Modelling and Simulation

1.0 What is modeling and simulation?

A model is a product includes physical or digital that represents a system of interest. A model is similar to but simpler than the system it represents, while approximating most of the same salient features of the real system as close as possible. A good model is a judicious tradeoff between realism and simplicity. A key feature of a model is manipulability. A model can be a physical model or a conceptual model. The example of the physical model is physical architectural house scale model, a model aircraft,  a fashion mannequin, or a model organism in biology research. While, the conceptual model are computer model, a statistical or mathematical model, and a business model.

            The word ‘simulation’ comes from the Latin simulare. Simulation defined as the imitation of the operation of a real world process or system over time. The act of stimulating something first requires that a model be developed. This model represents the key characteristics or behaviors of the selected physical or abstract system or process. The model also represents the system itself, whereas the simulation represents the operation of the system over time. It also involves the manipulation of a model in such a way that it operates on time or space to compress it, thus enabling one to perceive the interactions that would not otherwise be apparent because of their separation in time or space.

Simulation is usually understood as the process of generating reality. In its prevailing sense simulation is concerned with the representation of systems by suitably defined models and observing the operation of such models under a particular set of conditions. The simulation also includes the numerical technique for conducting experiments on a digital computer, which involves logical and mathematical relationships that interact to describe the behavior and the structure of a complex real world system over an extended period of time.

A simulation generally refers to a computerized version of the model which is run over time to study the implications of the defined interactions. Simulations are generally iterative in their development. One develops a model, simulates it, learns from the simulation, revises the model, and continues the iterations until an adequate level of understanding is developed.

2.0 What is modelling and simulation in education?

            In a general sense, a model is a representation of a phenomenon, an object, or idea (Gilbert, 2000). In science, a model is the outcome of representing an object, phenomenon or idea (the target) with a more familiar one (the source) (Tregidgo & Ratcliffe, 2000). For example, one model of the structure of an atom (target) is the arrangement of planets orbiting the Sun (source) (Tregidgo & Ratcliffe, 2000).

Models take many forms, including physical objects, plans, mental constructions, mathematical equations, and computer simulations. Modeling can enable students to share modeling and their perspectives of real scientists’ characteristics; that is, it can provide one situation to foster students’ knowledge of constructing and combing content, inquiry, epistemological realization. Models are tentative schemes or structures that correspond to real objects, events, or classes of events, and that have explanatory power . A model is, in general, a representation of an idea, an object, an event, a process, or a system. A mental model is an internal representation of an object, states of affairs, or a sequence of events or processes, of how the world is, and of physiological and everyday social actions.

There are two categories of models in science education which are conceptual model and mental model. The conceptual model is suitable to use in teaching and learning because this models are devised as tools for the understanding or teaching of systems. In addition to this, conceptual models are external representations--socially constructed and shared which are precise, complete and consistent with the shared scientific knowledge specially created to facilitate the comprehension or the teaching of the systems in the world (Greace & Moreira, 2000). On the other hand, mental models are what people really have in their heads and what guides their use of things (Norman, 1983). Buckley et al. (2004) also viewed mental models as internal, cognitive representations. Conceptual models include mathematical models, computer models, and physical models. Mental models are psychological representations of real or imaginary situations. They occur in a person’s mind as that person perceives and conceptualizes the situations happening in the world (Franco & Colinvaux, 2000). Norman (1983) indicates that mental models are related to what people have in their heads and what guides them using these things in their minds. In order to understand mental models, their characteristics should be considered.

            In science education, teachers should help students realize the importance of every question, and appreciate the need for such a comprehensive process for successful problem solving. Models and modeling already play an important role in teaching and teachers commonly use models to explain ideas to students.

Simulations are representations of situations or processes by means of something analogous. Computer simulations represent the real world by use of a computer program. Simulations can be a valuable tool in the science classroom. They can exemplify scientific concepts and situations thereby allowing students to explore the nature of things. Issues such as cost, safety, scope, time and scale can be overcome by the use of a scientific simulation. Computer simulations help visual learners understand the problems that they would not thoroughly understand simply through reading about them or solving word problems. The sophistication and variety of computer simulations in the field of science are increasing rapidly.

