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International Conference on Computers in Education
- an Iconic Modelling Tool for Children to Explore Complex Behaviour
Authors: Dr. Nancy LAW
Mr. Eric W. C. TAM
Affiliation: The University of Hong Kong
Address: Department of Curriculum Studies
University of Hong Kong
- an Iconic Modelling Tool for Children to Explore Complex Behaviour
Over the last two decades, the emergence of parallel intermaths, a new kind of computation that includes examples like cellular automata, genetic algorithms, artificial life, classifier systems and neural networks, has contributed to significant developments in the biological sciences and beyond. Intermaths builds on the capacity of electronic computers to break through the sequential math of the industrial age and supports the study of systems whose complex behavior derives from the interactions of the constituent parts rather than from within the individual components themselves (Bailey, 1996). This paper describes the design and intended usage for one such kind of modelling tool built for school age children - WORLDMAKER(HK), that supports teaching and learning of natural and social phenomena that results from parallel interactions of the constituent system components, e.g. ecological systems and molecular interactions.
Modelling in this context refers to the design, development, exploration and evaluation of models of real or imaginary situations. Modelling activities when carried out in the curriculum context of science or other discipline areas provide opportunities for children to engage in activities involving a high level of cognitive understanding and creativity in making sense of phenomena and possible contributing factors (whether tangible or abstract) for the domain context. The provision of appropriate modelling tools to enable children to create their own representations (“worlds”) and to explore other people’s representations would greatly enhance the accessibility of such activities to younger children. WORLDMAKER(HK) has a very intuitive user interface which makes the modelling and exploration of complex systems exciting and accessible to children.
Keywords: WORLDMAKER, iconic modelling, modelling tool, mindtool, cognitive tool, complex systems, adaptive systems, intermaths
Modelling and Modelling Tools in Education
A model is a simplified and idealized system that can be used to think about another. Key concepts and principles in many disciplines are often theoretical models of the phenomena under scrutiny. Einstein and Infeld (1938) gave a succinct description of the importance of model building as a scientific activity:
Science 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 impressions.
However, it is not easy for learners to develop such an understanding unless they have an opportunity to explore the consequences of different theoretical models. Information technology provides a particularly versatile and effective platform to support the creation and/or exploration of theoretical models by the learner. Computer-based simulations allow users to explore consequences of variations in the modelled domain and have been used in education and training for a long time. However, an important feature of simulations is that the models behind simulations are hidden from the user. There is no way for the user to actually inspect or modify the model in a simulation. One can try to hypothesize about the model used, but no definitive verification is possible, just as it is not possible to find out whether one’s theory about certain natural phenomena is the “correct” one. In this sense, the creator of a simulation is playing the role of god.
Computer-based modelling is fundamentally different from exploring with simulation software in that it is both an expressive activity as well as an exploratory one. It allows the user to externalize thoughts as well as to interact with them: computer-based models are “runnable” thoughts. As Ogborn (1990) pointed out, “To make a model on the computer is to create a world but a world which evolves or changes in front of ones’ eyes. It is an imaginary world which may or may not reflect something important about the real world” (p.103).
In order to support modelling activities by learners, the availability of appropriate modelling tools is essential. A modelling tool is one that allows the user to create, modify and interact with his/her own simulations. Much work has been done in this area by various groups on the development of different kinds of modelling tools for school age children (Bliss 1996; Mellar et. al. 1994). These vary from quantitative modelling tools (Boohan & Brosnan, 1994; Sutherland, 1994; Winbourne, 1994) to qualitative or logical modelling tools (Tompsett 1994) to semi-quantitative modelling tools (Bliss, 1994a). 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, 1994b).
Complex Systems and the School Curriculum
Complex systems (Bak, P. 1996; Schroeder, 1991) abound in the physical, biological, economic as well as the sociological world around us. Life is obviously a prime example of complex systems. Von Neumann’s adoption of Ulam’s “cellular games” to construct a universe of self-reproducing machines have aroused strong interest and stimulated a whole new paradigm of research on complexity. Conway’s Game of Life (Gardner, 1970) was a celebrated example of how “life” of increasing complexity can be generated by a computational system entirely based on a set of pre-defined simple rules (see Poundstone, 1985 for a comprehensive account of the developments). Recent work on various kinds of complex systems including earthquakes, economics and traffic jams have also successfully made use of models constructed from large arrays of simple units with simple rules defining local interactions to produce complex macroscopic behaviour.
