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OK. This seems very confused. Maybe it's just a language
difficulty, so let's start by agreeing on the mathematics.
(^{2) means "squared", \mu means the greek letter, n(\mu,\sigma^2)
stands for a normal distribution having mean \mu and standard deviation
\sigma. For more details see, e.g., Hogg and Craig, <An Introduction to
Mathematical Statistics>, ("H&G").
There is a theorem that a set of samples of size N from a normal
distribution having mean \mu and standard deviation \sigm will have means
that are distributed according to n(\mu,\sigma^{2}/N). "Standard
deviation" has two different meanings here. One, \sigma, characterizes
the original distribution from which the samples are taken. The other,
square root of \sigma^{2}/N, characterizes the distribution of means of
the samples. John clearly intends the first meaning.
But therein lies a difficulty. For John's usage to be correct we
must treat each student as a "sample" from a distribution that is:
1. Normal
2. The same for each student.
This would be tough to show.
A better approach is to view the two samples (before and after)
and ask for the probability that they come from the same (unknown)
distribution. Also relevant is the nature of the distribution of each
sample.
On Sun, 23 Dec 2001, John Clement wrote:
The effect is essentially an effect size of 1.0.Please translate that sentence. "Size" in what units?
Essentially the mean ofdeviation of
the curve was moved over by and amount equal to the standard
the original curve. For more information I would suggestreading the cited
paper.That wouldn't help me understand what <you> are saying.
When I looked at the actual curve I noticed that the final curveAre you saying that the second distribution was bimodal?
seemed to show that most concrete students were moved to higher thinking
levels.
An educational effect this large is considered to be VERY large.Considered by whom? On what basis?
The particular evaluation is not testing knowledge but thethinking ability
of the students. I have data spanning several years for students at ourindividual students
school, and this evaluation seldom shows a decrease for
and never shows a decrease for the average over a group. The questionsshowed any
involving proportional thinking do show some backsliding, but as many
students improve as backslide. I have only seen 1 student who
serious negative gain, and she was a foreign student with a language
problem. I have also seen many students show dramatic gain.
Yes, but do <you> have data taken after a time lapse?
One standard deviation change does not mean a 30% chance thatit was due to
random fluctuations. The particular study was over about 600students so
the error in the mean is quite small ( SD / sqrt(600) ).Depends on which SD you're talking about. See above.
understanding can be
I would like to point out that improvement in content
extremely stable even years later when the correct teachingtechniques are
used. FCI results have been found to be very stable after aninteractive
engagement style course up to 3 years later. See: G. Francis,J. Adams, E.
Noonan (1998). Do They Stay Fixed?, Physics Teacher, 36, 488-490.If this is the Minnesota group, I believe that I critiqued that
paper in a previous posting (which I apparently did not preserve).
However,memorization methods,
I will also agree that when students rely on purely
content material decays within about 2 weeks. Priscilla Lawspointed out at
a workshop that they observe rising gains for about 2 weeks onevaluations
after the concepts were presented using the type of labs that they havea new topic
found to be effective. This is consistent with Shayer&Adey's theory and
observations ("Really Raising Standards"). Incidentally my own testing
shows that after a 2 week Christmas break and several weeks of
that FMCE results show only a small drop. I have also tried tellingevaluation, and
students the answers to a question or 2 the day before an
many still miss it. The non Newtonian distracters are often too hard toIsn't that what they're for?
overcome with a little prepping.
I gave them the answers as part of a testexactly the answer
review, but did not tell them that the answer I gave was
to a question on the test.Thereby defeating the principle the you are testing for
grasp of concepts?
statistical measures
John M. Clement
Houston, TX
1. How did 1 SD get to be "very large"? And 1 SD of what? Usually in
educational circles people seem to quote the change in the mean of a
group. 1 SD means about a 30% chance that the change was a random
fluctuation. The physicists I know usually insist on 4 SD as the
threshold for evidence of a new effect. Also, these
semester, break.can be utterly misleading if one does not know the distributions.
2. Much more interesting than the improvement at the end of a course
would be the results of testing after a summer, or even a
very rapidly.My experience is that the apparent "improvements" dissipate
_________________________________________snip___________________________
Regards,
Jack
On Sun, 23 Dec 2001, John Clement wrote (in part):
their thinking.concrete level, it
Despite the fact that many students enter testing at the
is possible to structure the course so that they improve
AzState pushed upThis is now being routinely done in the intro. biology courseat AzState.
Anton Lawson has been a prolific publisher of papers on thesubject, and has
been pushing this idea for years. One of the latest paperspublished by one
of Lawson's collaborators mentioned that the course at
a very largestudent thinking by about 1 STD, which is considered to be
Undergraduateincrease. The article is Wycoff "Changing the culture of
the incomingScience Teaching", Jour of Coll. Sci. Teach. XXX #5 pp306-312.
I can tell you the statistics for my course. About 30% of
still at thatstudents are at the concrete level, but less than 15% are
formal thinkerslevel when they leave. Likewise only about 15% test as
One mightcoming in, and about 30% test as formal thinkers going out.
poets courses orpresume that courses which have a large number of physics,engineering, or
pre-med students would have a high proportion of formalthinkers at major
universities. I would guess 40-50% or more. While atcommunity colleges
the number would be more like 20%, and for physics for
will killcourses with a large number of elementary ed majors the numbermay be below
10%. This is purely conjecture because to my knowledge thissort of survey
has not been systematically carried out. About 30% of thestudents entering
the AzState general studies bio course tested at the formallevel, but the
vast majority were at that level at the end of the course (if Iread their
graph correctly in above mentioned paper). If we can pushthinking levels
up, and as a result have more success, shouldn't we do this?__________________________________________________________________
__________
--
"But as much as I love and respect you, I will beat you and I
and me, fish.you, because that is what I must do. Tonight it is only you
veritable potpourriIt is your strength against my intelligence. It is a
of metaphor, every nuance of which is fraught with meaning."
Greg Nagan from "The Old Man and the Sea" in
<The 5-MINUTE ILIAD and Other Classics>
--
"But as much as I love and respect you, I will beat you and I will kill
you, because that is what I must do. Tonight it is only you and me, fish.
It is your strength against my intelligence. It is a veritable potpourri
of metaphor, every nuance of which is fraught with meaning."
Greg Nagan from "The Old Man and the Sea" in
<The 5-MINUTE ILIAD and Other Classics>