is at too advanced a level, and requires pre-requisites that the student hasn't really understood yet, then he's going to be lost. On the other end of the scale, if the course is at too basic a level, and just goes over what the student already knows, then that's a waste of time, as well.

 

[mathwonk]

my dad taught me to read by reading to me as i sat on his lap looking at the words. by the time i was 5, i could read a little in the newspaper and tried to do so from his new york times. in school they spent all their time on kids who could not read at all so i learned nothing more. my mom taught me basic arithmetic with flash cards, and spelling from the old blue back speller, and i added nothing to those areas in school either. i recall learning one thing in 8th grade when a substitute teacher came in for a couple days from the college, namely that a = a + ar + ar^2 +... - r(a + ar + ar^2 +...) = (1-r)(a+ar+ar^2+...) so (a + ar + ar^2 +...) = a/(1-r), (correct when |r| < 1). I thought that was so cool.at the end of the year they gave us iowa basic skills tests and i recall my score graph was just a straight line literally off the chart at the top of the page in every category. of course all the questions were trivial.In high school algebra we learned that r is a root iff (x-r) is a factor, and that n things can be arranged in n! different orderings, and that sqrt(2) is not rational, and basic plane geometry facts like ”triangles are equal that look equal”. finally in senior year we learned something, namely propositional calculus of logical expressions, and i finally knew what a negation, and a contrapositive, and a converse were after hearing those meaningless words used in plane geometry. I loved that stuff. We also learned that complex numbers were ordered pairs of reals, the basic definition of a group, and the meaning of countable and uncountable infinity. By reading on my own I learned cantor’s diagonal arguments to prove the rationals countable and the reals uncountable. that’s about it, as bubba gump said.when i took the SAT I kind of enjoyed it. It was an easy test I could do all but one problem of in my head, and then on the basis of the score i got a merit scholarship. so i always viewed standardized tests as found money. you spend a couple hours answering easy questions and they give you a scholarship! you don’t even need to know anything.The basic rule of passing a test is that it is almost impossible to write a single question so that it can only be answered by someone who actually knows the general theory it is testing. Thus with a little cleverness you can almost always answer any specific question with enough time, especially if it is multiple choice. Of course you can’t answer one like “state taylor’s theorem” unless you have some idea what that is, but skipping those regurgitation questions just gives you more time to deal with the specific numerical or conceptual ones. So I was never bothered by standardized tests, they were kind of a fun challenge, with a financial payoff.then i went to college and found out i knew nothing at all, and that i actually needed to work hard and read and think to make up for that. the previous 12 years were basically wasted except for the time playing baseball and basketball, but eventually it didn’ t matter that much, i still got a phd in mathematics and became a hard nosed college professor expecting everyone to work hard all the time. in my 60's i even read euclid and finally learned some plane geometry. i never really figured out how to teach effectively to anyone other than those who were willing to work hard though. that's why i wound up on physics forum where the only people here are pretty much those who want to learn.

 

[Andy Resnick]

<snip>than deciding, based on results, what material students should learn and how best for them to show that they've learned the material. <snip>

This is the essence of the "pro-test" argument. But the reality is that it's impossible to generate statistically significant results in the first place- there are too many uncontrollable variables (e.g. home life) that strongly impact student ability. Further, while there is growing agreement with what minimum content constitutes a 'proper' STEM course, this concordance has not yet been reached for subjects like history, languages, art, etc.

 

[dlgoff]

Just thought I'd throw in my School Funding in Kansas thread, if anyone cares to read it.

 

[stevendaryl]

This is the essence of the "pro-test" argument. But the reality is that it's impossible to generate statistically significant results in the first place- there are too many uncontrollable variables (e.g. home life) that strongly impact student ability. Further, while there is growing agreement with what minimum content constitutes a 'proper' STEM course, this concordance has not yet been reached for subjects like history, languages, art, etc.