Computer simulations are a useful supplemental tool for student learning and understanding. Individuals who require more information on a topic or concept can be directed to a simulation to help further complete their knowledge building. Additionally, students with holes or gaps in their learning may find computer simulations a good way to incorporate foundational information into their understanding. Simulations also provide multiple chances to practice that including higher risk attempts that could cause spectacular failures and to learn, retry, and master new skills more rapidly and with less effort than through experiences not mediated by computers. In teacher preparation, simulations that provide targeted feedback can develop teachers’ understanding and practice, and may be as effective as in-classroom field experience.

3.0 Simulation Theory (ST)

The history of simulation theory reaches back quite far. Simulation (or empathy) has roots in Dilthey’s Verstehen methodology and Goldman (unpublished) argues that the great philosophers Hume and especially Kant had strong simulation in learnings. Similarly, Perner & Howes (1992) describe that simulation is an old idea in developmental psychology circles which has great importance in Piaget’s psychology. In particular, simulation – known as role-taking or perspective-taking in Piaget’s theory – helps young children overcome their egocentric views.

According to Fuller (1995), simulation and empathy were “killed and buried” by the positivists (p. 19). They distinguished between the context of discovery and the context of justification and claimed that empathy only belonged to the former context. While simulation can be used as a great heuristic device to suggest predictive and explanatory hypotheses, it cannot be used to justify these hypotheses – formulation and testing of generalizations have to be done for a proper justification. However, empathy and simulation have been resurrected in the last few decades. Putnam (cited in Fuller, 1995, p. 19), for example, argues that empathy plays a role in justification of hypotheses because it “gives plausibility”.

Simulation theory (ST) today has a strong influence on the philosophy of mind debate. ST suggests that we do not understand others through the use of a folk psychological theory. Rather, we use our own mental apparatus to form predictions and explanations of someone by putting ourselves in the shoes of another person and simulating them. ST is often described as an off-line simulation, although there are philosophers who maintain that off-line simulation is only an ancillary hypothesis of ST (see Davies & Stone, 1995a, p. 4). In off-line simulation, one takes one’s own decision-making system off-line and supplies it with pretend inputs of beliefs and desires of the person one wishes to simulate in order to predict their behavior. One then lets one’s decision-making system do the work and come to a prediction.

There are many variants of ST, some differing more than others. While some philosophers suggest a hybrid theory of Theory Theory (TT) and ST, others argue that ST should replace the predominant TT. Gordon, for example, who holds some of the strongest claims, suggests that simulation is fundamental to the mastery of psychological concepts and that it has ramifications for the ontology of psychological states (Fuller, 1995). While there are many varieties and different views of ST, all have in common that simulation acts as a very effective device for forming predictions and explanations. This leads to an important implication of ST. Since simulation depends on one’s own mental apparatus, it is clear that ST (in contrast to TT) is attributor dependent.

  

4.0 What are the differences between modelling and simulation?

            Modeling is creating a ‘model’ which represents an object or a system with its all or subset of properties. A model may be exactly the same as the original system or sometimes approximations make it deviates from the real system.

            Simulation is a technique of studying and analyzing the behavior of a real world or an imaginary system by mimicking it with a computer application. A simulation is working on a mathematical model that describes the system. In a simulation, one or more variable of the mathematical model is changed and resulted changes in other variables are observed. Simulations enable users to predict the behavior of the real world system. Simulations are also used to train people for some specific activities and react to unexpected situations.

5.0 Why use modelling and simulation?

Modelling is a method of solving problems, in which the system under study is replaced by a simple object that describes the real system and/or its behavior and is called a model. Experiments via simulation model have several important advantages versus physical experiments. For example is by using simulation, we can save our time. As we know, in the real world evaluating the long-term impact of process or design changes can take months or years. A simulation model will inform our thinking in only minutes. Besides, simulation also can save our money. Designing, building, testing, redesigning, rebuilding, and retesting of the whole project can be an expensive project. Simulations take the building or rebuilding phase out of the loop by using the model already created in the design phase. Most of the time the simulation testing is cheaper and faster than performing the multiple tests of the design each time. Furthermore, we can get accurate results from the simulation. A simulation can give the results that are not experimentally measurable with our current level of technology.

