Nearly two weeks ago, I asked for references to usability studies of
Petri nets for school-aged children, or any other Petri nets in school
(pre-university schools, that is) related works:
http://www.informatik.uni-hamburg.de/cgi-bin/TGI/pnml/getpost?id=2008/11/4406
The very small number of replies seems to confirm that this is a largely
uncovered area of education research, although alternative explanations
are possible.
Even assuming that this list still reaches a large part of the Petri net
research community, and that Petri nets are apparently used in some
schools, it appears that school teachers have their own online communities,
entirely separate from this list (is there any information on the range of
interests covered by list subscribers here?). Also, they might lack the
time/inclination/encouragement/support to publish their findings, or might
record their experiences in local language only, without wider distribution.
Researchers, on the other hand, might lack the contacts to local schools,
or find it difficult to imagine that their children, long advanced from
simple board games to multiplayer online dungeons, could be at all
interested in something as simple as Petri nets? I would hope not,
given work on team planning for robot agents, or game story plot
modelling, among others!-)
I would be interested in other explanations, but for now, it seems that
there is either an unexpected hole in Petri nets research, or an unfortunate
disconnect between research and education practitioners in this area.
Please note also that my search was limited to online resources,
as local university libraries in England tend to be unhelpful on the
subject of Petri nets (thinking back to the shelves of Petri net
publications in German libraries, a search in one of them might turn
up relevant older references).
Perhaps the topic could be emphasized in future events, and the
"Education with Petri Nets" section on the Petri Nets World could
be generalized from academia towards including schools (an unambigous
standard keyword for publications relating to this subject would also help,
as the ambiguity resulting from overloaded terms currently makes successful
search near impossible).
I'm not sure whether a Petri net education specific forum would attract
teachers more than this list, given that nets can only be one of very many
topics on their busy schedule. But a wiki dedicated to this subject, as part
of the Petri Nets World, would allow them to share tools, experiences,
best practice in a central place, more visible to the general Petri nets
community (contacts with other groups of school children working
on the same subject, or with researchers willing to offer teacher support,
tool expertise, and inspirational encounters with real-life applications
might also be popular).
Thanks to all who have replied!
Claus
-- summary of replies received
1. Rüdiger Valk sent me a copy of a report on an experiment conducted
at a German school in 1996, by Markus Christian Meyer. Unfortunately,
the report is not only in German, but is not available online, either.
Informelle Einfuehrung in Petrinetze
Markus Christian Meyer
Universitaet Hamburg, Fachbereich Informatik, FBI-HH-M-263/96
The motivation for this experiment was the need to test the viability of
an informal, non-mathematical introduction to Petri nets. The underlying
assumption was that schoolchildren past their first stages of qualification
(gymnasiale Oberstufe, zwischen Realschulabschluss und Abitur) would
offer a lower bound on the abilities to be expected from professional
target audiences, helping to expose issues with the introduction.
The report includes the slides for the introduction (a prelude starting
from a board game, transforming it into a Petri net, generalization to
full firing rule, several very simple real-life scenarios described as pictures,
then overlaid with Petri nets capturing the activities), the forms of a
multiple-choice test conducted after the introduction (90 minutes total),
the test results (the anonymised participants attended years 11-13 in a
Gymnasium in Hamburg, ranging in age from 16-19 years), and some
interpretation. It concludes that the introduction was suitable (and was
rated subjectively as understandable by the participants), leading to
objectively verified understanding of the principles, with minor difficulties
in practice (attributed to limited time/experience).
2. Srini Ramaswamy writes
Yes ofcourse. I have used PNs to help learn simple concepts - for
kids and for early college students. No books etc on this, but some
presentations and a paper.
Here is a recently published paper.
The paper attached was
S. Ramaswamy, R. Seker, S. Sudarsan, M. Itmi, A. Cabani,
W. Alshabi, "Modeling and Simulation: The basis for education
enrichment and software systems design",Invited paper, Journal
of Enterprise Information Systems, to appear
While not directly on the topic, it outlines an education-theory-based
approach towards motivating students in self-directed discovery. From
the conclusions:
.. we have presented the 8E model, where we suggest the use of
modelling and simulation is used as a fundamental basis to energise
and engaging students for developing well coordinated software
systems. For illustrative purposes and for its support of a visual
formalism as well as its ability to represent real-world constraints
(such as capacity, synchronous and asynchronous operations,
parallelism with appropriate tool support, etc.) we have chosen
to use Petri nets as the tool to illustrate the basic principles put
forth by this article.