I certainly agree that things like home life affect a student's performance on tests, but why does that make the test results not statistically significant? Certainly, tests can't accurately measure inherent ability, but that's only relevant if you're trying to use the test to decide a student's entire future. But if you're only trying to decide what courses the student should take next, and whether the student needs additional help in a subject, then I think a test can give you a lot of information about that. That's why I advocate lots of small, low-stakes tests. They would just be a snapshot of where the student is, academically, not some kind of Tarot reading of what they are capable of next year or 10 years from now.

Your point about external factors such as a home life that is not conducive to learning is very good, but I'm not sure how schools should address those kinds of inequalities, other than to give students lots of opportunities for extra help.

 

[Evo]

What I don't understand is why these tests are needed. Wouldn't the child's every day school work be the best indicator? Many kids have test anxiety and will do worse on tests like this than in normal school work. Of course some kids hate school and don't do well even though they are very bright and capable but a special test isn't going to change that.

 

[TheDemx27]

I can't imagine taking more than 3 standardized tests in my entire life.

Ha, I took the SAT last week, and will take the SAT Math 2 subject test and SAT physics subject test less than a few months from now. What annoys me the most is that the SAT claims to be an aptitude test, yet you can significantly improve your score by preparing for it. Preparing doesn't really improve your abilities, it just makes you good at taking the test.

I view test scores in the same way Al Gore views GDP.

It appears some major overhaul in education is needed.

AMEN.

Not test related, but I have a single physics class at my school. It isn't AP, just introductory. Its the middle of the last quarter, and we are answering questions phrased like this: "The seasons change because the Earth gets closer and further away from the sun?". The teacher is wrong half the time when dealing with something outside the book, is terrible at explaining things, and spends most of the class making small talk about sports. We get so little work that I have literally spent the last week doing absolutely nothing. It is extremely frustrating for me, because a class about physics - physics! - should be the most interesting, and the school somehow butchers it. I'm definitely going to a local college for physics with calc next year because my school is a joke.

It doesn't stop there. There is mediocrity and apathy penetrating every corner of my high school, and it isn't just me with this opinion. Me and everyone I know finds almost class at my school extremely easy and boring. Take for example my AP US History class. We had a paper assigned in December to be due in a month. Its May now and still hasn't been collected because the teacher saw people weren't doing it. Now its an "ongoing project". All classes follow this pattern but the math courses taught by a particular teacher.

Whatever the case is at other schools, for me high school is so boring it is painful, and I know the majority of students at my school would agree with me.

If I choose not to get a doctors in physics I would be just as happy to pursue a teaching career at the high school level. I would make sure that my students would have the best freaking physics class of their high school career. There is SO much you could do. Make a Rubens' tube and explain sound waves and pressure and make a cloud chamber and get to see the trails of beta and alpha particles. I would be satisfied in life just to teach others to love the subject, to give them the physics class I never had.

 

[rollingstein]

I don't understand the common critique of standardized testing, in general. Maybe because I'm unfamiliar with the US HS system.

But is the argument against any standardized testing, or are we only saying that the particular tests used are crappy? If so, I can understand but then we can focus on improving standardized testing not getting rid of standardized testing. I am sure nobody argues against testing itself (say, at MS or HS level) so how does standardization suddenly make it crappy?

I admit it would be problematic if we had a China-style college admissions system where a single standardized test was the only one that mattered. But the US universities seem to weigh multiple metrics including standardized tests but not only standardized tests. That seems an OK system to me.

I think the problems of US educational systems are multifold e.g. tying funds to local taxes, lack of parental support, general poverty, a societal apathy to school education, poor teacher salaries, a mocking of high academic achievement as nerdiness, evils of unionization, bureaucracy etc. But standardized testing seems like the one feature everyone loves to attack. I don't get that focus. Perhaps standardization is an evil but it is a necessary evil.