Wolfram gave the following description of complex systems:
“It is common in nature to find systems whose overall behavior is extremely complex, yet whose fundamental component parts are each very simple. The complexity is generated by the cooperative effect of many simple identical components. Much has been discovered about the nature of the components in physical and biological systems; little is known about the mechanisms by which these components act together to give the overall complexity observed.”
Wolfram (1984), p. 419
There are many topics in the school curriculum that can be better explored and understood using models created from a system of parallel locally interacting cells (an intermaths system), even though these are not treated as such in the current curriculum requirement. The following are just some examples:
Currently, these topics cannot be dealt with adequately in the curriculum since the behaviors of these systems come about as a result of the coordinated interplay of parallel interactions between a large number of component parts. The curriculum treatment at lower levels generally involves the presentation of static descriptions of the system interactions and the resulting behaviour. Students thus have to take these statements at their face value and the depth of understanding that can be resulted is necessarily limited. At higher educational levels, attempts have been made to provide a more dynamic understanding of the behaviour of these systems and how the behaviour is affected by the various pertinent system parameters through the use of systems of differential equations (Roberts et. al. 1983). Dynamic modelling tools have also been developed to support the modelling and exploration of these systems, e.g STELLA (Richmond 1987) and DMS (Bell 1988; Zinck et. al. 1988). However, dynamic modelling can only contribute marginally to the understanding of such systems: the knowledge of the overall quantitative change in the system as a result of changes in other quantitative parameters. These do not help the learner to visualize how the microscopic, local interactions characterizing a system contribute to its macroscopic, quantitative behaviour. It is not obvious how the mechanisms governing the behaviour of such systems translate into these highly condensed algebraic formulations. Further, such analytical descriptions only portray the mean expected behaviour of the systems. Students may thus not be able to understand the probabilistic nature of the system behaviour. This point will be elaborated in a later section in this paper.
In other words, dynamic modelling tools do not provide the necessary structures required to support the construction of runnable models of complex systems. Further, these are generally inaccessible to learners other than the mathematically competent ones. Just as ancient mathematics (geometry) lack certain concepts necessary for the development of classical physics, the mathematics of algebra and calculus are not sufficient to study the behaviour of complex systems. As Hanson (1962) has pointed out, thinking new thoughts in a conceptual framework not designed to express them requires unprecedented physical insights. The learning of concepts derived from the behaviour of complex systems would become rather difficult if done through the medium of dynamic modelling. Intermaths (Bailey, 1996 gives a succinct description of the significance of this new form of math that has developed on the basis on the modern digital computer) provides a more effective basis for the exploration of such systems as it supports the exploration of the effect of local interactions found in many complex systems, gives output that possesses a probabilistic “texture”, and at the same time be used to generate a parametric description of the system changes that can be used to link up with the analytic models of such systems if necessary.
Making Complex Behaviour Accessible - reasoning with objects and events
The quantitative approach to modelling requires rather sophisticated abstract reasoning ability and some mathematical competence. Children, on the other hand, tend to view the world in terms of objects and events (Boohan, 1994). The central objective in the design of WORLDMAKER(HK) is to provide an easy-to-use, intuitive modelling environment built on the basis of an intermaths system similar to cellular automata machines (Toffoli and Margolis, 1987). WORLDMAKER(HK) is different from a cellular automata system in that each cell can contain up to two entities: a ‘background’ and an ‘object’. The latter being able to move while the former cannot. Besides movement, the system can be used to define rules that lead to creation or destruction of entities, or a change in direction of the entities. In this environment, children are encouraged to think of rules of interactions as possible events that can occur in the “world”.
Forest fires – a percolation problem
To illustrate how the system can be understood by young children, a “world” created to explore the spread and control of forest fires can consist of three objects and two events. The three objects are trees, trees on fire, and ashes. The two events are fire spreading and trees burning out. To define fire spreading, a rule needs to be created to specify that there is a certain probability for a tree next to a tree on fire to become a tree on fire. To define trees burning out, a rule needs to be created to specify that a tree on fire has a certain probability to become ashes.
Fig. 1 A “world” created to explore the spread and control of forest fires.
