Making Physics Concepts Accessible and Explorable using WORLDMAKER - an Iconic Modelling Tool

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ICPT 1999


Guilin

World Maker

N. Law

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Making Physics Concepts Accessible and Explorable using
WORLDMAKER
-

an Iconic Modelling Tool


Workshop presented at the ICPT99, Guilin, PRC, 19
-
23/8/99


Nancy Law

Department of Curriculum Studies, University of Hong Kong



An important part of scientific
work is to theorize, to build explanatory models of the world around
us. Yet this aspect of science is generally less accessible to science education at the school level as
it has been difficult to develop such understanding in learners. With the advent of

computers,
various modeling tools have been developed to allow students to participate in such theorizing
activities.


This workshop introduces a modelling tool, the WORLDMAKER, which can be easily understood
conceptually and mastered operationally by mos
t students. This tool was designed as a modified
form of cellular automaton machines that supports reasoning in terms of interactions between
objects and backgrounds co
-
located in the same neighbourhood. The entire process of defining the
objects and inter
actions can readily be accomplished visually. WORLDMAKER can help students
understand how deterministic macroscopic trends can result from probabilistic interactions as well
as visualize theories involving microscopic interactions that cannot otherwise be
easily
understood.



Introduction


Scientific concepts and principles are often theoretical models of how particular aspects of the
world around us works. Einstein and Infeld (1938) gives a succinct description of this aspect of
scientific activity:

Scien
ce is not just a collection of laws, a catalog of facts, it is a creation of the human
mind with its freely invented ideas and concepts. Physical theories try to form a
picture of reality and to establish its connections with the wide world of sense
impres
sions.

Modelling as a learning activity in science would help students to develop an understanding of
scientific principles as theoretical models and not facts. It would also help develop a better
understanding of the nature of science and a deeper underst
anding of the specific principles
explored.


Modeling vs Using Simulations

Simulations also allow users to explore consequences of variations in the modeled domain.
However, an essential difference lies in the fact that the model behind simulations are hid
den
from the user. There is no way for the user to actually inspect or vary the model used in a
simulation. A user can certainly try to hypothesize about the model, but there would not be any
definitive way to ascertain the actual model used, in much the s
ame as there is no way for one to
find out whether one’s theory about particular natural phenomena is the “correct” one. In this
sense, the creator of a simulation is playing the role of god.


Modeling is fundamentally different from working with simulatio
ns in that it is both an
expressive activity as well as an exploratory one. It allows the user to externalize thoughts as
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well as to interact with them. In other words, a modeling tool is one that allows the user to
create, interact with and modify his/her

own simulations. Good modelling tools should provide
structures that help express thought. These tools thus provide new tools for thought and new
thoughts about the world through supporting interactions with external but artificial worlds
(Bliss, 1994).


Modeling and the Science Curriculum

Modeling has generally not been common in school science. In recent years, possibly due to the
increasing power of computing tools available in schools, there has been a rising interest in the
development of modeling to
ols and curriculum materials for use at school level (Mellar, 1994).
It is noteworthy that in the
new A Level draft syllabus specification for Physics B (Advancing
Physics) in the UK, developed by the Institute of Physics (IoP) and examined by the Oxford,
Cambridge and RSA Board (OCR), there is a module ‘The Rise and Fall of the Clockwork
Universe’, which specifically deals with modelling in Physics. The following extract from that
draft syllabus gives a very succinct description of the concepts that can be

developed through an
introduction of modeling in the curriculum:


“Models can be seen as artificial worlds over which the human maker has complete
control. This is the source of their definiteness and determinism. Models allow
analogies to be seen between

otherwise very different physical processes. A
difference can be seen between models whose well
-
determined behaviour is due to
exact rules operating on variables (as in the harmonic oscillator) or to smooth
averages over many particles (as in radioactive
decay). Both strategies inform the
structure behind the whole A2 course.”



Concept of a Cellular Automaton System as applied in WORLDMAKER


As mentioned, WORLDMAKER (hereafter referred to as WM) is a modified form of a cellular
automata machine (Law & Tam
, 1998). Cellular automata, as defined by Toffoli and Margolus
(1987), are discrete dynamical systems whose behaviour is completely defined in terms of a
local relation. In a classical cellular automaton system, which is built on a grid system where
the e
volution of any particular location on the grid depends on the configuration of cells in the
immediate neighbourhood of that location. World Maker is indeed a form of such a system that
is based on a square grid system: it is based upon the interactions of

entities that act locally.
However, it is a modified form in certain ways. Firstly, each cell may have two entities: an
object and a background, which may interact together or separately. Secondly, whilst most
cellular automaton systems evaluate the int
eraction of each cell with all members of is
neighborhood simultaneously, in WM, only binary interactions are evaluated between the cell
under consideration and each of the other cells in turn in the Moore neighbourhood, which
includes the eight cells arou
nd a central cell as well as the central cell. Whilst a cell may
interact with each of its neighbouring cells in turn, it nevertheless cannot interact with more
than one other cell simultaneously. One useful feature of WM is that one can alter the
neighb
ourhood that is being simulated by pre
-
defining the relative locations of the neighboring
cells that needs to be evaluated when the simulation is run so that the neighbourhood to be
evaluated is not restricted to the Moore neighbourhood.