Say, we got rid of standardized testing, how do we transition to a better scenario. It is fundamentally the training that is the major problem. Testing is the minor ill. If David cannot compute 8x7 it does not matter what sort of testing methodology you use to assess him; you still have a big problem.

OTOH, take the oft cited high quality student from Finland: I'm sure he'd do well on the many vilified standardized tests of USA if you had him take one.

 

[atyy]

What's the problem with googling 7X8?

It surely is much more important to know that 7 X 8 = 8 X 7 than to know that 7 X 8 = 56.

For example, in a mechanics problem, what is important is setting up the force diagram and writing the right equations down - in other words, it's the structure and logic that is important. Once you get to the final step, what;s wrong with plugging in the numbers and using a calculator?

 

[Fredrik]

I think there's something wrong if we start taking public policy advice from comedians and hosts of fake news shows.

I disagree with this view on comedians. Obviously we shouldn't just take someone's advice without first verifying that they're right, but the fact that Oliver is a comedian isn't a reason to think that that he's wrong. "Last week tonight with John Oliver" and "The daily show with Jon Stewart" (where Oliver's career started) seem to be doing more thorough research than all the actual news shows.

 

[rollingstein]

but the fact that Oliver is a comedian isn't a reason to think that that he's wrong

True. Even a madman can speak out silvers of sense sometimes.

I guess the point behind a comedian is "Don't take me seriously". So although, you are right that just because Oliver says the "Sun rises in the East" that doesn't automatically make it false.

But OTOH, a comedian isn't the source you ought to be looking for your dose of facts. Though it doesn't harm if he motivates you to look deeper into something.

 

[Fredrik]

What's the problem with googling 7X8?

It surely is much more important to know that 7 X 8 = 8 X 7 than to know that 7 X 8 = 56.

For example, in a mechanics problem, what is important is setting up the force diagram and writing the right equations down - in other words, it's the structure and logic that is important. Once you get to the final step, what;s wrong with plugging in the numbers and using a calculator?

I agree with what you're saying here, but it's certainly very useful to be able to do the most basic calculations without a calculator or Google. It's also natural to teach the multiplication table very early, so it's odd if someone who hasn't been taught the multiplication table is forced to take any test on math.

Also, somone who uses a calculator to find things like $\big(\frac 1 2\big)^2$ and $\frac{-1}{2}$ has a very seriously flawed understanding of multiplication. I don't think such people should be encouraged to keep using the calculator.

 

[JorisL]

What I don't understand is why these tests are needed. Wouldn't the child's every day school work be the best indicator? Many kids have test anxiety and will do worse on tests like this than in normal school work. Of course some kids hate school and don't do well even though they are very bright and capable but a special test isn't going to change that.

This.
About kids hating school, this could be the start of a new topic. "How can we improve quality in education?"

What's the problem with googling 7X8?

It surely is much more important to know that 7 X 8 = 8 X 7 than to know that 7 X 8 = 56.

For example, in a mechanics problem, what is important is setting up the force diagram and writing the right equations down - in other words, it's the structure and logic that is important. Once you get to the final step, what;s wrong with plugging in the numbers and using a calculator?

Fredrik beat me to it

I mostly agree but (there's always a but :-) ) how can one assess the result?
Given you never make a mistake in the first 100 problems you solve this way the intuition comes naturally. This is highly unlikely.
But if they are very confident in their calculating abilities it is easy to spot mistakes in my opinion.

I would conclude from this that we should find some sort of middle road here.
A slightly better example to support my point, integrals. Computer algebra packages sometimes cannot find the result while you can find a simple solution by hand.

I disagree with this view on comedians. Obviously we shouldn't just take someone's advice without first verifying that they're right, but the fact that Oliver is a comedian isn't a reason to think that that he's wrong. "Last week tonight with John Oliver" and "The daily show with Jon Stewart" (where Oliver's career started) seem to be doing more thorough research than all the actual news shows.