System Design of WORLDMAKER(HK)
Functionally, WORLDMAKER(HK) comprises 4 modules:
Only the user interface is described here.
The user interface
The World grid. The core of the user interface is a “world grid” - a 20x20 grid for visualizing the “world” and its development. Iconic images of defined objects/backgrounds can be placed here and “run” according to defined rules of interaction. Each position on the “world grid” can be occupied by at most two entities: one object and one background entity. The occupants and their respective directions (if applicable) at each position define the state of that position at that time. The “world” evolves by repeated iterations as the state of each position is updated at the end of each iteration, after the effect of the interactions has been computed. The user can observe the evolution of the “world” visually while the model is being executed.
The entities panel. There are two kinds of entities that users can define: objects and backgrounds. Both types of entities can interact and change or be changed. However, only objects can move. Entities only differ from each other in terms of their names, bitmap images and rules of interaction. In order that the modelling environment can be more appealing and intuitive for children, the user can edit or create images for the entities. These images can also be saved and stored in separate files for later use. Each “world” can define up to 6 objects and 6 backgrounds. Each entity can be defined by simple “drag and drop” of the desired bitmap image from the image panel onto the object or background panel. While each entity has been assigned a default name by the system, the user can edit the names of the entities at any time during the operation to reflect the nature of the entities being represented. For example, the entities can be rabbits, vegetables, trees, ashes, radioactive nuclei or a magnetic field.
Rule editing. This is a very important and exclusive feature of WORLDMAKER(HK) - the definition of the rules of interaction for the system is done through a simple iconic interface that is accessible even to children below the age of 10. (StarLogo, created by the Connected Mathematics project, is a similar modelling environment (http://www.tufts.edu/as/ccl/cm/) built for the creation of complex systems. However, the definition of the rules of interaction has to be done using a form of the LOGO language.) The development of an iconic interface for rule editing is a high priority in the design considerations of WORLDMAKER(HK) as this directly affects the extent to which the interactions behind the models are open and explorable by children and the extent to which children can participate in the creation of these models, which is the essence of modelling activities.
he rule editing panel. In WORLDMAKER(HK), rule editing is completed through “drag and drop” operations in three steps: defining the conditions for the firing of the rule (the initial state), the nature of the change involved, and the outcome when the rule is fired (the final state). Thus the rule editing process is in fact one of selecting the appropriate rule through a three-step process. There are over 200 rules in the system, accessed in a hierarchical manner according to the input steps in the selection sequence. Only binary interactions are allowed so that the initial and final states are defined through specifying the conditions of at most two adjacent positions. To illustrate how the rule editing works, Fig. 2 shows an example for the creation of a rule on fire spreading by allowing a “tree” next to “tree on fire” to change to “tree on fire”.
Statistical tool. In the study of complex systems, it is often very useful to monitor the change in the total population of particular states/entities in the system. WORLDMAKER(HK) provides a simple statistics tool in conjunction with the modelling environment through which the user can monitor the total number of cell locations that are in a particular state. The tool can monitor up to four different state definitions at any given time and allows the user to observe changes in the statistic count for each of the defined states concurrently while the “world” evolves. The user can also examine an expanded view of the statistical chart that also provide more display and analysis support tools, but the “world” would have to be stopped from evolving during the examination process. The accompanying statistics chart is saved together with the “world” and the data in the saved chart can also be examined and processed independently using other software tools. Fig. 3 illustrates an example of how the statistics tool can be used to compare the effect of different decay proba-bilities on the half-life of different radioactive substances.
Notepad. It is often the case that users may wish to note down some of their thoughts or the discussion that occurs during the process of working with WORLDMAKER(HK). Notes and memos could be added/printed using the notepad function. Such notes will be saved and retrieved the next time the same world is run.
Children Learning with WORLDMAKER(HK)
Initial trials using WORLDMAKER(HK) with children have produced very encouraging results. Some observations of children using Worldmaker are reported here to illustrate the kind of thinking that has been stimulated by modelling activities using this tool. A group of secondary school students who started building a predator-prey model with rabbits and grass were surprised to observe that the population of rabbits fluctuated in regular cycles with time and the fluctuation was out of phase with a similar cycle in the total amount of grass in the “world” (Shum, 1997). One of the students immediately interpreted the fluctuation in the amount of grass as a result of yearly seasonal changes and the fluctuation in the number of rabbits as a consequence of rabbits hibernating through winter. This suggestion sparked heated arguments within the group. The group started to argue about whether rabbits do indeed hibernate. However, a student soon pointed out that this point is immaterial to the behaviour of the model: there were simply no rules that said anything about hibernation or seasons. The level of discussion that took place around this model was remarkable and in the end they were able to relate the observed oscillations to instances of population oscillations that had been discussed briefly in their Biology class some time earlier.