Using WORLDMAKER

to Support Teaching and Learning in Physics


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Physicists appreciate that many natural phenomena are currently explained by assuming that
matter consists of microscopic particles, which act in certain, well
-
defined ways. Prime
examples of this include diff
usion and Brownian motion, both of which are explained by the
kinetic theory.


In a school laboratory situation, it is often difficult to explain how these abstract principles in
Physics relate to the macroscopic phenomena observed in standard experiments.

There are
some physical models that attempt to provide analogies for illustrating these microscopic
interactions. However, such models tend not to be very effective as the physical properties of
the “particles” used in these models, like beads and beans,
are rather different from the “ideal
particles” that they simulate.


Given that the structure of matter is one of the most fundamental and mind
-
boggling theories
about the universe (the atomic theory started with the Greeks, yet did not convince many
scie
ntists until the early 19
th

century, and was not proven until 1905 by Einstein), it is important
and yet not easy for the students of today to fully comprehend the nature and implications of
such a theory. By using a cellular automaton simulation system, o
ne can make it easier for
students to realize how the macroscopic phenomena may result from the random interactions of
microscopic entities. While physical models of the kind described above are effectively only
illustration tools, students can actually ex
plore the various features of the system using WM.
This allows them to make sense of and construct their own understanding of how a theoretical
model of microscopic entities can in fact produce deterministic macroscopic behaviour,
fostering the development

of deep cognitive understanding and meaningful learning.


The advantage of World Maker over other cellular automaton simulation system is that there is
no code/script writing required of the user


all properties of the simulated “worlds” including
the ty
pes and properties of entities as well as their possible interactions are definable through
drag
-
and
-
drop actions on a simple graphic user
-
interface. It is the intention that both teachers
and students, who may have little or no experience of programming,
can engage in creating and
exploring simulations through creating and altering ‘worlds’ using WM without having to go
through a scripting hurdle. The following are some examples taken from the Physics
curriculum that can be explored through WM.


Exploring
Radioactive Decay

One of the classic examples of probabilistic changes leading to deterministic macroscopic
behaviour in systems is radioactive decay. In this ‘world’, we have defined two types of objects:
atoms of a radioactive element A and atoms of a s
table element B which is the product of the
decay process. The only rule that needs to be defined for this world is a very simple one: there
is a certain probability that an atom of the radioactive element A would decay to become on
atom of the stable ele
ment B:



Insert fig. 1 about here


Fig. 1.

The rule definition for radioactive decay.



As the “radioactive world” is run, one can see visually on the grid that atoms of element B starts
to appear and accumulate while the number of element A atoms decreas
es. In order to facilitate
exploration of quantitative changes, WM contains a statistics module which can be used
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simultaneously to display a real time chart when the “world” is run as well as to store the data
for further exploration.


As shown in Fig. 2
, the time changes of the number of A atoms follow a characteristic
exponential decay curve.




Fig. 2

The graph of the variation of the number of A atoms with time produced by the
WORLDMAKER statistics module.


The probability of decaying can be easily a
ltered using the slide bar shown in Fig. 3, thus
simulating the effect of the differing half
-
life of various elements.




Insert Fig. 3 about here

Fig. 3.

The probability of firing for any particular rule can be changed using the slide bar
attached to ea
ch rule.




The following graph shows the time variation for the number of atoms remaining for two
different radioactive elements. Can you tell from Fig. 4 the relative probability ratio of decay
for these two elements? What is the relative magnitude of th
eir half
-
lifes?




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Fig. 4.

The graph of the variation of the number of atoms for each of two radioactive
elements.



Two Stage Decay Systems and Production of a Constant Strength Radioactive Source

One can also examine the effects of a two
-
step decay sys
tem, which is very difficult to imagine.
However, using WM, it is very easy to model the situation, and the result as seen in the
following graph is remarkably close to what should be seen in reality.




Fig. 5.

The graph of the variation of the number o
f atoms for each of two radioactive elements.
The red line represents the number of atoms of parent element and the blue line
represents the number of atoms of the radioactive daughter element existing at
different times.



Diffusion of Gases

More complica
ted phenomena can be examined using World Maker. For instance, one can
examine the way in which Bromine diffuses in air. For this situation the following ‘world’ was
used to examine the way in which a gas diffuses.


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Fig. 6.

The WORLDMAKER screen for t
he “diffusion world”.


In the “diffusion world”, we can illustrate some of the functions of “backgrounds”. In Fig. 6, the
two background colours represent the space for each of two inter
-
communicable “chambers”.
This

“diffusion world”

is defined such that

the gas molecules can ‘jump’.