I wish we had such a comedian over here. We came to a point where the most popular news papers do some of the worst research.
No background checking etc.
Lets hope he makes people think critically (over time perhaps)

 

[Fredrik]

True. Even a madman can speak out silvers of sense sometimes.

I guess the point behind a comedian is "Don't take me seriously". So although, you are right that just because Oliver says the "Sun rises in the East" that doesn't automatically make it false.

But OTOH, a comedian isn't the source you ought to be looking for your dose of facts. Though it doesn't harm if he motivates you to look deeper into something.

That's not at all the argument I'm making. I'm saying that Jon Oliver is likely to get it right because of the research that his staff is doing to put the story together. It's obviously not at the level of science, but unless you're actually studying the science on this (if it exists at all), you will have a hard time finding a better source.

Edit: I watched the clip again, and I should add that it's not hard to find some flaws in Oliver's reporting. In particular, why does it matter that when Pearson wanted to hire some test scorers, one of the places they advertised was craigslist? I also looked up the story about the hare and the pineapple, which according to Oliver "doesn't remotely work as a test question" and was so bad that he and his staff weren't able to answer the questions. There's nothing really wrong with the text. Some of the questions are kind of bad, but I found it easy enough to answer them all.

This illustrates one thing that's problematic when comedians do reports like this. If something can be made fun of, they can't resist, even if it means including a flawed argument in the report.

 

[rollingstein]

That's not at all the argument I'm making. I'm saying that Jon Oliver is likely to get it right because of the research that his staff is doing to put the story together. It's obviously not at the level of science, but unless you're actually studying the science on this (if it exists at all), you will have a hard time finding a better source.

Okay. I just think it's unfair to quote him as a source because if he does get a fact wrong people can always say "Oh, but he's just a comedian".

Personally I like his show a lot and also Jon Stewart's too & they have very scathing commentary on a lot of the stupidities & incongruities of the world we live in. I just would not use them as a source.

 

[vela]

What I don't understand is why these tests are needed. Wouldn't the child's every day school work be the best indicator?

For individual teachers, perhaps. But what about when you want to compare the performance of students from different schools?

 

[JorisL]

Okay. I just think it's unfair to quote him as a source because if he does get a fact wrong people can always say "Oh, but he's just a comedian".

Personally I like his show a lot and also Jon Stewart's too & they have very scathing commentary on a lot of the stupidities & incongruities of the world we live in. I just would not use them as a source.

I don't think that's their goal either. He succeeded in starting a discussion on this forum. And that appears to be the goal to me.
It worked at least once so to say, all we can hope for is that this brings back critical thinking.
It's clear from social media (to me at least) that a lot of people just buy everything classical media feeds them.

 

[Intraverno]

This is the essence of the "pro-test" argument. But the reality is that it's impossible to generate statistically significant results in the first place- there are too many uncontrollable variables (e.g. home life) that strongly impact student ability. Further, while there is growing agreement with what minimum content constitutes a 'proper' STEM course, this concordance has not yet been reached for subjects like history, languages, art, etc.

This, and also, as I said, in my school nobody takes it seriously. There are maybe 4 or 5 kids in the whole school who actually their best on the PARCC.

 

[stevendaryl]

What I don't understand is why these tests are needed. Wouldn't the child's every day school work be the best indicator? Many kids have test anxiety and will do worse on tests like this than in normal school work. Of course some kids hate school and don't do well even though they are very bright and capable but a special test isn't going to change that.

I think that one-on-one interaction with a teacher would certainly give as good (or better) indication of a student's competence than a test would. But I don't think that that happens on a regular basis. The problem with every day school work (to me) is this: What is the interpretation of homework that contains mistakes? Was the student just being careless, or does the mistake indicate some gap in the student's knowledge or skills that needs to be addressed? In mathematics and other "hard" sciences, the topics build on each other. If a student's understanding of, say, arithmetic, is faulty, then he is going to have trouble with fractions. If he has trouble with fractions, then he's going to have trouble with algebra, and with trigonometry and with calculus. So what I think happens (in my observation) is that children miss key concepts or skills at an early age, but still manage to do well enough to pass. But then each new mathematical topic puts them farther behind their peers until eventually they give up and decide mathematics is beyond their abilities. My feeling is that if gaps in understanding can be caught and addressed at the earliest moment, then this can be avoided.

