“Teaching is not filling a pail, it is lighting a flame.”
— attributed to Heraclitus of Ephesus (535–475 BCE) —
In this chapter, we will show the importance of the self-teaching educational-research projects as an extension of compulsory education and a psychological motivation underlying the understanding of galaxy dynamics.
2.1 Attractive science education in basic curriculum
Technology, the use of scientific knowledge for practical purposes, has a profound impact on the way we live and on the quality of our lives. A powerful method of science and research endeavor brings us every aspect of our comfort. People should know merits behind their everyday lives brought by the science. A science teacher that serves as a local expert in some specialized field of the science should teach others about these advantages.
Until the 18th century, great scientific discoveries were not explained nor popularized. Scientific knowledge was gathered for its own sake and it had a few practical applications. Scientific knowledge should be disseminated to a wider audience of people, even if they are not directly involved in scientific research. Scientific work should be made clear from its foundations. In an open and democratic society, science should be accessible to everyone and not become an exclusive domain of specialists. All people are able to understand science; scientific knowledge should be available to all of them. When new findings are not transferred to people, they lose their significance; instead, a mix of pseudoscience emerges.
The role of a traditional teacher in every educational system is to transform the majority of students from a state of pure desire to receive good grades and succeed (secondary motivation) into a state of desire for the knowledge itself (primary motivation). From my experience as both a student and as a teacher, I believe that teachers at lower educational levels should always serve physics in the basic curriculum in an easy and interesting way, together with a classical lecturing.
Astronomy is probably the most visually exciting science and it can capture the attention of those students, who would otherwise hesitate to choose a physics course (seminar, field of study, etc.). The universe has interesting topics to study for nearly all students without a difference in age or abilities. The universe is the source of inspiration, unusual images and information, which can capture the students’ attention and awake other questions and curiosity. However, studying the universe is more than looking to exciting pictures of space with a great aesthetic experience. It also answers the most fundamental questions for which every human being need to know an answer. From this point of view, the knowledge of general physics might be more interesting. Students can be motivated by the space science.
Very little of this curiosity of physics is present in the traditional physics course. Students usually associate learning physics with a rote memorization of laws.
2.2 Self-teaching with educational-research projects
Primarily motivated students can easily start their own education. Many people think of education as something that occurs in a school or classroom. However, knowledge-eager students can gain additional skills behind the walls of schools. This self-teaching approach in the “New Pedagogy” is based on motivated people studying outside of general compulsory education. For example, a study conducted in the United Kingdom revealed that one in six people undertakes a learning project outside of formal education system. Students should have a chance to acquire other knowledge based on their interests, which are not the interests of their teachers through the self-teaching approach – from an arbitrary area of art or science. This approach is the part of lifelong education. Anyone who does not engage in the self-education, voluntarily or not, lags behind the demands of the time.
The self-teaching project requires an active approach from the student. Students are learning when they are active and remember information they understand. “Learning is not a spectator sport.” Students are not learning only compiled knowledge, but they are constructing and updating a memory map of abilities through their own activity and effort. Students are subsequently able to apply the acquired knowledge in other situations. Students remember competences they gathered through their own endeavors and efforts. Students should look for information on the internet and classify it independently. Students should learn to read technical writings of others. In educational-research projects, students are developing a whole spectrum of cognitive abilities – thinking and reasoning, memory and learning, attention, perception, judgment, imagining and problem solving.
Every student as a human being is different, with different abilities, interests, needs, different learning curve and speed. The self-teaching approach has many humanistic effects leading to the student’s individual personal development. Self-teaching gives to the student a greater degree of self-fulfillment, the liberty of action and the power of control. The student then has a positive enjoyment from an education. This will eventually start positive student attitudes towards the science and high technology. A free choice raises a motivation and the education is more meaningful. Education is spontaneous and naturally rises from individual abilities, interests and needs. Such activity, arising from personal interest leads to a concentrated work and self-nurture. Output of such a creative education is a product, which can serve as the learning material for others – the student is in the role of the teacher of others. On the other side, the student is completely responsible for his or her actions and asserts.
