Re: Test writing

[Brian Whatcott <inet@INTELLISYS.NET>]

> At 11:16 PM -0500 4/26/02, Brian Whatcott wrote:
> >
> >Given a moderate tract of novel information from you, one asks a
> >student to teach it back to you and the remaining students, and
> >encourages critique, and expects the fullest participation from the
> >  assembled body, as each succeeding tract is successively presented.
> >
> >You can be quite certain the student speaker's level of recall will
> >comfortably exceed any presentation you might dramatize,
> >  though you pop balloons, swallow liquid nitrogen and
> >dazzle with witty repartee.

At 08:59 PM 4/27/02, Tucker Hiatt <hiattu00@USFCA.EDU> responded:

> I do believe you're right, Brian.  But witty repartee takes seconds
> (that's all the wit I I have!), and students teaching students takes
> hours.
>
> Could it be that all the thoughtful talk about different approaches
> to teaching ("physics modeling," "active physics," the
> "students-teaching-students" approach that you describe, etc.) all
> succumb to the rule of breadth vs. depth?  Let me even try to make it
> quantitative ...
>
> Let's suppose that students acquires a certain (non-negligible!)
> "volume" of understanding during a year-long physics course.
> Perhaps, for ANY sensible teaching method, the volume of the average
> student's ultimate understanding is given by
>
>   V = kdA
>
> where:
>
> k = coefficient of teacher enthusiasm (dimensionless  ... and
> priceless for high values)
> d = average depth of topics taught (proportional to time spent per topic)
> A = breadth of topics taught (proportional to number of chapters "covered")
>
> Any thoughtful, new approach to teaching may inspire higher values of
> "k", just because of its novelty.  But perhaps it doesn't
> significantly affect the product dA.  And, after all, perhaps k is
> inversely proportional to time!
>
> - Tucker (tryin' to keep k high)
> --
> ***********************************
> Tucker Hiatt, Director
> Wonderfest
> P.O. Box 887
> (39 Fernhill Avenue)
> Ross, CA  94957
> hiattu00@usfca.edu
> 415-577-1126 (voice)
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> http://www.wonderfest.org
>
> Truth is a great flirt.  - Franz Liszt
> ***********************************

I taste the bitter fruit of Tucker's experience: I know it cannot be
laughed away.
I agree that an inspired teacher can make chalk and talk an act of divine
academic inspiration.
Then, there are the rest of us. We in general, will not grab the student body
by the intellectual throat, so that the new information is inspired
willy-nilly.

But a student, relaying an information tract, is investing considerably more
than an attentive listener and reaps a greater reward.
 There is a question about the remaining student auditors, I agree.
 They might be said to get even worse fare than we, the unwashed many,
 can offer even on our bad days. But if they have a mechanism to
actively object, so they are engaged in the offering, I believe it works,
even where the inspired teacher is on his long sleep.

And the breadth depth product may well be maintained.
Let me suppose that the student reteacher method is twice as
expensive in time - at least - as chalk and talk.   I want to rationalize
that chalk & talk provides 25% retention, and reteaching provides
75% retention. I'll count retention % as depth. I'll count breadth as
diminished from 100% to 50% I'll count k as a teacher constant.
Then the chalk and talk method gives k.25%.100% and
the student reteaching method gives  k.75%.50%
I plucked the numbers from the air. They are plausible in my
experience - and they are testable. And the strangest thing of all:
 when I have worked this way, I got the reputation of knowing the
material superbly - while the people who were doing the teaching
 and the critiques were in fact the students.
A confidence trick like this, is not to be sneazed at!


Brian Whatcott
  Altus OK                      Eureka!