Chaos Theory

Over the last fifty years Chaos Theory has evolved as a new science which assumes that the natural order is irregular, discontinuous and erratic (Gleick, 1987). Newtonian physics implies that there is a rational order to everything, that we can predict the events of any system if we are able to plug in enough variables. The idea behind “chaos theory” is that we can predict what systems might do, but we cannot be sure. Everything exists as a series of possibilities.

Since the beginning of the twentieth century several other sciences have evolved that have sought to solve the problems in prior models. For example, the theory of relativity eliminates the illusion of absolute time and space. Quantum mechanics eliminates the Newtonian dream of controllable measurement processes, as well as the fantasy of deterministic predictability. Chaos theory, the third new science, embraces irregularity as a norm. Scientists from different fields have begun to observe the regular patterns within the irregularity of the natural world.

In the old views of nature, notes Gleick (1987), it was held that simple systems behave in simple ways while complex systems imply complex causes. In the new view, it is believed that simple systems give rise to complex behaviors and complex systems give rise to simple behaviors (Snyder, 1995).

The new science of chaos centers around two points. The first is the exploration of the hidden order that exists within the chaotic systems. The second is the study of how self-organization emerges from chaos (Hayles, 1990).

The three principal conditions for a chaotic system are: (1) that it operates in a non-linear way; (2) that it is iterative (the output of one cycle becomes the input of the next); and (3) that small variations in initial conditions lead to large differences in outcomes. Many systems within educational organizations appear to meet these conditions (Cunningham, 2000).

The concepts of chaos theory can explain the way schools work. For example, teachers do not exist as separate entities, but are affected by the relationships that exist within schools. It may also shed some light on how we can deal with and understand how things in our classrooms, schools, and entire communities are interrelated and all reflect in some manner upon each other.

There are several aspects of chaos theory such as nonlinearity, complexity, butterfly effect, fractals and feedback mechanisms that may have significance for educational settings.

Nonlinearity

In a linear system there is a simple cause and effect relationship; A causes B which causes C, and so on. However, a chaotic system is nonlinear. A may not necessarily cause B at all times. Lots of variables come into play and interact with each other. School systems look like nonlinear chaotic systems, too. In school district A, the purchase of new computers might have a positive impact on student achievement, while in school district B, this might bring little or no gain in student achievement.

It is widely believed that experienced teachers have better classroom control. If you have a veteran teacher in a classroom, you will have an orderly environment and the administrators, thinking in a linear way, might believe that the more veteran teachers in a building, the more orderly the environment will be. That might not be the case in every school district, especially in urban schools; there are instances where young and inexperienced teachers contribute positively to the school environment much more than veteran teachers.

Complexity

Chaotic systems take complex forms, making their precise measurement difficult if not impossible (Glickman, 2001). Different measurement instruments have been put in place to evaluate and compare the performance of a school. However, due to the complex nature of schools, none of these assessment methods seem to measure precisely the school performance and have very limited validity for the following reasons (Cunningham, 2000):

• The prior achievement of pupils is not taken into account and this is a major factor in pupil achievement at a later stage.

• Schools are differentially effective in different subjects and with pupils of different ability, which is not reflected in a single figure.

• Schools change over time; however, the achievement data used reflects only one group and is essentially historical data.

• Student mobility between schools is not reflected in the assessment.

• Social factors, sex of students, ethnic origin and social background are not taken into account. These factors are out of the school’s control.

Therefore, assessing school performance and comparing one to another have become increasingly difficult given the complex nature of today’s schools.

The Butterfly Effect

The butterfly effect means that a small and seemingly unrelated event in one part of a system can have enormous effects on the other parts of the system. Theoretical meteorologist Edward Lorenz made the term ‘butterfly effect’ famous when he argued that a butterfly stirring its wings in Bejing today could unleash powerful storms in New York city next month. One implication of sensitive dependence on initial conditions is the impossibility of predicting not only next year’s weather, but the long term future of any chaotic system (Glickman, 2001).