A teacher usually plays a leading role and determines the speed of education. I am convinced that it is insignificant to go sit on a lecture and write down derivations lasting several pages. A better scenario is that a tutor should give to the student a complete derivation with all related thoughts. The student should be provided with educational materials showing problems from various viewpoints. The student then walks through the educational materials by the self-teaching approach through a trial and error. For this purpose, a recorded form of language is better than a spoken language, because students can jump over things known to them, and return back and read over and over the things that they do not understand.
Educational-research projects from various areas of the science are on the Internet and there should be more of them. I would like to encourage others to make their software and thoughts freely available so that everyone can learn and appreciate them. Accompany your scientific software with documentation and publish it on your webpage so that it will serve for the greatest possible use to the public. These projects contribute to the globalization and democratization of education and research.
Piet Hut and Junichiro Makino started the initiative Open Knowledge based on educational-research project. Basic underlying goals of this initiative are namely
· self-contained description: a high-school student should be able to start at page 1, and work her or his way through the educational series,
· provide all the details needed when starting from scratch,
· walk through the actual process of learning through trial and error,
· audience: anyone interested.
I am convinced that education will evolve closer to an ideal model of total differentiation or individualized learning together with forms of social and interpersonal education. Apart from the latter, thanks to the development of computer and information technology, there is a glimmer of light for the individualized education with self-teaching educational-research projects and e-learning programs made-to-measure to student’s needs right now.
2.3 Research method as the form of education
Teaching methodologies can be arranged on the basis of relative amounts of the teacher’s and student’s contribution to the education. A similar division depends on how much emphasis the teacher puts on learning and how much is placed on student’s personal individual cultivation. At one end of the spectrum the teacher is the controller of the class and the facilitator of knowledge. At the other end is a free discovery method, which is characterized by students exploring subjects of their own interest in ways most comfortable to them.
The research method of education requires individual problem solving of students for an integrated problem assignment. Teacher’s activity is suppressed in this form of education. Teacher’s task is to identify and select right problems that evoke a student’s complex creative behavior, and let them select their own decision procedure. Teacher’s role is no longer central; the teacher becomes an adviser. Teacher’s duty is to stimulate and cooperate with the student, not just examine the student’s knowledge.
The research method of education is a method of active learning that develops complex intellectual abilities in connection with a work on a complex and uneasy project. Active education-research demands from the student thinking not only about technical matters of the project, but also about activities encompassing this project, such as a stress, time schedule, relaxation, sport and free time usage.
The research method of education requires classical forms of perception and reproduction, which are directly incorporated inside it. The research method, however, also requires the discovery and fixation of complex cognitive operations and the interiorization of algorithms to solve problems. The research method is more demanding than a formal learning process in the education system and involves various activities and resources.
The self-teaching in research method also has social aspects. The self-teaching does not mean that all learning will take a place in isolation from others. Although students work in part independently, they must always cooperate in larger educational-research projects. Students must participate in study groups and the overall success of the project depends on each member of the group. Students must develop communication skills and use a global consciousness to solve problems with others on the Earth via the Internet.
I am convinced that students must be exposed to research level problems at an early stage of their education in order to sustain a continuous advancement of technology and science in long terms. On the other hand, education is a complex system concerning very complex people. The research method of education is not suitable for every educational situation or every student on every school. It depends on the teacher how wisely she or he will choose the methods of education.
2.4 Student’s motivation
Why should students want to start learning about galaxy dynamics simulations?
There are psychological aspects motivating our will to understand the universe (nature) around us. For people, it is not sufficient to accept natural phenomena as they are. Our brain needs to understand causes of phenomena, what is their deeper nature. When there is no scientific clarification, a human mind is looking for an alternative mythological explanation. As the only known species of billions that ever lived on the Earth, modern humans were posing questions concerning the nature of the world around them since they had ability to ask questions more than 100,000 years ago. We are an integral part of cosmos, so we want to deeply understand the patterns of its behavior.
