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Re: Harvard Calc and "feel good"
Posted:
Jun 9, 1997 1:48 AM
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Dear Phil, June 10, 1997
Our fractured conversation needs a little review for the benefit of those
who will have lost the thread and perhaps some of the intervening
conversation. On 5/22/94, Philip Larson posted a message that included the
following two paragraphs:
"I also teach a fairly traditional Pre-Calc. And right now, my 8th grade
Algebra 1 class students have as good a sense of the nature of linear,
quadratic, rational, and exponential functions than do my juniors in
Pre-Calc--and these latter students are no dummies.
As far as I'm concerned, feeling good is not the point in reform calculus
or reform algebra or reform anything else. Understanding is. And just
because a student can manipulate symbols (or even calculator buttons)
means nothing."
I challenged that statement on 5/23/97 with:
"I'm (almost) from Missouri. Can you share with the group your data-based
support for such an apparent "feel-good" conclusion? For example, share
with us the exam that you gave to both classes that covered "the nature of
linear, quadratic, rational, and exponential functions" and their
comparative results?"
To which Phil responded, and I in turn,
">Maybe I'll do this--give the Advanced Math exam to the Algebra 1
>students, and give the Algebra 1 exam to the Advanced Math students.
Great. I'll look forward to your posting of the exams and of their results.
>>(WB)Entitle it something like "Crow for a California Curmudgeon."
>(PL)Or "Phooey on Pheel Good"?!
Sounds good, as the data appear to indicate.
<snip>
>How does one quantify understanding?!
We'll soon have a good start at answering that question: Remember your
words, "I'll do this--give the Advanced Math exam to the Algebra 1
students, and give the Algebra 1 exam to the Advanced Math students."
<snip>
I know there's always a chance of a security breach but the general
enlightenment of all could make it worth the risk to share in advance, with
some of us at least, the Advanced Math exam that you are giving to your
Algebra 1 students and the Algebra 1 exam that you are giving to the
Advanced Math students. If any of us have comments as to questions that we
think would help indicate a good a sense of the nature of linear,
quadratic, rational, and exponential functions we could make your test
preparation even easier."
****************
With that background, the following should be more coherent (> is Phil
Larson 6/7/97):
>I only gave the Algebra 1 exam to the Advanced Math
>students--that is, a reform exam to both.
I can only impugn, "why am I not surprised?" Recall your own words, "my
8th grade Algebra 1 class students have as good a sense of the nature of
linear, quadratic, rational, and exponential functions than do my juniors
in Pre-Calc." I never doubted that you might be able to concoct a "feel
good Algebra 1" exam that was so devoid of traditional Algebra 1 content
that your Advanced Math students would not know how in the world to proceed
(although even that's a stretch, please post the exam and the results from
both classes). What I was really trying to imply is that you could not
create even a feel-good exam - let alone one that would please the
succeeding AP Calculus instructor - on "the nature of linear, quadratic,
rational, and exponential functions" that would anything but paralyze most
of your eighth grade Algebra 1 students.
>>>(PL)How does one quantify understanding?!
>>(WB)We'll soon have a good start at answering that question:
>>Remember, "I'll do this--give the Advanced Math exam
>>to the Algebra 1 students, and give the Algebra 1 exam
>>to the Advanced Math students."
>I was asking a philosophical question. Giving a test under
>any conditions won't settle this issue.
Then why did you avoid giving the Advance Math test to your Algebra 1
class? I was hoping that you might see some connection between the abysmal
performance that the students would surely have exhibited and the lack of a
solid understanding of the nature of linear, quadratic, rational, and
exponential functions and perhaps extrapolate all the way to an attempt to
quantify your unquantifiable, "understanding." Terrible performance may
not completely demonstrate lack of understanding nor superb performance the
opposite but it comes closer than unsupported statements about how well
your eighth grade Algebra 1 students understand the nature of these
functions.
>Well, I just pulled out the Algebra 1 exam. I haven't looked at the
>responses yet.
I'm looking forward to seeing the results of both classes and to a copy of
the exam itself. It is unfortunate that we don't have the information from
the other half of the experiment but the term is now over so it is too late
to rectify that problem. Still there may be some insight into quantifying
"understanding" even with the wrong half of the experiment. Thank you in
advance,
Wayne.
>Phil Larson
>Upper Bucks Christian School
Wayne Bishop
Math & Comp Sci
Cal State LA
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