After many iterations, the gas density (which is reflected by the number of atoms in each of the
chambers which are equal in size), shown in Fig. 7, in both chambers is found to be roughly
equal. This, coupled with a demons
tration on bromine diffusion, should help students to
understand what happens in diffusion



Fig. 6.

The graph showing the number of atoms in chamber 1 (red) & chamber 2 (blue).

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Here, the red line shows the number of molecules in the originally filled ch
amber whilst the
blue line shows the number of molecules in the originally empty chamber. One sees from this
graph, as well as the resultant ‘world’ situation pictured below, that the diffusion process leads
the atoms to move randomly to a situation where

they are more or less evenly distributed. The
graph, in this process, is especially helpful as it shows that the trends are average trends that
happen throughout the time, and not a process that is strictly controlled, as they can see from the
fact that
there are random fluctuations in the graph notwithstanding the overall trend.


Critical Mass and Chain Reactions

Other worlds can also be run using WM for clarifying and demonstrating Physics principles. A
good example would be the concept of chain reactio
ns and critical mass in Physics. The
condition for chain reactions is the successful establishment of a dynamic equilibrium state
where the number of neutrons leaving the system is smaller or equal to the amount that are
produced by the fission reaction.
This is a rather difficult concept to clarify, probably even more
so than gaseous diffusion. Further,
one cannot possibly do any schools experiments on nuclear
fission for obvious reasons! Using WM we can demonstrate that, when the volume/mass of
Uranium
-
2
35 is less than a certain critical amount, the fission process will eventually stop when
all the neutrons are absorbed. However, when the amount of U
-
235 in the ‘world’ increases
above a certain level, the ‘critical mass’, fission will be sustained.


Other

examples

We can also explore some of the principles in material physics using WM. For instance, we can
look at
crystallisation

using WM. It is possible to show that similar configurations of crystals
form will result from a given set of crystallization ru
les while different rules will lead to
different crystal configurations.


Another topic that can be explored is
change of state
. Simulations of the liquid state and the
temperature dependence of evaporation as well as simulations of boiling can be easily
created
by inputting the rules for the kinetic theory as well as intermolecular forces.



Teaching activities using WORLDMAKER


Trials carried out with secondary school students showed that WM is a useful tool for teaching
difficult, hard
-
to
-
demonstrate
topics. One of the trials was done with a group of secondary 6
(Year 12) students when introducing the topic radioactivity (Shum, 1997). The students
immediate reactions when observing the decay curve was that it looks like an exponential curve
(they have
studied the topic on exponential curves in Mathematics). However, as the “world”
developed, they rejected this hypothesis because “An exponential curve should never touch
become zero but now there is no radioactive atoms left!” This provided a very good op
portunity
for the teacher to understand the kind of conceptual difficulties students may have in connecting
theoretical probabilistic functions and real probabilistic events and a platform for further
exploration and discussion about the topic..


Another t
rial, again conducted by Shum (1997), was done on the study of ecology with a group
of secondary students doing AL Biology. The students wanted to build a stable ecological
system using WM. They started by putting in rabbits and grass, introducing probabil
istic rules
on rabbits eating grass, rabbits dying if they do not eat and barren ground growing grass if next
to a patch of grass. On monitoring the amount of grass and number of rabbits over time, they
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were surprised to see the oscillations in both popula
tion curves (a typical predator
-
prey graph).
They were very much surprised by the periodicity of the curve and tried to explain why this had
occurred. One student promptly offered “seasons” as a possible hypothesis. Another one
quickly offered a more compl
ete “theory”: that rabbits hibernate during winter, thus reducing
the number of rabbits around to eat the grass. Then a heated debate took place around whether
rabbits do hibernate or not until one cool
-
headed student remarked, “But we did make any
referen
ce to seasons or hibernation in our rules!” This is an excellent example of how modeling
activities can promote theorizing and thus helping students to articulate their thoughts and
explore their consequences.



Conclusion


WORLDMAKER is a useful teaching

and learning tool in science education. By offering an
iconic tools to build “worlds” where events involving objects and backgrounds take place,
learners can explore a wide range of scientific phenomena. It is especially helpful in supporting
the learning

of macroscopic trends resulting from microscopic probabilistic interactions and for
visualizing micrsocopic phenomena. Classroom trials with WM indicate that it is best used in
group situations where students can explore, discuss, explain to each other.



Reference:


Liang, S. S. (1996), The Theory of Physics Learning (), 1
st

Ed., Nanning: Guangxi Educational
Publishing Co. ()


Ogborn, J. (1994). Overview: The Nature of Modelling. In Mellar, H. et.al. (Eds.)
Learning
with Artificial Worlds: Computer Base
d Modelling in the Curriculum
. London: The Falmer
Press.


Oxford, Cambridge and the RSA Examining Board (1999),