Other motivation rises from the desire to be able to control state-of-the-art technological devices – the simulations of galaxy dynamics are very demanding in terms of computational power. From the dawn of computer technology, leading role for pushing its limits was in the hands of physicists and astronomers. In 1990s, several Gordon-Bell prizes won N-body simulations for the most powerful numerical calculations (e.g. Warren et al., 1997). The GRAPE-4 computer, which exceeded as the first computer on the world 1 TFLOPS ( calculations with “real” numbers every second, literally “floating-point operations per second”) performance limit in 1995 was dedicated to N-body simulations of star clusters. Motivation is still going on as the GRAPE-DR is expected to be the first computer breaching 1 PFLOPS ( FLOPS) barrier in 2008. It will be used for N-body/SPH (Smoothed Particle Hydrodynamics) simulation of the Milky Way galaxy.
Students may be also motivated to excel in some field of the science. In many countries and schools, where the teaching of physics and astronomy is limited to theoretical equations and some old instruments, the usage of computers would be a great improvement. N-body simulations have led to a significant progress in the galaxy dynamics understanding. Once the student learns the basics of N-body simulations, he or she may begin to improve it by adding other physical phenomena while creating an astrophysical laboratory, obtaining completely new results and become researcher in a highly attractive and developing field of astrophysics or cosmology.
Motivation for choosing the field of computer simulations in physics can also stem from a practical aspect of employment. Education should prepare the student for a future occupation. Computational physics and programming is good for many jobs both in industrial and academic sectors.
The student can also visit many N-body schools arranged all over the world, e.g. MODEST (MOdeling DEnse STellar Systems), Cambridge N-body School, Computing Our Universe! or Late Summer School on N-body Simulation.
2.5 Computer models and simulations in education
A virtual nature, virtual universe or virtual reality is essential for the science education. The virtual reality mimics the real world and students can safely perform experiments on it. Students can perform thought experiments otherwise impossible to do in reality. Moreover, a computation is becoming as important as a theory and experiment. In the past, the natural sciences were characterized by interplay between an experiment and theory. This has gradually changed and instead the theory, experiment and simulation are three equally essential elements of natural sciences today. Yet, the classical education is still lagging behind the teaching simulations of nature in a whole way.
Physics as a school subject should reflect the methods of physics as science. Computers are inherent tools in physics from the basic scientific research to commercial and industrial applications. If computer modeling and simulations are important in physics science, they should play a comparative role in the physics education. Through computer simulations, students are able to explore new phenomena that were not accessible previously. Modeling and simulations expose students to contemporary modern physics.
Modeling and simulations are very effective for vivid education. Students manage the simulation and are free to vary inputs to obtain outputs according to their choice, to form hypotheses and to test them, asking questions such as “how?” and “what if?” Numerical models and simulations give to students a deeper understanding of the physics they have learned in classes. They can confront analytically solvable models acquired during classes and compare them with cases that are more realistic. Alternatively, they can just play with a working model.
From the theoretical point of view, numerical models and simulations are the best tool to understand physics involved in galaxies. Modeling and simulations allow the students to understand basic galaxy dynamics concepts that need a high degree of abstraction. Fantasy and creativity are important qualities of students that create computer models and simulations. The student integrates theory and experimentation in computer simulations, and then modifies computer models and tunes numerical solutions.
Computer experiment connects a model provided by a theory with calculation carried out by a machine simulating the real experiment. Numerical computational techniques can be used to improve our understanding of nature. Students can learn about the science through an experience.
Models of physics and computer simulations can also be used in mathematics, so that the student can identify the usability of mathematics in physics applications. It is easier to understand, solve and receive the solution of mathematical problem when it has a physical background and relations. I recognized that some students of mathematics or physics are a bit fearful of programming computer models. On the other hand, students of computer science are usually intimidated by the mathematics.
This is the next dimension for which current pedagogical theories call: an interdisciplinarity in education – a connection between many fields of science: computational physics, which includes theoretical physics as the main driver, computer science with numerical analysis and computer languages as an expression for mathematical and computational representation of physics and observational (experimental) astronomy. Moreover, this can be expanded into other highly attractive fields like biology, chemistry or biochemistry.