I actually don't care about tests, but what I care about is preventing a certain kind of complacency on the part of students and teachers, which is for them to feel that, even though something is not understood, it's good enough, and it's time to move on to something else. I think it's bad for kids to have the gnawing feeling that they don't understand something that they are expected to understand, and that they have to pretend to understand it, because it would be too embarrassing to admit that they don't.

Ultimately, what I want to instill in students is an internal drive to understand things deeply, not to be satisfied with superficial understanding. Because the superficial understanding is just pretend understanding.

 

[mathwonk]

Here is an actual example of the challenge of writing a good test question, taken from an hour exam I was given at Harvard in about 1963. The class was linear algebra and I had neglected to learn the tedious looking and unmotivated Gram Schmidt formula for reducing a spanning set to an orthonormal one. On the test however there was a quesion meant to measure command of this topic: "find a maximal orthonormal set in the space of polynomials of degree at most 2, with respect to the pairing <f,g> = f(0)g(0) + f(1)g(1)." The average student would begin with the standard basis { 1, x, x^2} and perform Gram Schmidt on it, getting some hideous answer. My paper had only a few stray marks and calculations on it for that question, and the professor initially gave me a zero for it.

Afterwards I pointed out to him that prominently displayed among those marks was the simplest possible maximal orthonormal set {x, 1-x}, and he was forced to raise my score to 20 points for that question. I just noticed that in his example, I only needed a couple of functions f,g that vanished respectively at zero or at one, and equaled one at the other point. I also had an intuition that two was a maximal number of orthonormal functions for that pairing. So his question seemed reasonable but failed to measure what he wanted it to in this case. This changed my grade from a D to a B, and for years after that I still was innocent of the general Gram Schmidt process, until in graduate school someone drew a picture showing how it is just a simple projection process. This ability to pass tests that I did not know the material for was actually quite harmful since it allowed me to bump along for years without learning anything before hitting the wall at a certain point and having wasted many years of "schooling". It also hurt me on placement tests when I regularly placed into classes well over my head.

I agree by the way that one on one oral exams are potentially the most accurate way to measure understanding, except however for the crucial fact that they can be very intimidating, and hence the nervousness factor can enter significantly and hinder a student's performance unfairly. I have had impatient professors bark at me when I hesitated at choosing the right words, "well if you don't know just say so!" and I would say well ok, I don't know, when actualy I did know, but was trying to phrase my answer precisely.

 

[mathwonk]

A more common challenge for the professor than writing questions one cannot get right without knowing the material, is writing ones that a student cannot get wrong who does "know" the material. E.g. I gave a calculus class a problem to maximize the area of some figure subject to certain conditions and it came down to multiplying 13 by 65 to get the answer. No calculators were allowed and one B student did not know how to multiply two digit numbers without one, so she added up a column of thirteen 65's. I was scandalized at such basic ignorance and felt guilty at giving her full credit, since in my opinion, contrary to some expressed above, knowing how to do basic arithmetic and utilize positional notation, is much more important than say knowing differential calculus. You really cannot always google every question safely.

E.g. when purchasing a load of soil recently I measured my needs at 95 cubic feet and the salesman told me that would be about 1.5 cubic yards. I objected that since one cubic yard equals 27 cubic feet it should be more like 3.5. He said "no, I typed it into my calculator twice and it still says 1.5", so that was that. This conversation went on a depressingly long time in that vein until he eventually found another calculator on which he knew better how to manage the parentheses function and got the right answer. Out of fairness I might say he had actually taught me what calculation to do, he just didn't know how to multiply. So we made an adequate team eventually.

