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