Physics as the connecting link between natural sciences can be very useful. Research conducted among students of different branches of science showed that undergraduate physics students display more understanding of physical models versus reality than did a graduate students of biology and chemistry faculties. N-body simulation as the versatile method in computational physics is well suited for the science education with computers.
This thesis is giving strong emphasis on using numerical models of nature. Students are sometimes confused with the relation between “laws of physics” and reality, identifying specific physical model or theory with the reality. In the virtual nature, student is able to change “laws” governing the behavior of their universe and has a power to create her or his own universes. Through this experience, the student will learn that contemporary models are imperfect models and just try to imitate reality.
Computational physics gives to the student many competences:
1. The ability to express the laws of nature in the form of equations and to manipulate them in a variety of situations: analytic skill,
2. the ability to express these laws in the form of quantifiable entities,
3. the ability to understand natural scales and the estimation of scales,
4. the ability to have approximation skills,
5. numerical skills,
6. intuition and large problem skills.
When students learn a computer how to solve the physical problem in the form of computer program, they will have a perfect understanding about how to solve the problem without the computer. More important, the student will develop the ability to think in a critical sense, because the student will not be a mere user.
Therefore, I propose a four-level educational architecture (Figure 2–1), which is divided into four levels. The first level is for casual students who are interested in nothing more than in animations that are suitable for public presentations. Students in the second level will use an existing simulation program, change input parameters and look for results. Third level students will be more interested and will read technical information written in the second part of this thesis to get a better insight. The four-level architecture culminates with students reading, programming, analyzing and expanding galaxy dynamics simulations, and with a deep understanding of numerical simulations.
Students in the first level are only occasional people caught by a nice animation. Since galaxies evolve very slowly in comparison with one lifetime, it is hard to see any changes in real galaxies. Galaxy simulation allows to actually see a model galaxy evolving with student’s own eyes, something that is not possible in the real universe, but what is actually happening. The second level is for users who are interested only in using galaxy models and simulations, executing the software applications. Having some deeper doubts, the user might want to know how galaxy dynamics simulation works: its concepts, routines and different approaches.
The level 3 user will be interested in reading the technical part of this work. It focuses on the theory behind the galaxy dynamics, and on algorithms used in the simulation software. In each chapter, there are explanations of the algorithms. In addition, the user can access the project’s web site, where all materials including codes and animations regarding this work are listed and can be downloaded. If the student is willing to contribute, she or he will also look at commented source code, to better understand how the software works.
Figure 2–1: The four-level educational pyramidal architecture that is grounded on the solid foundations of primary motivated students. Upper levels contain students with the high interest and understanding of numerical simulations.
At this point, the student will be able to develop a new module (which could be an assignment, for instance) or upgrade the old ones. This is the fourth level. People who get into this level become developers that extend the code and make up the part of the galaxy dynamics worldwide team. It is our desire that all users reach this level, but no one is obliged to do so. The final goal of this four-level user approach is to provide to the student with a means of learning simulations of galaxy dynamics in a whole way. The student will be able to read about it, understand its principles and further expand it.
Now numerical galaxy dynamics should not be a mystery to the student, and the gap between the concepts being taught in classes and the state at the research level will be minimized.
2.7 Concluding remarks
In Chapter 2, we have shown that physics education is an important and crucial element for human society. Students should be more motivated by their teachers with less importance on learning and more emphasis on differentiation, individualization and self-teaching. It is for this purpose that the formation of self-teaching projects is suggested. Together with advancement in science and technology, an early connection of education and research should be made. Self-teaching educational-research projects created by specialists in their fields should be made freely available on the Internet as a service to society. A research method of education can develop student’s abilities in a complex way. Computer models and simulations of nature’s behavior are acknowledged as useful, providing connections between various fields of science education. A scheme incorporating these approaches is suggested in the “four-level educational architecture”. Surely, education is a complex system and this concept may not be valid for every student.