In terms of school improvement, what we understand from the butterfly effect is that it is impossible to predict the long-term effects of school improvement efforts. Planning in a chaotic system like a school should be medium range (one or two years) rather than long range (five to ten years). Formal planning in an unpredictable system needs to focus on process rather than product with the goal of producing “a stream of wise decisions designed to achieve the mission of the organization” (Patterson, Stewart and Purkey, 1986).

The butterfly effect ensures that no lesson will ever go completely as planned, or have the same effect on any two students. It indicates the need for teacher flexibility in teaching, as well as the need for individual attention to students, each of whom is experiencing a given lesson within his or her own personal context (Glickman, 2001).

Fractals

A fractal is a geometric shape that is similar to itself at different scales. Mid-sized branches of a tree are remarkably similar in shape to the larger branches from which they come. Smaller branches, in turn, are the same shape as the mid-sized branches from which they come, and so on.

Through work with fractal generations, it has become apparent to scientists that predictability does exist (known shapes re-appear), and randomness plays an important and unexpected role. What has been learned is that, within chaotic and seemingly unpredictable systems, structures of order exist through which the system recreates itself.

Complex social systems can also reveal self-similarity on different scales: at each level of the system, specific patterns of organization and culture reappear. Like fractals in nature, schools reveal self-similarity in different scales. For example, a school-wide staff development day, a department meeting, a classroom lesson, and a halfway interaction between a teacher and student might all reveal the same cultural characteristic. Thus, reflective inquiry at the school, team, classroom and individual level can help educators better understand their school culture, change needed, and pathways to improvement (Glickman, 2001).

By being reflective practitioners, teachers can develop their teaching skills, acquire more insightful experience in their fields and learn to look at problems from a different perspective. They also understand their weaknesses, areas of strengths and recognize the repeating patterns of their teaching styles.

Feedback Mechanisms

Chaotic systems contain feedback loops enabling outputs to feed back into the system as input. Feedback can bring stability or turbulence to a system. For example, a thermostat is a feedback mechanism that causes temperature stability. Conversely, when the sound from a loudspeaker feeds back through a microphone, it is rapidly magnified to create a disruptive shriek (Gleick, 1987). Feedback can also cause a system to move toward greater levels of complexity.

Feedback in schools can take the form of student performance data, survey results, quality circles, third party reviews, and so forth. The important thing is that meaningful data on the results of change efforts be made available to teachers, and that they be given opportunities to reflect on the data and redirect their change efforts accordingly.

With all the unpredictability present in classrooms, beneficial feedback is critical for both teachers and students. For teachers, student performance data, direct student feedback, and classroom observation data can all assist them to improve classroom instruction. For students, feedback on their cognitive and affective performance-from teachers, parents, and peers-is an essential part of the learning process. The fact that in chaotic systems like classrooms output becomes input means that the artificial distinctions we often draw between learning and assessment need to be removed: in reality, learning and assessment cannot be separated (Glickman, 2001).

Conclusion

The deterministic view of education that schools are simplistic, cause-effect systems which can be easily manipulated, quantized and controlled is not addressing the problems of today’s schools. From an alternative perspective, chaos theory gives us an understanding that the things we consider unimportant or trivial in our daily lives might have an equal weight in terms of affecting the results as the things we consider important. Just as it is characterized in the Qur’anic teaching that every minute thing or action is recorded in a Book regardless of its proportion. “Whatever your preoccupation (O Messenger), and whatever discourse from Him in this (Qur’an) you may be reciting, and whatever work you (O people) may be doing, We are certainly witness over you while you are engaged in it. Not an atom’s weight of whatever there is in the earth or in the heaven escapes your Lord, nor is there anything smaller than that, or greater, but it is (recorded) in a Manifest Book” (Yunus 10:61). It further suggests that everything we do has a significant impact on us, our communities and ultimately society as a whole.

In conclusion, chaos theory has the potential to offer deeper understanding of how today’s schools function in an ever changing world of our times.

Aydin Kara is a graduate student at University of Dayton. He studies educational leadership and administration. He can be reached at aydinkara33@hotmail.com.