The simulation also can give benefits during conducting experiments or any projects. For example, computer simulation offers the opportunity to experiment with phenomena or events, which for a number of reasons, cannot normally be experimented with in the traditional way. Bork (1981) remarks: 'Simulations provide students with experience that may be difficult or impossible to obtain in everyday life'. In class, it is not possible to experiment actively with an economic system. The only thing the teacher can do is to discuss the nature and content of the system. Experimenting would surely be useful because this can generate an insight into the functioning of the economic system. Besides, computer simulation programs can be used in education to give the student more feeling for reality in some abstract fields of learning. Foster (1984) says about this: 'Simulations can be entertaining because of dramatic and game-like components'.

6.0 When to use modelling and simulation?              

Researchers studying the use of simulations in the classroom have reported positive findings overall. The literature indicates that simulations can be effective in developing content knowledge and process skills, as well as in promoting more complicated goals such as inquiry and conceptual change. Gains in student understanding and achievement have been reported in general science process skills and across specific subject areas, including physics, chemistry, biology, and Earth and space science (Kulik 2002).

Simulation is used before an existing system is altered or a new system built. The reason is  to reduce or minimize  the chances of failure. So, the specifications will be meets, unforeseen bottlenecks can be eliminated, the resources will be prevented under or over-utilization and the system performance can be optimized. Simulations should be used in conjunction with hands-on labs and activities that also address the concepts targeted by the simulation. A simulation generally refers to a computerized version of the model which is run over time to study the implications of the defined interactions. Simulations are generally iterative in their development. One develops a model, simulates it, learns from the simulation, revises the model, and continues the iterations until an adequate level of understanding is developed. Simulation should be used when the consequences of a proposed action, plan or design cannot be directly and immediately observed. When preceding a hands-on activity, a simulation may familiarize students with a concept under a focused environment.

Modelling and simulation is fast becoming a familiar term and tool among students in the science subjects. But it is more than that. Modelling and simulation is a discipline with its own body of knowledge, theory, and research methodology. At the core of the discipline is the fundamental notion that models are approximations of the real-world. Models are created approximating an event. The model is then followed by simulation, which allows for the repeated observation of the model. Analysis, the ability to draw conclusions, verify and validate (V&V), and make recommendations based on various simulations of the model, is the third component to modelling. These basic precepts coupled with visualization, the ability to represent data as a way to interface with the model, make modeling and simulation a problem-based discipline that allows for repeated testing of a hypothesis. Teaching these precepts and providing research and development opportunities is core to modeling and simulation education and research.

7.0 What is modeling and simulation experiment?

            Simulation experiments are no less instructive, but are typically best run using a structured and organized methodology. Once, finish the system model, to get the most out of simulation experiments, we need to manage what design factors to consider, what analyses to run, and what performance metrics we want to analyze. With these and other options, it’s easy to see that the experiment matrix can get pretty complicated. So, a way to manage simulation experiments is important.

STELLA software is an example of simulation and modelling that can be used to conduct any experiment or projects. It is a flexible computer modelling package with an easy, intuitive interface that allows users to construct dynamic models that realistically simulate biological systems. Given the combination of ease of use and modeling power, the STELLA system is ideal to interface with student investigative experiences.  In its most basic form, modelling in STELLA proceeds in three steps which are constructing a qualitative model, parameterizing it, and exploring the model's dynamics. STELLA modelling is employed in combination with investigative exercises and experiments. The modelling helps students develop hypothesis, explore predictions, summarize experimental results, and extend their results to novel scenarios.  STELLA provides the flexibility to allow students to model a variety of experimental systems and the power to provide for meaningful outcomes that relate to specific biological content.

