Metaphors of Chaos Theory for MOOCs and Engineering Education

Available online at www.academicfora.com _ Academic fora Abstract proceeding book BESSH-March 17-18, 2016 Shanghai China ISBN 978-969-670-279-5 Metaphors of Chaos Theory for MOOCs and Engineering Education Sajid Iqbal1, Xizhe Zang2, Muhammad Majid Gulzar3*, Muhammad Yaqoob Javed4, Yanhe Zhu5, Jie Zhao6 3,4 University of Science and Technology of China, China, 1,2,5,6 Harbin Institute of Technology, China Abstract Since its inception in 1989, World Wide Web has been reshaping the idea of open learning. But in the field of distance education, Massive Open Online Courses (MOOCs) are the latest innovation. This paper presents concepts of chaos theory for developing a framework for this rapidly emerging form of online learning in general and engineering education in particular. The metaphors of chaos theory can be used in education because a MOOC classroom is a complex dynamical system. The authors find the metaphors of deterministic chaos like sensitive dependence on initial conditions, nonlinearity, and complexity relevant to teaching and learning MOOCs. Keywords: Chaos Theory, Engineering Education, Moocs, Nonlinear Dynamics, Online Learning *All correspondence related to this article should be directed to Sajid Iqbal, Harbin Institute of Technology, China Email: sajidiqbal62@gmail.com International conference on “Business, Economics, Social Science & Humanities”-BESSH 2016 13 Metaphors of Chaos Theory for MOOCs and Engineering Education Sajid Iqbal, Xizhe Zang, Muhammad Majid Gulzar† , Muhammad Yaqoob Javed† , Yanhe Zhu, Jie Zhao † University of Science and Technology of China. China Harbin Institute of Technology, China. sajidiqbal62@gmail.com Abstract Since its inception in 1989, World Wide Web has been reshaping the idea of open learning. But in the field of distance education, Massive Open Online Courses (MOOCs) are the latest innovation. This paper presents concepts of chaos theory for developing a framework for this rapidly emerging form of online learning in general and engineering education in particular. The metaphors of chaos theory can be used in education because a MOOC classroom is a complex dynamical system. The authors find the metaphors of deterministic chaos like sensitive dependence on initial conditions, nonlinearity, and complexity relevant to teaching and learning MOOCs. Keywords: Chaos theory, engineering education, MOOCs, nonlinear dynamics, online learning 1. Introduction Online learning is an old phenomenon. But with the advent of MOOCs in 2011, free online courses reached another milestone and 2012 was christened as the “ Year of the MOOC” by the New York Times [1]. MOOCs allow learners around the world to participate in online instruction through short video lectures embedded with automated MCQs tests, quizzes, peer evaluation and discussion foras. Thus, this new online pedagogy in higher education may boost the millennial tradition of lecturing. IEEE CS Report 2022 included MOOCs amongst twenty-three state-of-the-art technologies that could change the world by 2022 [2, 3]. 1 Since 1687, with the publication of Philosophi Naturalis Principia Mathematica, Newtonian physics started working as the model for early developments in the sciences. Classical physics emphasized linearity and determinism and behavioral psychology advanced this linear view. It proposed a universe that contained order, determinism, and predictability. Chaos theory questions all of these archaic linear constructs [4]. The educational model of Industrial Age focused on linear transmission of knowledge. Traditional learning is based on linear metaphors. The eccentricities of social interaction and human mind render the linear teaching paradigm deeply flawed and ineffective in the Information Age. Our educational institutions are dynamic, complex, and organic systems. Chaos theory offers useful metaphors for examining teaching-learning process. Little things teachers do or say in classrooms may end up having large unpredicted effects [5]. 2. Chaos theory: The End of Newtonian Metaphor Chaos theory (a section of nonlinear dynamics) is relatively a new mathematical concept. It is the outgrowth of breakthroughs in the field of nonlinear dynamics. The study of the temporal evolution of nonlinear dynamical systems is termed as Nonlinear dynamics. The famous American physicist, Heinz Pagels said, “ Life is nonlinear, and so is just about everything else of interest [6], p. 1-15.” Chaos theory also known as Dynamical System Theory is defined as the mathematical study of chaotic systems and their behaviour. And it deals with deterministic processes which look random but whose dimensions are finite [7, 8]. Greek philosophers developed the premise that universe is predictable (and deterministic) and the main aim of scientists is to find the deterministic rules for control and prediction. The Newtonian dynamics governed every sphere of life since 1687. The triumph of Newtonian deterministic, clockwork worldview led to the philosophy of determinism—the systems dynamics can be predicted for all time knowing the initial conditions and differential equations of