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Re: Harvard Calc and "feel good"
Posted:
Jun 9, 1997 1:48 AM


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 PreCalc. 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 PreCalcand 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 databased support for such an apparent "feelgood" 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 thisgive 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 thisgive 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 >studentsthat 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 PreCalc." 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 feelgood 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 thisgive 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



