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RE: Alg2Trig exam
Posted:
Jun 21, 2011 7:44 PM
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The scoring guide for #16 gives both 1 and 3 as correct choices. I can't
believe this was deliberate so I suspect this was a poorly worded question
and the key was fixed after the tests were all printed and the question
couldn't be changed.
Meg
From: owner-nyshsmath@mathforum.org [mailto:owner-nyshsmath@mathforum.org]
On Behalf Of Evan Romer
Sent: Tuesday, June 21, 2011 7:05 PM
To: nyshsmath@mathforum.org
Subject: Re: Alg2Trig exam
I think the SED scoring team should expect a bunch of calls tomorrow. I
think the scoring guide needs clarification or changes for several
questions.
On Tue, Jun 21, 2011 at 5:34 PM, Meg Clemens <mclemens@twcny.rr.com> wrote:
#16) 2 correct answers to a question! ...
I don't have the scoring guide, but if it doesn't accept both answers it's
simply wrong: both #1 and #3 are equivalent and SED needs to issue a scoring
update. (It didn't ask for simplest form: it said "equivalent.") And even if
SED marks both correct, that was needlessly confusing to students, and
upsetting for some.
#19) I know #3 is the least wrong but I think y = cos^-1 (x) implies a
function and graph #3 does not have a restricted range.
Either the range is restricted to make it a function, so the range is
[0,pi], or the range is not restricted and the range is (-inf,inf). There is
no interpretation that makes any of the given choices correct. On the other
hand, I don't see that this will lead students astray: even if they know
it's wrong, #3 is clearly "least wrong."
#30) I'd like to give full credit to an equation with either y = x^2 - 6x -
27 or 0 = x^2 - 6x - 27.
>From NYS Glossary for A2T:
"root of an equation (A) (A2T) A solution to an equation of the form f(x)
= 0.
Example: A root of the equation y = 6x - 18 is 3 because when 3 is
substituted in for x, the value of y = 0.
Example: The roots of are and. The equation is true if we substitute
either or into the equation."
I'm a little unclear myself on "root of an equation" vs. "zero of a
function" vs. "root of a function." etc. (Steve Goldman's can of worms in a
separate message.) But that glossary entry is unambiguous: both of Meg's
answers should be accepted.
#32) Doesn't using f^-1(x) imply that answer should be a function? I think
stating just one branch of the inverse of the parabola should be accepted.
Really, there should be a stated domain restriction so it is clear which
branch to choose.
I agree. If the question said "find the inverse," then the inverse could be
a relation, not a function, and the only correct answer would be both
branches: plus/minus sqrt(x+6). But f^-1(x) implies an inverse *function*,
so the only actually correct answer is "no inverse function." But that's not
what the question intended, so SED should accept both +sqrt and +/-sqrt, and
they should accept "no inverse function." (And they should accept -sqrt from
the student who is mathematically confident enough and deliberately
contrarian enough to give that answer.)
On #31, I think I agree with Cindy Kohl: what work is needed?? But I don't
teach A2T: for a plug-it-in-to-the-calcualtor question, is the student
expected to say what she did on her calculator?
And I'll add one more: I'm not very happy about #27. Just looking at it, it
looks like either a log function or a sqrt function (0.5 power), so either a
log or power regression seems reasonable. Sqrt would go through the origin
and log would not, but can you tell if that scatter plot goes through the
origin or not? I can't.
If I take the time to type all the data into my calculator and do the
regressions, log is clearly better. But was the student expected to do that?
Finally agree with Jonathan Halabi:
> I have no confidence in the ability of NYSED to produce a good examination
in
> mathematics.
And I think our A2T teachers will agree with Lin Chen:
> Did I miss a memo about a new curriculum named
> "Algebra 1.5 with limited Trig" between Algebra I
> and Algebra II?
Evan Romer
Susquehanna Valley HS
Conklin Ny
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