systems. Determinism tells us that the accurate future predictions can be made, if we have information of the initial conditions (events). In 1814, in his Essai philosophique sur les probabilities, the eminent French mathematician Laplace advanced Newton’s canon as [9], p. 4: Given for one instant an intelligence which could comprehend all forces by which nature is animated and the respective situation 2 of the beings which compose it—an intelligence sufficiently vast to submit these data to analyses—it would embrace in the same formula the movements of the greatest bodies and those of the lightest atom; for it, nothing would be uncertain and the future as the past would be present to its eyes. This passage is a classic narrative of a clockwork universe. This ordered cosmos followed deterministic rules, which could be used to explain causal and linear relationships of all occurrences. About a century later, Henri Poincare, one of the founders of the field of chaos theory, hinted that the universe truly acted rather differently [10], p. 68. He articulated the sensitivity to initial conditions, which is the terminology for a notion of the chaos theory—the butterfly effect as: Even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible. Hence, Poincare was the first scientist who realized the failure of predictability in Newtonian mechanics. Edward Lorenz, a pioneer of chaos theory, introduced the contemporary interest in Chaos theory and coined the term butterfly effect, which is the occurrence whereby a very insignificant change in a complex system can notably change a predictable course of events [11]. Small changes in a system could make large alterations later. Deterministic chaos deals with dynamical systems which exhibit apparently random behavior. However, they have an underlying order (geometry). In 1986, the British mathematician Sir James Lighthill realized this determinism-chaos paradox and published a remarkable collective apology on behalf of all scientists as [12], We collectively wish to apologize for having misled the general educated public by spreading ideas about the determinism of systems satisfying Newton’s laws of motion that, after 1960, were proved to be incorrect. 3 In the last century, Newton’s dream shattered in the physical sciences. Chaos theory has a great impact on scientific thinking. The main consequence of deterministic chaos is that complex behavior, sometimes, have simple causes. Thus, the famous theoretical biologist, Robert May stressed the educational significance of studying nonlinear dynamical systems to balance the misleading linear intuition advanced by traditional learning in his celebrated review article [13]. He highlighted that even simple nonlinear equations could produce complex dynamics. His paper ended memorably with an evangelical plea for the induction of nonlinear dynamics into primary courses as: Not only in research, but also in the everyday world of politics and economics, we would be better off if more people realized that simple nonlinear systems do not necessarily possess simple dynamical properties. The terms nonlinear dynamics and chaos have become known to most scientists during the last three decades. Nonlinearities occur in the systems containing interacting subsystems and in feedback processes. Complex events (e.g., weather) and simple devices (like a double pendulum) remarkably follow the same erratic dynamics. The availability of fast digital computers and new-fangled analytical techniques have proved that chaotic phenomenon is ubiquitous in nature and has far-reaching implications in all fields of human study and endeavor. These books are mines of valuable information on chaos theory for additional study [14, 15]. 3. MOOCs: A Brief Review Often drawing thousands of learners to a single section MOOCs present free, high-class, university education to anybody with Internet connection. In IEEE CS 2022 report, IEEE Computer Society leaders spotted major industry advances that promise to change the world by 2022 and MOOCs are among the top 10 technologies in the list [2, 3]. MOOCs have opened up learning opportunities and given masses access to knowledge that was previously unimaginable [16, 17]. MOOCs are vehicles for democratizing higher education. MOOCs promote ideas like self-pacing, peer assessment, instant feedback, and active learning,. In traditional residential course, students passively absorb lectures and lack rapid feedback. Learners also have limited opportunities to ask questions. Famous American writer Mark Twain complained 4 about the lecture-based format as, “ College is a place where a professor’s lecture notes go straight to the students’ lecture notes, without passing through the brains of either”. Like the monolithic hour-long lectures, pupils cannot learn by passively watching videos. Hence, the video content for MOOCs is based on Khan-style of tutoring [18]. Outside brick-and-mortar classrooms, MOOCs offer immense opportunities such as adult education, lifelong learning, and vocational training. Professional teachers are big audience of MOOCs. Teacher training is important because teachers pass on to their own students, what they learn [19]. Likewise, doctors, engineers, and computer scientists can make the most of online courses to enhance their expertise [20]. 