Maria Knobelsdorf, University of Dortmund, Germany - Didaktik der ...

The Monkey Puzzle
Sometimes you know exactly how to solve a problem but fail
nonetheless, because it would cost too much time or is "not
scalable". Problems of that kind exist in many disciplines.
If you need a bridge over a ditch 1m wide, you only need to lay a
metal or stone plate across it, and it‘s done ! However, a bridge
across a gap of 10m cannot be made of ten such plates laid end to
end; we need first a precise static analysis of the construction,
with an outlay considerably greater than 10 times that of the first
example. If you want a bridge over a gap of 100m , the necessary
outlay will be many times greater. The longest bridge span
achieved to date is about 2000m. Each additional meter requires
an immeasurably greater planning effort and immense material
and building costs.
The peculiarity of the second set of monkey puzzles is not just
that the computer would take a very long time to find a solution;
it is fundamentally incapable of answering this problem! So
computational thinking provides means of recognizing, that there
are certain problems, which by their nature can never be
completely solved algorithmically.
Informatics Letter by Letter
The formal term "information" is very important to computer
science, as expressed by the also used "informatics", which is
derived from Informatik, build of information and automation.
Information is important to all disciplines in our modern world -
but what is information at all?
An approach by Shannon to use language for defining information
can easily be adapted for computational thinking. Please try to
decipher the following text. It is from a well known story, but is
missing all except the frequently used letters.
hen aune as tee eas o, the enhantess shut he in a toe, hih a in a
oest. e toe ha no oo, ut hih u as a ino. hen the enhantess ante to
o in, she ae hese eo the ino, an ie „aune, aune, et on ou hai.“ aune
ha aniient on hai, ine as sun o. hen she hea the oie o the enhantess
she oun he hai oun a hoo o the ino. e hai e tent as on, an the
enhantess ie u it.
Interesting, isn‘t it? Here we have retained about 70% of the
original letters, but the result is gibberish. Below is the same text,
with almost the same number of letters as in the previous
example, obtained by removing only the vowels from the original.
Can you read the story now?
Whn Rpnzl ws twlv yrs ld, th nchntrss sht hr n twr, whch ly n frst.
twr hd n dr, bt hgh p ws wndw. Whn th nchntrss wntd t g n, sh
plcd hrslf blw th wndw, nd crd „Rpnzl, Rpnzl, lt dwn yr hr.“
Rpnzl hd mgnfcnt lng hr, fn s spn gld. Whn sh hrd th vc f th
nchntrss sh wnd hr hr rnd hk f th wndw. hr � l twnty yrds dwn,
nd th nchntrss clmbd p by t.
Apparently the amount of information has to do something with
the frequency: A text containing just common symbols contains
no information or at least less information than the text with
infrequent symbols.
In computer science, this knowledge is used to encode texts and
other information and save memory or bandwidth, e.g. by using a
huffman-tree or just zipping files. In other disciplines, this is used
as well - like in linguistics: In ancient sanskrit the symbol for T
followed by A, which is a very common combination, is written
as
156
If you want to use T without A, which is shorter, but less
common, you have to write with more strokes:
So computational thinking is not a new discipline, but known for
some millennia...
Abenteuer Technik
In our science lab for children we implicitly use computational
thinking too. We give out tasks like "building wings for an
efficient wind generator out of some cardboard, wood and plastic
film" or "building a water wheel generator out of milk carton".
The degrees of freedom are intentionally set very high, so the
children have to model the problem first and then make a
conscious decision to focus on optimizing one or two out of more
than 100 possible parameters.
4. Conclusion
Approaches to teach computer science and engineering without
using complex and abstract technology, like [Bell 2006],
[Gallenbacher 2008, 2012] are most suitable to implement
computational thinking in computer science education.
5. References
[1] [Bell 2006] Tim Bell, Ian H. Witten, Mike Fellows:
Computer Science Unplugged - Teachers edition,
downloaded from http.//www.csunplugged.org/
[2] [Biundo 2006] Susanne Biundo, Volker Claus, Heinrich C.
Mayr: Was ist Informatik, unser Positionspapier,
Gesellschaft für Informatik, 2006
[3] [CSTA 2010] Cameron Wilson, Leigh Ann Sudol, Chris
Stephenson, Mark Stehlik: Running On Empty: The Failure
to Teach K–12 Computer Science in the Digital Age, Report
of the ACM-CSTA, http://www.acm.org/Runningonempty/
[4] [CSTA 2011] Deborah Seehorn, Stephen Carey, Brian
Fuschetto, Irene Lee, Daniel Moix, Dianne O’Grady-
Cunniff, Barbara Boucher Owens, Chris Stephenson, Anita
Verno: CSTA K–12 Computer Science Standards Revised
2011, Report of the ACM-CSTA, ISBN 978-1-4503-0881-6
[5] [Gallenbacher 2008] Jens Gallenbacher: Abenteuer
Informatik, Exhibition, http://www.abenteuer-informatik.de
[6] [Gallenbacher 2012] Jens Gallenbacher: Abenteuer
Informatik, Springer-Spektrum, ISBN 978-3827429650
[7] [Wing 2006] Jeannette M. Wing: Computational thinking,
COMMUNICATIONS OF THE ACM March 2006/Vol. 49,
No. 3
[8] [Wing 2008] Jeannette M. Wing: Computational thinking
and thinking about computing, Philosophical Transactions of
the Royal Society A (2008) 366, 3717–3725
[9] [Wing 2010] Jeannette M. Wing: Computational Thinking:
What and why?, CMU, 17. November 2010