CHAPTER III-3
ON TEACHING RESAMPLING AS A BASIC TOOL FOR EVERYDAY WORK
THE PRO'S AND CON'S OF RESAMPLING
1) Does Resampling Produce Correct Estimates?
If one does not make enough experimental trials with the
resampling method, of course, the answer arrived at may not be
sufficiently exact. For example, only ten experimental bridge
hands might well produce far too high or too low an estimate of
the probability of five or more spades. But a reasonably large
number of experimental bridge hands should arrive at an answer
which is close enough for any purpose. There are also some
statistical situations in which resampling yields poorer
estimates about the population than does the conventional
parametric method -- usually "bootstrap" confidence-interval
estimates made from small samples. But on the whole, resampling
methods yield "unbiased" estimates, and not less often than do
conventional methods. Perhaps most important, the user is more
likely to arrive at sound answers with resampling because s/he
can understand what s/he is doing, instead of grabbing the wrong
formula in error.
2. Do Students Learn to Reach Sound Answers?
In the 1970s, Kenneth Travers, who was responsible for
secondary mathematics at the College of Education at the
University of Illinois, and Simon organized systematic controlled
experimental tests of the method. Carolyn Shevokas's thesis
studied junior college students who had little aptitude for
mathematics. She taught the resampling approach to two groups of
students (one with and one without computer), and taught the
conventional approach to a "control" group. She then tested the
groups on problems that could be done either analytically or by
resampling. Students taught with the resampling method were able
to solve more than twice as many problems correctly as students
who were taught the conventional approach.
David Atkinson taught the resampling approach and the
conventional approach to matched classes in general mathematics
at a small college. The students who learned the resampling
method did better on the final exam with questions about general
statistical understanding. They also did much better solving
actual problems, producing 73 percent more correct answers than
the conventionally-taught control group.
These experiments are strong evidence that students who
learn the resampling method are able to solve problems better
than are conventionally taught students.
3) Can Resampling Be Learned Rapidly?
Students as young as junior high school, taught by a variety
of instructors, and in languages other than English, have in the
matter of six short hours learned how to handle problems that
students taught conventionally do not learn until advanced
university courses. In Simon's first university class, only a
small fraction of total class time -- perhaps an eighth -- was
devoted to the resampling method as compared to seven-eighths
spent on the conventional method. Yet, the students learned to
solve problems more correctly, and chose to solve more problems,
with the resampling method than with the conventional method.
This suggests that resampling is learned much faster than the
conventional method.
In the Shevokas and Atkinson experiments the same amount of
time was devoted to both methods, but the resampling method
achieved better results. In those experiments, learning with the
resampling method was at least as fast as the conventional
method, and probably considerably faster.
4. Is the Resampling Method Interesting and Enjoyable?
Shevokas asked her groups of students for their opinions and
attitudes about the section of the course devoted to statistics
and probability. The attitudes of the students who learned the
resampling method were far more positive -- they found the
subject much more interesting and enjoyable -- than did the
attitudes of the students taught with the standard method. And
the attitudes of the resampling students toward mathematics in
general improved during the weeks of instruction, whereas the
attitudes of the students taught conventionally changed for the
worse.
Shevokas summed up the students' reactions as follows:
"Students in the experimental (resampling) classes were much more
enthusiastic during class hours than those in the control group,
they responded more, made more suggestions, and seemed to be much
more involved".
Gideon Keren taught the resampling approach for just six
hours to 14- and 15-year old high school students in Jerusalem.
The students knew that they would not be tested on this material.
Yet Keren reported that the students were very much interested.
Between the second and third classes, two students asked to join
the group even though it was their free period! And as the
instructor, Keren enjoyed teaching this material because the
students were enjoying themselves.
Atkinson's resampling students had "more favorable opinions,
and more favorable changes in opinions" about mathematics
generally than the conventionally-taught students, according to
an attitude questionnaire. And with respect to the study of
statistics in particular, the resampling students had much more
positive attitudes than did the conventionally-taught students.
The experiments comparing the resampling method against
conventional methods show that students enjoy learning statistics
and probability this way. And they don't show the usual panic
about this subject. This contrasts sharply with the less
positive reactions of students learning by conventional methods,
even when the same teachers teach both methods in the experiment.
page # teachbk III-3day May 7, 1996