4. Engineering MOOCs Engineering education is the endeavor of instructing concepts and principles associated to the practice of engineering occupation. Practice is the key in engineering profession and in this regard concept building is significant for engineering students [21]. Thus, the laboratories are a distinct component of engineering education, as the theory must be supplemented by practical training. Computer simulation is an alternate for expensive laboratories. In engineering learning, the computer simulators strengthen the student understanding of abstract ideas by means of graphical aids [8, 22]. Simulations emphasize the resemblances and dissimilarities between the theoretical and real properties of devices. In engineering MOOCs, remote and virtual laboratories can fulfill theory-to-practice gap. Stanford University and MIT offered initial MOOCs in Electrical Engineering and Computer Science. Since engineering courses necessitate prerequisites so firstly advanced-level engineering courses were almost absent from MOOC list. Nevertheless, now many universities are presenting preliminary and upper-level engineering courses [17]. Many instructors have also been describing thriving results of inverting (flipping) the engineering courses around MOOCs [23, 24]. 5. Metaphors of Chaos Theory in Education For three centuries, the predictable clockwork philosophy has been the dominant dogma. The Newtonian worldview profoundly influenced our conviction, psyche, and institutions. The Newtonian model explained the world by reducing intricate systems into smaller entities so they can be understood 5 and manipulated [25]. Since Chaos theory focuses on nonlinearity, instability, and uncertainty, so its application to the social sciences was plausibly an anticipated outcome. While chaotic dynamics occur within defined parameters, it appears random and without pattern. However, chaos is a random-like behavior as it can be produced with a completely deterministic equation [6]. Table I compares key notions of linearity and chaos theory [26]. Linearity Chaos and complexity Seeks to predict Recognizes that many occurrences are sudden and unpredictable Input is proportional to expected output Small input may have much greater output Values stability and equilibrium Values turbulence and far from equilibrium conditions Takes apart to look at component parts (reductionism) Views entities and phenomena holistically to discover underlying pattern Views effect as result of singular cause Regards effect as outcome of multiple causes Does not take context and connections among entities into consideration Recognizes influence of context and interconnectedness of multiple variables Attempts to solve problems by control Recognizes that control efforts may lead to intensification of the problem Seeks simple, rational solutions Addresses complex problems without simple solutions Table 1: The linear and chaos worldview [26] Human behaviors evolve from eccentricities (nonlinearities). Before digital computers, when analytical solutions were the only available technique, necessity enforced a practice of ignoring nonlinearity. The convention of linear thinking has became so firmly instituted that it has distracted most researchers from even identifying the worth of nonlinearities. In nonlinear dynamical systems, results are less simple, but more relevant. Social scientists can understand the world better by appreciating complexity and adopting new nonlinear analysis and modeling methods [27]. Many educators consider teaching-learning process to be a complex activity. Despite the best-developed lesson plans and class management techniques, the class is always subjected to many unpredictable factors. Teachers must accept uncertainties as a natural condition and prepare themselves for all eventualities [28]. Metaphors drive theory and practice of education. The metaphor of Newtonian determinism has failed social sciences. Education is a societal process and, in the jargon of chaos theory, it is one of the arrows in time—an arrow targeted by human choices. Educational researchers have started to employ chaos theory in future didactic frameworks [29]. The metaphors of Chaos theory have been used in different facets of education like teacher training, curriculum, lesson planning and delivery etc [30, 31, 32, 33, 34]. The authors find the metaphors of chaos theory like nonlinearity, sensitive dependence on initial conditions, and strange attractor pertinent to teaching 6 Figure 1: Determinism vs. Chaos: comparison and contrast [37] . and learning MOOCs. The Butterfly effect proposes that just a minute variation in the initial conditions can severely change the long-term behaviour of a dynamical system. Similarly, an unanticipated comment from a student, a small change in the way the teacher conducts an activity, can have a large effect on the course of the lesson and its entire value [31]. Chaos theory emphasizes the importance of initial events (conditions). A single event can cause