8.0 Constructivist lesson design that integrates modelling and simulation

Constructing a STELLA model involves three steps which are constructing a model, parameterizing a model and exploring model dyanamic. Constructing a Model is to build a qualitative model, modelers first define stocks.  Stocks represent anything that can accumulate or changes in number and are related to the biological question of interest. In addition to tangible, physical accumulations, stocks can represent degrees of non-physical entities such as knowledge.  Next, users construct links to variables that affect the size of the stocks.  These are usually direct inputs or outputs modeled using flows.  For example in a population, births would represent a flow into the population.  The magnitude of these flows can be adjusted by converters using links or be affected by the size of stocks in a density-dependent manner. During this first modeling step, students are forced to consider what the essential elements of the biological problem are, and how they qualitatively influence one another.  Their resulting models are not unlike concept maps.

The second step is parameterizing the model. During this step, students quantify the relationships among elements in their model.  STELLA allows both linear and non-linear relationships to be expressed.  Once again, students need to apply their understanding of the biological problem to assist in this process. The last step is exploring model dyanamic. This is to explore the model output.  Modelers generate output in tabular and/or graphical form to explore quantitative or qualitative outcomes.   Also, modelers can manipulate parameters easily and perform sensitivity analysis.   

STELLA modeling is combination with investigative exercises and experiments.  The modeling helps students develop hypotheses, explore predictions, summarize experimental results, and extend their results to novel scenarios.  STELLA provides the flexibility to allow students to model a variety of experimental systems and the power to provide for meaningful outcomes that relate to specific biological content. 

There are many samples of simulation experiment in STELLA software. The example of an experiment that I choose is a Simple Nitrogen Cycle.

            The nitrogen cycle is the process by which nitrogen is converted between its various chemical forms. This transformation can be carried out through both biological and physical processes. The important processes in the nitrogen cycle include fixation, mineralization, nitrification, and denitrification. The nitrogen cycle is of particular interest to ecologists because nitrogen availability can affect the rate of key ecosystem processes, including primary production and decomposition. Human activities such as fossil fuel combustion, use of artificial nitrogen fertilizers, and release of nitrogen in wastewater have dramatically altered the global nitrogen cycle.

            Nitrogen is present in the environment in a wide variety of chemical forms including organic nitrogen, ammonium (NH4+), nitrite (NO2-), nitrate (NO3-), nitrous oxide (N2O), nitric oxide (NO) or inorganic nitrogen gas (N2). Organic nitrogen may be in the form of a living organism, humus or in the intermediate products of organic matter decomposition. The processes of the nitrogen cycle transforms nitrogen from one form to another. Many of those processes are carried out by microbes, either in their effort to harvest energy or to accumulate nitrogen in a form needed for their growth. The diagram above shows how these processes fit together to form the nitrogen cycle. The nitrogen Cycle includes nitrogen fixation, conversation of N_2, assimilation, ammonification, nitrification, denitrification, and anaerobic ammonium oxidation.

By using STELLA software, there are four parameter involves such as humification fraction, mineralization fraction, nitrogen per unit biomass and fixation productivity. Humification process is the transformation of organic matter into humus, is a fascinating process. Organic materials such as manure or field wastes,when disked into the upper three to six inches of topsoil, will undergo several changes. The humification process involves first catabolism, then anabolism. Mineralization is the process by which microbes decompose organic nitrogen from manure, organic matter and crop residues to ammonium. Because it is a biological process, rates of mineralization vary with soil temperature, moisture and the amount of oxygen in the soil (aeration). 

The experiment was run. The result includes four graphs. At the beginning, the experiment was run without changing any parameters. This result will act as a controller for the whole experiment.

Graph 1

Graph 1 act as a control for this experiment. The values of all parameters were fixed and will be referred to the next experiment. From the graph, students will observed that, when the value of  the humification fraction is 0.2500 and mineralization fraction value is 0.0500, all the values of nitrogen in humus (humus: refers to any organic matter that has reached a point of stability, where it will break down no further and might, if conditions do not change, remain as it is for centuries, if not millennia), nitrogen in organic matter, nitrogen in biomass and available nitrogen constant for each time. This is because, the organic matter becomes the limiting factor.