By the way, in controversies like this one, I have learned that jumping up and down and screaming "I have a PhD in mathematics!" does not help the situation.

 

[atyy]

Well, mainly I am so bad at arithmetic I always use a calculator (yes, even my literature teacher complained to my parents that I have to use my fingers and toes).

Anyway, another interesting example is whether there are cases where all the logical up to the last step is right, but the final answer being wrong can be argued to indicate a gross lack of understanding. I have a friend who got zero marks on a physics problem, because he failed to include an "i" in the final answer, just out of carelessness. All his steps were right up to that point. The lecturer said a zero was justified, because an exponentially decaying or exploding solution is qualitatively different from an oscillating one, and that missing an "i" showed that he had not understood the physics at all. I think the lecturer went overboard on this, but I concede he had a point.

 

[WWGD]

<Snip>

Anyway, another interesting example is whether there are cases where all the logical up to the last step is right, but the final answer being wrong can be argued to indicate a gross lack of understanding. I have a friend who got zero marks on a physics problem, because he failed to include an "i" in the final answer, just out of carelessness. All his steps were right up to that point. The lecturer said a zero was justified, because an exponentially decaying or exploding solution is qualitatively different from an oscillating one, and that missing an "i" showed that he had not understood the physics at all. I think the lecturer went overboard on this, but I concede he had a point.

Unless this is advanced level, it seems unfair to expect a student put things in context with time constrains and nervousness of an exam. Besides, this can be corrected much more easily than structural misunderstandings.

When I taught as an adjunct, for undergraduate classes, I either assigned problems that did not require much thought, to be done in class, or, for problems requiring more thinking or creativity, I gave the assignments to be done at home. Does not seem to be fair at this level , to expect students to perform creatively while under pressure, under time constraint and nervousness.

 

[mathwonk]

atyy, would you say giving a negative answer (with the correct absolute value) to a physics question whose answer must be a positive quantity would justify a zero score?

The whole question of how to assess something or someone correctly is a very hard one in my experience and requires diligent attention. The personal interview method is one that is used by people I respect in some technical business situations. E.g. I know someone with responsibility for recruiting, hiring, and when necessary firing, for a global high tech company. He always does all three of these tasks in person face to face, even if he has to fly 5 or 10 thousand miles to do so. Certainly he never hires anyone based on performance on a standardized written test.

 

[rollingstein]

He always does all three of these tasks in person face to face, even if he has to fly 5 or 10 thousand miles to do so. Certainly he never hires anyone based on performance on a standardized written test.

Which makes a lot of sense. Standardized testing for the masses & for initial screening followed by more expensive, time consuming methods for the really important decisions.

 

[PWiz]

As an HS student, I can't agree more. I can feel the immense pressure of the need to perform well in these standardized tests. It's like everyone around me is emphasizing how much of a passport high scores are to a good college, but I can't help but feel that the focus is less on learning and more on blind analysis of performance under stress. Everyone is not built out of the same wood you know.

 

[atyy]

atyy, would you say giving a negative answer (with the correct absolute value) to a physics question whose answer must be a positive quantity would justify a zero score?

My personal view is that as long as the steps are correct, I would only take off the mark for the final answer in a classroom test situation. Generally I would grade according to the marking scheme that is determined before the test.

Another friend of mine took an economics class and ended up with a complex profit in a test. She left the answer intact and got partial credit. It clearly didn't mean anything about her deep undertstanding of economics, since even a complete idiot knows a profit cannot be complex.

The whole question of how to assess something or someone correctly is a very hard one in my experience and requires diligent attention. The personal interview method is one that is used by people I respect in some technical business situations. E.g. I know someone with responsibility for recruiting, hiring, and when necessary firing, for a global high tech company. He always does all three of these tasks in person face to face, even if he has to fly 5 or 10 thousand miles to do so. Certainly he never hires anyone based on performance on a standardized written test.