References

• Cunningham, R. 2000. Chaos, Complexity and the study of Education Communities. Institute of Education.
• Gleick, J. 1987. Chaos: Making a new science. New York: Penguin Books.
• Glickman, Carl D. 2001. Supervision and Instructional Leadership: Allyn and Bacon
• Lortie, D. C. 1975. Schoolteacher. Chicago: University of Chicago Press.
• Patterson, J. L., Purkey, S. C., and Parker, J. V. 1986. Productive school systems for a nonrational world. Alexandria, VA: Association for Supervision and Curriculum Development.

Yet, how can the Web be used for something more than surfing, chatting, making money, or wasting time? Can it provide an environment for learning? Can it be used with other educational technologies? What pedagogical possibilities do these technologies bring to schools, teachers, and students? In this article, I discuss this aspect of Internet.

One of the more explosive growth areas of the Web is distance learning. Web-based distance courses can run the range from text-based, e-mail, correspondence courses to full-blown interactive multimedia presentations. The vast majority of courses more closely resemble the text-based model, while many offerings use video, audio, and even some interactivity. Of particular interest is the newer interactive multimedia technologies found on the Web, such as Java, VRML, Shockwave, and others.

Several sites offer distance-learning offerings. The World Lecture Hall (www.utexas.edu/world/lecture/) offers hundreds of courses from universities all over the world, many with multimedia components. Java and VRML applets used in education are featured at www.gamelan.com. The Internet University (www.caso.com and www.internet-university.com) offers more than 500 courses. Other exemplary sites include San Francisco State University’s “Introduction to Multimedia” course, which features excellent design, interactive multimedia, graphics, streaming audio, and chat features (www.cel.sfsu.edu/MSP/msp.html). Also there are many homepages that offer free online courses, like www.learn.com and www.free-ed.net.

Educational Uses of the Internet

The following is a list of different educational uses of Internet. This is not exclusive, but rather a starting point.

Communication: Educators and students use the Internet to communicate when they exchange e-mail, contribute to electronic discussions groups, participate in Internet Relay Chat (“chat rooms”), and use video conferencing. These tools allow Internet users to send and receive messages from one or more people at the same time. The message may include words, pictures, illustrations, sounds, or movies (Education and the Internet 1996).

Collaborative Learning: Collaborative learning involves communication as well as individuals working in a cooperative team (Erkens & Kanselaar 1995). Team members share a common task and/or project. Collaborative projects may be student-based, for example, student-to-student and classroom-to-classroom projects that rely on teamwork established by teachers from different classrooms. Teacher-to-teacher and teacher-to-expert projects provide additional assistance and create a collaborative environment (Story 1996).

Resource Sharing and Information Gathering: Resource sharing consists of publishing information on the Internet for others to view and use. For educators, this includes lesson plans, learner activities, research papers, articles, newsletters, announcements, and school policies. The Web can serve as a gateway to the Internet’s vast resources. Educators and students use the Internet to solve problems, gain knowledge, and research almost any topic (Edwards, Havriluk, and Roblyer 1997).

Presentation Medium: Educators can use electronic presentation aids rather than overhead transparencies. For electronic presentations, users need a personal computer, presentation software (e.g., Adobe Persuasion, ClarisWorks Slideshow, Microsoft PowerPoint), and a projector. Software, hardware, and/or HTML scripting allows electronic presentation aids to be viewed via the Internet.

Interacting with Web Applications: With the Web’s multimedia capabilities, Web pages are being developed in such a way that users can input data and receive an output or a product. Search engines and dictionaries are examples of such interaction. Internet users can obtain e-mail addresses, interact with “live” animation, take virtual museum tours, locate an individual’s phone numbers, play games, and create their own Web pages. Feedback and assessment can be used to monitor student progress, control the learning pace, and evaluate teaching strategies. Using HTML Forms is a simple but powerful way to collect student feedback and control it to improve teaching. Forms collect data from students using Web-based course materials. Student feedback provides instructors an informed evaluation of their teaching. By using this evaluation method, instructors can get immediate feedback on course material, teaching style, and student progress. After this, they can make the necessary adjustments.

