Bob LeChevalier wrote:
>> "John Knight" <johnknight at usa.com> wrote:
> >Believe me, Parse, you don't need algebra or calculus to calculate the
> >statistical average for American girls in TIMSS math. Even adjusting for
> >guesses doesn't require anything but some very basic probability theory.
> >
> >It's as simple as this:
> >
> >If you're asked a question which has four multiple choice answers, and you
> >haven't got a clue what the answer is, what is the probability of getting a
> >correct answer? Since you have once chance in four of getting the right
> >answer, your probability is 0.25. If you guess on two questions, your
> >probability is .5, and three it's .75, and four, it's 1.0.
> >
> >In other words, over the long run, or over millions of test takers, guessing
> >on such a question will yield 25% correct answers, or conversely, every
> >fourth answer will be correct.
>> This makes the assumption that those who know nothing guess randomly. IN
> reality, we don't know that people guess randomly when faced with a test
> question they do not understand. Indeed, we know that they do not.
>> But the assumption becomes totally meaningless if in fact they know
> SOMETHING. If 100% of them know something, but not enough to solve the
> problem, then it is quite plausible that 100% of them will get the answer
> wrong. Thus someone knowing Newtonian physics perfectly will get the wrong
> answer on a question that uses special relativity theory. A good test
> designer will know that the Newtonian approximation is a likely error, and
> will include that answer among the incorrect alternatives.
Then the article makes the shockingly stupid conclusion that NONE of the
girls who got the answer right understood the problem!
>> >No algebra. No calculus. A bit of probability theory, and you already know
> >that 25% of all students will get the correct answer if they only *guess* on
> >a four part multiple choice question.
>> But you have no evidence that any kid "guessed" on any problem.
>> >Now here's the hard part:
> >
> >Question H04 on TIMSS had four multiple choice answers, so you would think
> >that no country or age group or race or sex would answer less than 25% of
> >them correct, right?
>> Wrong. I would think that if the question were difficult and well designed,
> that this would be quite possible.
>> >How do you think that's possible?
> >
> >You can probably figure this out with no knowledge of algebra or calculus,
> >and you already know all the probability theory that might be needed, so
> >what is your explanation?
>> I've given an explanation, and mine explains how on question D12, both boys
> and girls in the US scored less than 17% and South Africans scored only 6.4%
> correct.
Isn't it odd that someone who is harping on math ability doesn't seem to
realize that 17 and 6 are both lower than 25? :)
J
You can look at the breakdown of the answers and see that the kids
> did NOT guess randomly; they intentionally selected particular answers, which
> were the wrong ones.
>> lojbab
