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Harmony

Some tasks have a natural positive harmony; I find that's the case with training where an enthusiastic tutor, trainees who are attending because they want to learn, a good piece of software as the subject for the course, and a quiet and well thought out learning environment all contribute to a positive and enjoyable experience for everyone ... with any little glitches rapidly being corrected by the natural balance I'm talking about.

With the right approach, a sales deal can work with the same harmony. A product offered at a sensible price by a supplier that knows his product, and to a prospective customer who requires a product such as the one that's on offer. An ability for both seller and customer to listen to the customer's needs and the product on offer in detail, and to marry the two - perhaps with a little bit of flexibility and tailoring all around - to produce the right result for everyone.

Other tasks, alas, don't have that same natural harmony. At times, it's very hard for potential trainees to know whether they should book on beginner or intermediate, or intermediate or advanced courses ... and about 4 years ago we came up with a "quiz" tools where people could test our their knowledge online to get a flavour for their level. Alas, experience showed that the natural harmony wasn't there. People failed to celebrate getting 12 out of 15 questions right and rather grouched at getting 3 out of 15 wrong and, looking for "why" sometimes felt that these questions were poorly worded, off the topics that were relevant to them, too difficult, or just bad luck. I'm not sure that really was the case; I reviewed every question that was queried (and in some cases changed them), but I felt that the system as it was set up had, alas, a natural negative harmony.

The tragedy is that the quiz system, taken as a guideline is a very useful tool, and in the last few weeks I've revived it. Partly as an example of good CGI scripting using the 6 step and 4 layer models. And partly so that I can throw up a few questions at random in front of a class I've just met to help me help them get the best from their course. In the last few days, it's already proved its worth in both those areas.

So - how can I add natural harmony? I don't want to "dumb down" the tests like the school education system in the UK has been accused of doing. That would make the tests pointless. And I don't want to discourage reports about individual questions which could be clarified - feedback is vital. Tricky one, but I'm going to take three steps.

Firstly - a note on scoring. We set 15 questions, all multiple choice with on average 4 possible answers. If you get JUST TWO THIRDS of the questions right, you're showing substantial subject knowledge - the chance of getting that high a score by guessing is statistically insignificant. Please consider 10 out of 15 a good score if you're a user of the language in question; only folks like myself who have to know ALL the facets of a language to teach it can be expected to get a score of 14 or 15 as a matter of routine.

Secondly - I'm publishing a table of those statistics ... if you tried to answer every question with a random guess:
Chance of 0 out of 15 wrong is 0.00%
Chance of 1 out of 15 wrong is 0.00%
Chance of 2 out of 15 wrong is 0.00%
Chance of 3 out of 15 wrong is 0.00%
Chance of 4 out of 15 wrong is 0.01%
Chance of 5 out of 15 wrong is 0.07%
Chance of 6 out of 15 wrong is 0.34%
Chance of 7 out of 15 wrong is 1.31%
Chance of 8 out of 15 wrong is 3.93%
Chance of 9 out of 15 wrong is 9.17%
Chance of 10 out of 15 wrong is 16.51%
Chance of 11 out of 15 wrong is 22.52%
Chance of 12 out of 15 wrong is 22.52%
Chance of 13 out of 15 wrong is 15.59%
Chance of 14 out of 15 wrong is 6.68%
Chance of 15 out of 15 wrong is 1.34%

Here's the program:


$nquestions = 15;
$noptions = 4;

@pascal = (1,1);
foreach $row (1..$nquestions+1) {
$pnew[0] = 1;
for ($k=1;$k<$row;$k++) {
$pnew[$k] = $pascal[$k-1]+$pascal[$k];
}
@pascal = @pnew;
}

for ($wrong=0; $wrong<=$nquestions; $wrong++) {
$chance[$wrong] = ((1/$noptions)**($nquestions-$wrong) *
(($noptions-1)/$noptions)**($wrong))
* $pascal[$wrong] ;
printf "Chance of $wrong out of $nquestions wrong is %.2f%%\n",
$chance[$wrong]*100;
$cr += $chance[$wrong];
}
print $cr*100," total\n";


Thirdly, to remind you that this a bit of fun and gentle guidance - it doesn't pretend to be anything more and we can't provide a detailed evaluation from such a short quiz. Having said that, go and enjoy. You can reach the Quiz front page from here
(written 2005-03-31, updated 2006-06-05)

 
Associated topics are indexed as below, or enter http://melksh.am/nnnn for individual articles
P774 - Perl - Good CGI scripting.
  [4391] Refactoring Perl applications to give them a rosy future - (2015-01-11)
  [4320] An example of Model-View-Controller techniques in a Perl / CGI script - (2014-11-20)
  [262] A little bit of fun - the new Perl Quiz - (2005-03-30)
  [261] Putting a form online - (2005-03-29)


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