For the second time running, the parameters of humification fraction was acting as manipulated variables. The humification fraction button was adjusted and the value is increased to half of the fraction,0.5100. The result obtained must compared to Graph 1.

Graph 2

From Graph 2, when the humification fraction increased, students will observed that, the nitrogen in humus also increased  and the value of nitrogen in organic matter becomes decreased. It is because, when the process of humification increased, the amount of organic matter transforms into humus become greater. So, the nitrogen in organic matter reduced (due to a large number of nitrogen in organic matter converted into humus).

 The values of nitrogen in organic matter higher than nitrogen in biomass in time 0.00 to 5.00. Over time 5.00, both values were same and constant. While, the values of nitrogen available were lowest than others. At a certain time, all the values of parameters become constant due to limiting factor of organic matter.

For the third time running, the parameters of humification fraction was acting as manipulated variables. The humification fraction button was adjusted and the value is increased to the maximized values which is 1.0000, higher than the second run. The result obtained must compared to Graph 1.

Graph 3

From Graph 3, when the humification fraction maximized, students will observed that, the nitrogen in humus also increased (greater than Graph 2)  and the value of nitrogen in organic matter becomes decreased (lower than Graph 2). It is because, when the process of humification increased, the amount of organic matter transforms into humus become greater. So, the nitrogen in organic matter reduced (due to a large number of nitrogen in organic matter converted into humus).

The values of nitrogen in organic matter lower than nitrogen in biomass in time 0.00 to 1.00. Over time 1.00, both values were same and constant. While, the values of nitrogen available were lower than others but precise to the values of nitrogen in organic matter. At a certain time, all the values of parameters become constant due to limiting factor of organic matter.

For the last time running, the parameters of mineralization fraction were acting as manipulated variables. The mineralization fraction button was adjusted and the value is increased  to 0.1000. The result obtained must compared to Graph 1.

Graph 4

From Graph 4, when the mineralization fraction increased, students will observed that, the nitrogen in organic matter increased and the value of nitrogen in humus decreased. It is because, when the process of mineralization increased, more nitrogen in organic matter will decompose into ammonium. So, the nitrogen in humus reduced (due to a large number of nitrogen in organic matter decomposed into ammonium)

The values of nitrogen in organic matter higher than nitrogen in biomass in time 0.00 to 5.00. Over time 5.00, both values become constant. While, the values of nitrogen available were lower than others. At a certain time, all the values of parameters become constant due to limiting factor of organic matter.

After run the experiment by using STELLA software, students will realized that, the results was changing due to the adjustment of each parameters. Students also can relate the humification fraction and mineralization fraction was closely involve in humification process and mineralization process. Both process very important and will affect the nitrogen cycle.

At the end of simulation experiment, students can conclude that, the values of humification fraction and mineralization fraction are dependent on the amounts of organic matter. If the amount of organic matter become the limiting factor, the process will affected.

9.0  Conclusion

            STELLA software is an example of the best computer simulation experiment. After run the experiment by using this software, the experiment becomes more interesting and easier. As we know, simple nitrogen cycle occurs for a long time. So, by using  this software, I realize that simulation in education is very important. As we know, science subject has many experiments to do. By using simulation experiment, teacher and students can run the experiments in class easily.  Additionally, we can change the  parameters to get different result. Furthermore, graphs analyzing become more easier and interesting.  

           

For the conclusion, computer simulation has the potential to enhance the way of teaching and learning. It allows us to bring even the most abstract concepts to life for students and incorporate otherwise impossible or impractical experiences into daily instruction. The students will engage in inquiry, further develop their knowledge and conceptual understanding of the content, gain meaningful practice with scientific process skills and confront their misconceptions. Additionally, the students also will gain scientific habits of mind that are both encouraged in the recent reform documents and necessary for future careers in Science.