Another example also arising from Shum’s work relates to students building a model on radioactive decay. The students were surprised to find that the radioactive nuclei placed on the grid would decay completely after some time. They had learnt about radioactive decay and the exponential curve earlier in their Physics curriculum: the amount of a radioactive substance decays exponentially with time and this is a result of the random decay of the radioactive nuclei. According to their understanding, the value of an exponential function will never drop to zero, no matter how long the time factor is. They thus find it hard to reconcile the observations made with and what the theory seems to predict. This shows that the students do not really understand the meaning of random processes which also hinders their understanding of radioactivity. An exponential function only provides an idealized description of the general behaviour of radioactive systems, which is different from specific observations of actual radioactive decay. WORLDMAKER(HK) thus provide students with a modelling tool that can provide the rich texture to investigate random behaviour which abounds in nature. Further, it allows students to explore the deterministic macroscopic trends that result from random interactions, which sound rather paradoxical at first sight.
WORLDMAKER(HK) have also been used in experiments to support the teaching of various scientific concepts, for example, genetics. Some of these trials have been designed such that students were first asked to predict the outcomes from given simulations and then observe the outcome from running the simulations. It has been generally found that discrepancies between prediction and observation provided very stimulating contexts for discussion and further exploration. Comparison of situations where students were using the software in individual settings with those in group settings consistently revealed that the latter led to more fruitful learning. Group discussions provide a non-threatening environment for expressing and exploring ideas, allowing deeper understanding to develop.
Observations have also been made of students spontaneously using WORLDMAKER(HK) models to support problem solving. One such example occurred when a group of students was exploring the composition of the offspring from normal, hemophiliac and hybrid parents. The students had only learnt about cases where a genetic trait is determined by two alleles in a pair of chromosomes and were not aware of sex-linked traits. They were puzzled that in the model only the X chromosome had indications for the content of the relevant allele while the Y chromosome had none. A heated discussion ensued over the interpretation of such omission and they eventually arrived at four possibilities: (i) Y contains only normal alleles, (ii) only hemophiliac alleles, (iii) Y can contain either alleles, or(iv) Y has no allele relevant to this trait at all. They then devised systematic tests to work out which of the four possibilities is the most probable and arrived at the conclusion that in fact Y has nothing to do with the trait, a conclusion that they did not quite think was possible before. This indicates that WORLDMAKER(HK) can be also be used as a cognitive scaffold to support problem solving activities.
After multiple cycles of improvements on the interface design and functionality of WORLDMAKER(HK) based on feedback from teachers and students who attempted to use the tool for teaching and learning activities, the tool is now relatively mature and stable, providing two language versions, English and Chinese, with identical functionality. In the shorter term, the main improvement planned on the design of the tool is to extend the world grid to at least 40 x 40. The next phase of the project will focus on two activities. The first focus will be on the creation of curriculum materials based on activities with WORLDMAKER(HK) that can enhance the learning of science at upper primary and secondary levels. Another focus would be the systematic exploration of children’s thinking and learning as they interact with different models built with WORLDMAKER(HK). This latter research is especially important in helping us to understanding the real potentials of using an iconic modelling tool for the learning about complex systems and whether complex behaviour can be understood by young children if supported by the use of such a tool.
WORLDMAKER(HK) was developed at the University of Hong Kong based on the conceptual design of an earlier work, WORLDMAKER, developed on a different hardware and software platform in the U.K. by Richard Boohan and Jon Ogborn of the University of London Institute of Education. It was developed as a collaborative project between the two institutions. The software development was funded by a CRCG grant from the University of Hong Kong. We are also grateful to the British Council for the award of a UK/HK Joint Research Grant which supported the travelling necessary to facilitate the collaboration and the contribution of Mr. M W Tse to the design stage of the project.
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