.. modelling and simulation can be used as an effective means to
improve our students HOT [higher-order thinking] skills, as seen
from Bloom's taxonomy of learning. Such skills come in very
handy for the students in their real-world jobs
..Training students in modelling and effective modelling and
simulation and boosting their creativity (by addressing the three
essential HOT skills of evaluate, synthesise and analyse) can help
students become improved radical thinkers; ones that make a big
impact on organisational revenues. As long as this impact is focused
by helping students learn 'standards-based' development practices,
highlighted by out inability to integrate some modelling tools, it is our
belief that the approach can help students acquire the necessary skills
to become future business innovators.
3. Eugenio Dawis writes:
I just recently started a project with my son's junior high school (ages
11-13). It is obvious I believe as you do about the importance of
learning what I refer to as Process Architecture as a major tool in
critical thinking. Since this is part of the school's mission, the
proposal has been well received.
I hope to have a presentation by the end of the school year (June 2009)
From the proposal:
Process systems thinking is something we all do one way or another: working
out schedules, planning out projects, programming games, navigating through
traffic, or just figuring out the fastest way to get something done. Learning
dualistic Petri nets gives a person a powerful capability to be able to think
critically in almost every aspect of life: Life is a process system!
The presentation involves the following discussion:
- What is a system?
- What is a process?
- Introduction to dualistic Petri nets
- Net building rules
- Simulation rules
- Example model
- Class participation: simulation of example model
- Student group model building
- Student group demonstrations (time permitting)
- Introduction to hierarchical abstractions: Architecture
The class participation portion should be fun for the students. It involves
each student taking the role of one of two process components: a
"transformation" or a "place". Students who are "transformations"
will hold a plastic square box and students who are "places" will hold
circular boxes as that is the typical convention used in Petri nets.
Marbles representing "marks" will be used and passed from one
place to the next through transformations according to the simulation rules.
[This was the first time I heard about dualistic Petri nets, so please take
this comment with a grain of salt, but intuitively, I'd prefer if the visual
representation distinguished clearly between hierarchical and basic nodes
- while children new to the subject will be less confused by this than
I was, the use of tokens on all nodes, with no visual difference between
substitution transitions/places (graphical abstraction over subnets) and
basic transitions/places robs them of the essential mental scaffolding
provided by distinguishing between instantaneous events and states
with duration; cf
http://en.wikipedia.org/w/index.php?title=Process_architecture ]
4. Andrea Bobbio mentions:
when my children where at the elementary school, their textbook
explained the elementary arithmetic operations using a graph which
was a Petri net (of course without saying it).
-- additional resources
Petri nets are mentioned briefly in some Teaching plan frameworks
for informatics teaching in German schools (if you will excuse the
transliteration of the German "Rahmenplan Informatik", eg, in Bremen
and Hamburg) and module catalogues for school teacher education,
but I have received no direct information on whether this actually leads
to the use of Petri nets in German school practice (although I've
encountered vague references, eg, one school's informatics course
did a project with German Telekom, some institutions used Petri nets
for open days involving school children).
This is in spite of various recommendations/plans/suggested school
teaching units involving Petri nets for conveying fundamental computer
science concepts such as concurrency and modelling, as found, for
instance, on these pages (HyFISCH, btw, is one of those forums for
informatics education in schools):
"Vorschlag für eine Unterrichtseinheit zur Vermittlung des Themas
Nebenläufigkeit" (German)
http://www.informatikdidaktik.de/HyFISCH/Produzieren/SeminarDidaktik/Nebenlaeufigkeit/sek_II.htm
further references (German)
http://www.informatikdidaktik.de/HyFISCH/Informieren/Nebenlaeufigkeit
publications "Didaktik der Informatik in Potsdam" (mostly German,
look for "Petri" or "Nebenlaeufigkeit", perhaps also "Modell")
http://www.informatikdidaktik.de/Forschung/sv.htm
Other items encountered in the search for multiple overloaded search
terms include the use of Petri nets as a planning tool for developing
courses in conformance with complicated educational standards, and
this interesting sounding reference in the PN bibliography:
Description of Problem Solving Using Petri Nets, Trentin, G.
In: Winterburn, R.: Aspects of Educational and Training Technology,
Vol. XXIV. (Conference: Realizing Human Potential, 1990, London,
UK), pages 122-128. London, UK: Kogan Page, 1991.
Abstract: The possibility of using Petri nets as a formal language for
pupils to represent their own personal knowledge is examined. The
underlying hypothesis is that the process of identifying and defining
the knowledge structure of a given content area makes it easier for
the pupils to use the knowledge itself. The remarks refer to experiments
carried out with pupils in the first years of higher secondary school
(14-15 years old) and deal with the graphical representation of
problem-solving procedures for some simple mathematical problems.
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