On Mon, 9 Oct 2000, I wrote:
> ----- Forwarded message from Michael Granaas -----
>
> I honestly believe that there is something to be learned from
> memorizing several of the basic formulas that are involved in defining
> statistics. I, less elegantly, tell my students that it is important
> to have this basic understanding so that it can 1) be utilized when we
> have the machines start doing the computations for us and 2)be drawn
> on for understanding when the mathematics is no longer so simple.
>
> ----- End of forwarded message from Michael Granaas -----
>
To which Bob Haden replied:
> I doubt your students will gain ANY understanding from memorizing
> formulae. Once they have the understanding, then formulae MIGHT
> provide a summary or reminder -- but only for students who are VERY
> fluent at READING mathematics -- as opposed to mindlessly manipulating
> formulae. I do not see any such students in the undergraduate
> introductory course that I often teach. I noted that Karl presented
> all the understandings he sought verbally on the list. Why not do the
> same in class?
I do explain some of my reasoning in class, but usually I find it about as
useful as explaining the long-term benefits of doing a share of the
household chores to my 10 year old. All she understands is that her
playtime is being shortened. Any arguments that I make will not be
understood or appreciated for several years. So I don't explain.
I have always used a mix of problems, short answer, and multiple choice
items on my exams. There was a time when I gave the exam in two parts so
that notes, books, whatever, could be used on the problem portion of the
exam. Like others I reasoned that in the real world nobody actually
memorizes formulas, they look them up or trust the computer to carry out
the computations correctly.
The split exam format became a problem as enrollments in my classes
climbed so I reluctantly abandoned it and went to a completely closed book
exam format. Much to my surprise student scores improved on both
computational and conceptual items. (I fully expected scores on
computation items to drop noticeably with the loss of book and notes.)
This forced me to reconsider my original stance that formulas should just
be looked up.
I decided that the use of books or notes for formulas encourages a form of
laziness that interferes with learning. The student who is paging madly
through their text looking for the formula they need, or who is staring
blankly at their card full of formulas, has not put the intellectual
effort into learning what is going on. If you truly know what it is that
variance describes how can you not pick the definitional formula for it
off of a page? And if you understand the formula you have a much easier
time selecting or generating an answer with words like "dispersion"
correctly used.
A few folks in this discussion have argued that many students simply view
formulas as no more than procedural directions otherwise void of meaning.
I would agree. I see "cheat sheets" as continuing the misperception and
exacerbating the problem. Sure, it would be a lot easier for me to let
students use formulas soley as recipies to be followed blindly, but I
spend a good deal of time explaining the message of the formula trying to
improve their understanding a bit more.
I addition by using definitional formulas it is obvious that the mean
squared error is just a general form of the variance, or that the variance
is just a type of mean. The student who does not remember the formula for
variance, however, can only see the mean squared error as a whole new
thing to be learned. These links between related concepts can serve to
strengthen learning of both concepts if students can see those links. But
they can only see them if they have a certain amount of material,
including formulas, committed to memory.
I will also mention that I use exclusively definitional formulas in my
classes. I won't even use a text that has computational formulas in it.
I am not interested in computational accuracy so much as I am conceptual
understanding. Clearly computational formulas are designed to simplify
computation, not facilitate understanding. If your text uses
computational formulas then I agree that there is no point in having folks
memorize anything...let them look it up.
Michael
*******************************************************************
Michael M. Granaas
Associate Professor [EMAIL PROTECTED]
Department of Psychology
University of South Dakota Phone: (605) 677-5295
Vermillion, SD 57069 FAX: (605) 677-6604
*******************************************************************
All views expressed are those of the author and do not necessarily
reflect those of the University of South Dakota, or the South
Dakota Board of Regents.
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