I think that Bob Hayden is on to something essential here ("I noted that
Karl presented all the understandings he sought verbally on the list. Why
not do the same in class?"). I think of the "definitional formulae" just as
a convenient shorthand for the verbal definition of a construct. But it may
be the case that most of our students assume that something that looks like
a formula is just for use with mindless computations. They may have learned
this in their first 12 years of schooling, where formulas may indeed be
presented as nothing more than mindless recipes for getting some quantity
not really well understood. How can we break our students of that bad
habit? I do frequently verbalize the 'formula' after writing it on the
board -- for variance, saying something like "look at this, we just take the
sum of the squared deviations of scores from their mean, which measures how
much the scores differ from one another, and then divide that sum by N, to
get a measure of how much scores differ from one another, on average." The
shorthand is really convenient, I don't know how I would get along without
it.
I have always thought that success in stats courses was much more a
function of a student's verbal aptitude and ability to think analytically,
rather than mathematical aptitude. Has anybody actually tested this
hypothesis?
----- 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 -----
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?
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