I think it is impossible to have a fail-safe algrorithm in real life! Personal interactions and luck are so essential.

But most of the time, I don't know if one is trying to things that require luck in the classroom. Thinking a bit about your example of 13 X 65, I do find it a bit perturbing too. However, what part of arithmetic is really "essential"? To do the calculation by hand, one only needs to memorize 3 X 6 and 3 X 5, or more generally working in base 10, I guess one only needs the multiplication table up 9 X 9. Naively, is there anything deep about 9 X 9 = 81, or would it be ok to know how to set up the calculation by hand, but use a multiplication table?

 

[mathwonk]

I want to repeat my point about one positive aspect to standardized tests, namely they allow anonymous students with no connections or social status, to make an argument that they belong up there with the privileged few. In the 1960's, SAT scores and the consequent merit scholarships they brought, sent hundreds of relatively poor boys from low socio economic families like mine, to schools like Harvard, where we met sons of famous wealthy people, and future national politicians and scions of business. And the test itself is relatively cheap and easy to prepare for, all you need is a $20 prep book with old tests in it to practice on. I.e. anyone can afford the test, anyone can afford the practice materials, and the benefit is a chance to compare yourself favorably with much more privileged students, and possibly get accepted at top schools with financial assistance. I.e. the very definition of a standardized test is one that tests everyone the same, and hence let's you compete against people you have never met and who go to schools you can't afford. This is essentially the only way a high school boy from Tennessee can show he is comparable in ability and potential to a prep school boy from Connecticut. This is a very useful tool for social advancement. But of course you have to prepare or you don't benefit.

 

[stevendaryl]

But most of the time, I don't know if one is trying to things that require luck in the classroom. Thinking a bit about your example of 13 X 65, I do find it a bit perturbing too. However, what part of arithmetic is really "essential"? To do the calculation by hand, one only needs to memorize 3 X 6 and 3 X 5, or more generally working in base 10, I guess one only needs the multiplication table up 9 X 9. Naively, is there anything deep about 9 X 9 = 81, or would it be ok to know how to set up the calculation by hand, but use a multiplication table?

To me, the critical thing about arithmetic is the relationship between addition and multiplication, understanding integer multiplication as repeated addition, and understanding multiplication of a pair of positive reals as the area of a rectangle. The specific times facts are not as important as understanding the meaning of place notation for decimals.

 

[Redbelly98]

Ha, I took the SAT last week, and will take the SAT Math 2 subject test and SAT physics subject test less than a few months from now. What annoys me the most is that the SAT claims to be an aptitude test, yet you can significantly improve your score by preparing for it.

Actually, they do not make that claim about the SAT anymore. SAT no longer stands for "scholastic aptitude test", it is simply the name of the test and does not stand for anything.

 

[HomogenousCow]

I don't know if any of you remember what it's like being 17 and in school, but the majority of people would not study AT ALL if not from exam pressure. The sad truth is that you need a short term incentive for teenagers to learn, a long term incentive such as a "good job" is simply too far off to significantly motivate the majority of people.

 

[stevendaryl]

I don't know if any of you remember what it's like being 17 and in school, but the majority of people would not study AT ALL if not from exam pressure. The sad truth is that you need a short term incentive for teenagers to learn, a long term incentive such as a "good job" is simply too far off to significantly motivate the majority of people.

I think that's absolutely right. If you aren't challenged to do something (such as pass a test) with knowledge, it tends to go in one ear and out the other. I don't remember the reference, but there was a study that showed that frequent quizes on what someone has learned tends to improve his ability to recall what he learned.

 

[HomogenousCow]

The simple truth is that most high school students do not care about the intrinsic value of whatever they are being taught (assuming there is any, I'm looking at you Samuel Beckett). There seems to be some grand fantasy that students are inquisitive angels, oppressed by "The Man" and his weapon of choice-the SAT.