long-lasting effects like low motivation, lack of self-confidence and insecurity among learners [30]. New knowledge is created by processing information and integrating it with prior knowledge. Knowledge acquisition is also a complex process. Neuroscientists told us that brain works in nonlinear path as opposed to digital computers [4]. MOOCs appear to be a chaotic learning environment in which properties of connectedness and openness bring about a high degree of complexity and the need for greater self-organization. Some social scientists argue that it is neither needed nor valuable to introduce chaos theory to comprehend education. They exclaim that the arbitrary application of chaos theory to every kind of complex phenomenon handles it like a fixed set of rules and consequently is misleading and misapplication [35, 36]. Anyhow, Chaos theory, engineering education, and current online education generate synergy for preparing future engineering MOOCs. which may provide a comprehensive knowledge base and critical thinking expertise. 6. Implication of Deterministic Chaos in Engineering Education and MOOCs Current engineering education is deeply rooted in the scientific standard of the past—determinism. The engineering education has been mostly underscoring linear modeling because linear systems theory has been fully de7 veloped and instilled in engineering courses for decades. The caveat is that this philosophy ignores many observed intricate dynamics because it cannot explain them. Chaos theory is a fascinating new area of modern science, which is transforming our understanding of world [7]. The apparent paradox of randomness appearing in simple deterministic systems has been making investigators believe that a comprehension of deterministic chaos may explain the deviations between analytical predictions and experimental results, see fig. 1. Deterministic chaos can be integrated into undergraduate engineering curriculum at different levels and in multiple ways [37, 8]. For instance, in numerical analysis course, logistic map (given by equation 1) can be taught as an exemplar of chaos [38]. xn+1 = kxn (1 − xn ) (1) Where k is a factor symbolizing growth rate and xn is the variable at the n iteration and n is the running variable. The control parameter range is 0 ≤ k ≤ 4 and x ∈ [0, 1]. Fig. 2 shows time-series plots and fig. 3 illustrates bifurcation diagrams of logistic map. th (a) (b) (c) (d) Figure 2: Time-series plots for different values of k showing periodic (period−1, −2, and − 4) and then aperiodic (chaotic) behavior of logistic map [8] 8 Figure 3: Bifurcation diagram of logistic map showing periodic and chaotic dynamics [8] . In electronic devices and circuits, major concepts of chaotic dynamics can be introduced [39, 40]. In mathematical modelling courses, chaos-based modelling, instead of reductionistic approach, may prove useful. The integration of chaos theory in education will develop holistic and dynamic thinking instead of reductionistic, static philosophy. It will encourage multidisciplinary studies and promote synthesis and analysis. As educators, we must nurture analytical (left-brain) thinking skills as well as creative (right brain) skills. We should reimagine our engineering curricula. 7. Conclusion Current MOOCs are immense didactic experiments. Open online courses are disrupting traditional education and they may bring major changes in higher education. The consequences of these courses are different in different sectors and these implications must be contextualized. MOOCs are establishing education as a basic human right. Needing intrinsic motivation, massive online courses can be used for continuing professional education and undergraduate courses, leading to graduate education. MOOCs will help us identify new ways to think about online education and they may complement the current teaching models and become part of education ecosystem. Chaos theory strives to understand complex systems and it considers world as an open system and learning as dynamic, holistic and constructive process. It acts as a channel between the determinism of Classical Physics and the unpredictability of Modern Physics. Chaos theory can offer edu9 cators with a more precise picture of teaching-learning process. This paper discusses the role of chaos theory in engineering MOOCs. It also calls for involvement of nonlinear approaches to teaching of thinking. Chaos theory provides useful metaphors for understanding dynamics of MOOCs. The authors consider that the metaphors of chaos theory e.g., ergodicity, sensitivity to initial conditions, and complexity relevant to teaching and learning MOOCs. The world of engineering MOOCs is still in its early years and it is full of possibilities and further innovations. 8. Acknowledgement This work was supported by the National Magnetic Confinement Fusion Science Program Multi-Purpose Remote Handling System with Large-Scale Heavy Load Arm (2012GB102004). References [1] L. Pappano, The year of the mooc (2012). [2] H. Alkhatib, P. Faraboschi, E. Frachtenberg, H. Kasahara, D. Lange, P. Laplante, A. Merchant, D. Milojicic, K. 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