Interactive Multimedia Technologies

Every day Netscape, Microsoft, or another company announces an exciting new piece of technology that will deliver audio, animation, 3-D graphics, or allow one to wander through virtual spaces on the Web for free. Some of these are Live Audio, Shockwave, Java, Virtual Reality Modeling Language (VRML), Active X, and QuickTime Video.

What is new about such technologies? Physics teachers using Java created an applet for projectile motion that allows users to set the launch angle and coefficient of linear air resistance.

It then animates the body’s trajectory and calculates some of its properties numerically. (http://www3.adnc.com/~topquark/fun/applets.html.) What’s new and fascinating about such applets is that they offer hard-to-do simulations of physical events, are free, can be demonstrated on several computer operating systems, are highly interactive, and can be accessed at any time by anyone in the world with an Internet connection.

What would an interactive multimedia course module delivered over the Web look like? Physics teachers could videotape real-world phenomena depicting certain laws of physics, for example, the Ferris wheel and the “whip” for circular motion. They could supplement the video with audio lecture material, allow students to manipulate variables in a Java program, use VRML to create 3-D walk-through virtual models of how the laws of projectile motion apply, animate the behavior of balls on a track, conduct a synchronous two-way conversation with one student or the entire class via chat lines, correspond with individual students asynchronously via e-mail, and then quiz and grade students using online interactive exams.

Are there other reasons for using multimedia in teaching? The power of multimedia to impact learning positively can be seen in physics. Laws of physics that run counter to students’ commonsense notions of how the world works provide a stimulating catalyst for further investigation. In “The Initial Knowledge State of College Physics Students” (Journal of Physics 1986), I. A. Halloun and D. Hestenes demonstrated that freshman physics students’ intuitive notions of the behavior of a ball leaving a track are often contrary to the laws of circular motion, a major topic in freshman physics.

Other research indicates that these misconceptions may be overcome through video and animation. In one experiment conducted at the University of Massachusetts, the path of a ball on a circled track was videotaped. A segment of the track then was removed, and another video segment captured the ball’s path as it was about to leave the track. When queried at this point as to where the ball would go next, many students get stuck: their instinctive senses tell them it will go off in an upward path or a downward, not the straight-ahead path that it actually takes. A third video segment showed the actual straight-lined path of the ball leaving the track. An animation done in Director and then put on the Web with Shockwave showed that a circle is really composed of an infinite number of straight lines, and that when the ball hits one of them it goes off in a straight line. This straight-line path is, in fact, counterintuitive to many students. Using these multimedia supplements to regular course materials could improve test grades significantly. Web-based course materials are being used extensively to provide supplementary as well as standalone instruction in educational settings. One of the Web’s most powerful elements is its ability to engage learners in an interactive format. Although many technologies allow teachers to develop interactive Web course materials and receive student feedback, many continue to use the Web only for distributing static documents. This severely limits its potential to improve the teaching-learning process. Most education Web sites provide such basic course information as syllabus, schedule, announcements, and reading lists. Others include synchronous or asynchronous communication, online testing, discussion groups, conferences, bulletin boards, and streaming audio and video. These materials are available for courses that meet in classrooms regularly and use Web materials as supplementary tools, as well as for courses delivered entirely over the Web and without any traditional classroom meetings.

Web Interactivity

Web interactivity helps engage students in the active application of knowledge, principles, and values. It also provides them with feedback that allows their understanding to grow and evolve. Chickering and Ehrmann (1998) suggest that while using technology to teach, educators should avoid didactic materials and search for technology-assisted solutions that are interactive, problem-oriented, and motivate students. Students can either read or print a static Web page; with an interactive Web page, they can interact with content, other students, and instructors, as well as participate in discussion groups, quiz questions, simulation program, conferencing, live chat, or fill out a feedback form. This Web-based informal assessment represents a cognitive behavior-modification technique designed to help students develop goal-setting behavior, planning, and self-monitoring. It also allows them to master concepts (Good and Brophy 1995). For example, students can regulate and monitor their own learning in a sequential and constructive fashion as they respond to the questions and receive ongoing feedback. In traditional, as well as Web-based courses, there is a gap between what is taught and what is learned. Reid (1997) mentions that methods of assessing the teaching and learning experience in online education are in high demand but short supply. No existing measurement adequately evaluates how well a teacher performs in a virtual classroom. Angelo and Cross (1993) observed that by cooperating in assessment, students reinforce their grasp of course content and strengthen their own self-assessment skills. Furthermore, student motivation is increased when they realize that teachers are interested in their success as learners. Teachers can empower themselves by using technologies to facilitate a proven educational process of receiving and acting on feedback from learners. This will lead to pedagogical improvements in interactive Web environments for assisting teaching and promoting learning.

