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Re: Algebra 2/Trig Regents
Posted:
Jun 22, 2011 5:47 AM
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The authority should rest in the mathematics, not a school principal. NYSED
has made a fairly serious mathematical error - that is the level at which it
should be fixed.
A quick review of a handful of calculus and analysis texts shows the
notation is commonly used as the teachers on this list assert, not as the
authors of the examination intended.
If their mathematical expertise is insufficient (this seems clearly to be
the case), they should call in those with greater knowledge to assist.
Jonathan Halabi
HS of American Studies
the Bronx
On Tue, Jun 21, 2011 at 11:31 PM, <elizwaite@aol.com> wrote:
> Doesn't the school principal have the right to allow teachers to use their
> best judgement? In other words, if the teachers explain to the principal
> that question 32 is flawed and that the teachers would like to award full
> credit for various answers based on that, can't the principal give his/her
> permission?
> I'm pretty sure they can
> Liz Waite
>
>
>
> -----Original Message-----
> From: Nick B <nbianculli@gmail.com>
> To: nyshsmath <nyshsmath@mathforum.org>
> Sent: Tue, Jun 21, 2011 10:18 pm
> Subject: Re: Algebra 2/Trig Regents
>
> She's correct in saying that the inverse relation of a function may not be a
> function itself. Every function has a corresponding inverse relation; however,
> we usually say a function is invertible iff its inverse relation is a function.
> However, the question specifically asked to find f^-1(x), which implies that the
> inverse relation is a function. After all, the letter f stands for function and
> any good book will define the notation f^-1 to stand for the inverse function of
> f. So for the question to ask for an inverse function of f(x) = x^2 - 6 requires
> a domain restriction. If the question asked to find the inverse, then I could
> see her point but since the question specifically used the notation f^-1(x), I
> completely agree with you.
>
> In higher mathematics, there are such objects called multivalued functions, but
> we certainly don't study these concepts in any detail in high school.
>
> The following Wikipedia article does the topic justice, and introduces
> multi-valued inverses:
> http://en.wikipedia.org/wiki/Inverse_function
>
> It's the same concept in question 19. y = cos^-1(x) denotes the inverse cosine
> FUNCTION, which is the inverse of y = cos x restricted to a domain of [0, pi].
>
> What's sad is that we're the concerned, diligent math teachers who want to get
> it right and you bring a legitimate concern to light and are told that you won't
> "win the argument". At the minimum the question is ambiguous and poorly posed,
> regardless of whether SED thinks you didn't win the argument. What's even sadder
> is that this test is supposedly reviewed by trained eyes. How are
> mathematically educated people not picking up on these glaring errors and
> ambiguities? I saw the ambiguities within seconds of reading the questions (as
> I'm sure most all of us did) and somehow those questions ended up on the test.
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