Top Educational Resources on the Web

Education World (www.education-world.com): A free resource for primary and secondary school educators. It includes lesson plans, articles by education experts, and information on using technology in the classroom. Developed by people with backgrounds in education, the site contains more than 8,000 pages, a weekly e-zine, and a searchable database of over 115,000 education links. Strength: a well-organized interface to the world of primary and secondary education; original material and good annotations. Weakness: needs more quality evaluation of the links so that educators are guided toward the most valuable resources. GSN (http://www.gsn.org): Global School Net Foundation is a non-profit organization dedicated to the instructional application of telecommunications at the primary and secondary school levels. It includes a registry of the best curriculum projects, tutorials, articles about Internet use in the classroom, news and discussion, and events and contests. It also includes a link to the collaborative project with Microsoft to create a comprehensive site for education resources on the Internet. Strength: appealing interface; good selections from many sources. Weakness: inconsistent design does not do justice to the depth and breadth of offerings. Blue Web’n (http: //www.kn.pacbell.com/wired/bluewebn): This is a library of Internet-based instructional information for primary and secondary school levels. You can search this database quickly by audience type, application type, content area, and other search terms. It contains activities, lessons, references, tools, and projects listed for a variety of educational audiences, and is part of the Pacific Bell initiative (Education First) and umbrella program to benefit education (Knowledge Network). Strength: quick way to search for lessons and resources; good method for reviews of resources; Weakness: a bit over-generous with the ratings stars, caveat surfer. AskERIC (Educational Resources Information Center) (http://ericir.syr.edu): ERIC is a clearinghouse on information and technology. Its collection of education-related resources is funded by the American government. AskERIC includes a question-and-answer service, a virtual library, and a research and development team. Collections are well-organized and frequently updated. Strength: broad coverage of many educational topics; extensive support for educators. Weakness: graphic slab design of Web; coverage is not deep in all areas; some resources are outdated. EDUCAUSE (http://www.educause.edu/): This association manages and uses information technology in higher education. The site includes a discussion of current issues, conference information, professional development, publications, information services, and collaborative alliances with other organizations. It focuses on the future of higher education in the information age. Strength: this site is well organized and has breadth and depth; Weakness: not all content is available online.

References

Angelo, T., and K. Cross. Classroom Assessment Techniques: A Handbook for College Teachers. 2d ed. San Francisco: Jossey-Bass Publishers, 1993. Chickering, A., and S. Ehrmann. “Implementing the Seven Principles: Technology as a Lever.” Retrieved November 3, 1998 from www.tltgroup.org/resources/darticles.html Edwards, J., M. A. Havriluk, and M. D. Roblyer, M. D. (1997). Integrating Educational Technology into Teaching. Upper Saddle River, NJ: Prentice-Hall, Inc., 1997. Erkins, G., and G. Kanselaar. “A Cooperative System for Collaborative Problem Solving.” 1995. http://www-cscl95.indiana.edu/cscl95/kanselaar.html Good, T. L. and J. Brophy. Contemporary Educational Psychology. 5th ed. New York: Longman, 1995 Knuth, R. A., and D. J. Cunningham. “Tools for Constructivism.” In T. Duffy, J. Lowych, and D. Jonassen (Eds.), Designing Environments for Constructivist Learning. Berlin: Springer-Verlag, 1993, 163-87. Reid, J., Jr. “Measurements in Online Study: Items Useful in Quantifying Pedagogical, Social and Technical Issues.” 1997. Retrieved November 3, 1998 from www.caso.com/articles/reid05.html Story, D. “World Wide Web 101.” 1996. www.thejournal.com/magazine/vault/M2311.cfm