Skinned Knees and ABCs

The Complex World of Schools

Debarshi Roy

• Publisher: Routledge India
• Year: 2020
• Print ISBN: 9780367775643
• eBook ISBN: 9781000095296
• Topic: Éducation
• Subtopic: Gestion du comportement

Skinned Knees and ABCs critically analyzes schools as sites for applied behaviour systems. It delves deep into the origin of various behavioural theories that affect these institutions and utilizes scientific theories in mathematics, behavioural economics and psychology (social, cognitive and educational) to examine the complexities, failures and successes of school systems.

The book discusses the complex and chaotic nature of schools and the fundamental psychological constructs which form the basis for curriculum and behavioural designs. It also highlights the problems and peculiarities faced by students, parents and educators and suggests alternatives and solutions through real-life case studies.

Drawing on in-depth research and theoretical know-how, the book will be of interest to students, teachers and researchers of school education, organizational behaviour, behavioural sciences and applied psychology. It will also be of interest to parents of school-going children, school management heads, policy makers and educators.

Part 1
Nature and characteristics

1 Schools as complex systems

Humans are fundamentally programmed to find comfort in an orderly world where positive and negative outcomes can be predicted in order that consequent interventions may be designed to prevent the negatives and ensure the positives. Furthermore, the human yearning for predictability finds its presence within the domains of human relationships by encouraging a sense of comfort and security among the entities involved. The unpredictable nature of situations scares humans; thus, the vision of a predictable universe has formed the basis of most intellectual and philosophical pursuits that human civilization has encouraged. Isaac Newton’s laws of physics were based on the premise of a linearly predictable universe. Linear equations were formulated to predict outcomes wherein all the variables were designed to fit into the equations. The predicted outcome would be subsequently accepted or rejected per convenience. An alternative outcome could then be effectuated through a manipulation of the variables which were causing the result. When a variable did not fit in the predicting model, it was derisively termed an outlier and discarded. The concept of a linear and predictable universe represents a utopian idea with no realistic foundations. A large part of the universe and its contents do not follow Newtonian predictability.

The discussions of complex systems should prudently begin with a caveat; complex systems are difficult to define and comprehend. A complex system is one where a large number of interacting components and processes interact to produce an emergent behaviour. The outcome of these interactions and processes is nonlinear. Nonlinear systems are those where the output of such systems do not vary proportionately to the change in input. Gleick (1987) described nonlinearity as “the act of playing the game has a way of changing the rules.” Complex systems present with some unique differentiating characteristics. Complex systems are robust systems; if an element is extracted from such systems, the systems do not collapse. An additional characteristic of complex systems is that the systems contain within them both order and disorder. Such systems collapse when there is a deviation from the right balance of order and disorder. Complex systems are never at equilibrium but are guided by the dynamics of feedback loops. A feedback loop can be described as a part of the system wherein the system’s output (either whole or in part) is used as input for future processes in the system.

The characteristics of complex systems can be effectively extrapolated to the context of school systems. Schools systems witness a large number of entities indulging in immeasurable levels of interactions and activities each day, and the results of the activities and interactions are not linear. School children do not manage to double their test scores by doubling their study time. A child with an IQ of 80 may not secure half the scores of another child whose IQ is 160. The outputs do not vary proportionately to the inputs, thus making such systems nonlinear and inherently unpredictable. School systems are robust and do not collapse easily. The noted complexity theorist Karoline Wiesner (Wiesner and Ladyman, 2016) has described the nature of complex systems through the example of a watch and a beehive. If a small part is removed from a watch, it has an immediate systems collapse and stops working. In the case of a beehive, even if the queen bee is removed from the hive, it does not collapse, and the hive produces another queen bee. Quintessentially, schools can be compared to beehives; if an element (a student, a teacher or even the principal) is removed from the school, the school system will compensate for the loss and not collapse. Schools continue with vigour even centuries after the founder has passed on. School systems present a delicate balance between order and disorder. During breaks, the school presents a cacophony of screams, shouts, running feet, balls being kicked and baskets being shot at. As the bell rings for the classes to begin, order sets in. If the teacher is late or absent for the day, disorder prevails in the classroom, only to be brought to order by the sight of the principal at the door. The fine balance of order and disorder keeps school systems functioning effectively. The system might collapse when the sight of the principal at the door does not bring about order in the classroom or when the sound of the bell does not bring students back to the classrooms from the playing fields. The system might also collapse if children are not allowed to play and are confined within the strict order of the classrooms throughout the day. Since schools have the essential characteristics of complex systems, a strong case can be made for schools to be thus.

An extension of the study in complex systems leads to a form of systems known as chaotic systems. Chaotic systems are a form of nonlinear systems which are closely related to complex systems. The mathematical term “chaos” was first used by Li and Yorke (1975) in their paper titled “Period Three Implies Chaos.” While the word “chaos” might conjure images of disorder, mayhem, turmoil or disorganization, chaos when used in the context of chaos theory merely refers to a mathematical term for an unpredictable system (Devaney, 1990). Greenwood et al. (1992) posited that chaos presents a seemingly random behaviour which has a fundamental aspect of order. The study of chaotic systems is a relatively new endeavour, and the current enthusiasm with the subject can be traced to the hallowed portals of the Massachusetts Institute of Technology, where on a winter’s day in 1961, a meteorologist named Edward Lorenz, while conducting some calculations on his computer, decided to take a coffee break. He had conducted the same calculations earlier and was expecting the computer to return the same values. However, when he returned from his break, he noticed that the computer had produced a very different set of results from the earlier one. The reason for the change, as Lorenz discovered, was in the nature of the inputs. While conducting the previous calculations, he had input numbers with six decimal places; however, in the subsequent iteration of the calculations, he had used inputs of only three decimal places. Hence, if the previous input were .456782 instead of .456, it could and did create vast differences in the result. Since Lorenz was a meteorologist, the unpredictability and frequent futility of predicting weather phenomena was justifiable because it was established through this experience that long-term weather prediction was not possible (Gleick, 1987). A small change in one part of such systems could thus result in a large change in another. The name for this phenomenon as coined by Edward Lorenz was the butterfly effect (Lorenz, 1963). The butterfly effect has been summarized by the following statement: “Can the flapping of the wings of a butterfly in Brazil cause a tornado in Florida?” In other words, small changes which take place in one part of the system create very large changes elsewhere (this phenomenon is technically known as sensitivity to initial conditions). Lorenz’s accidental discovery was important to the field of nonlinear dynamics, and research in the area was subsequently further enhanced by scientists like Mitchell Feigenbaum at Los Alamos, who experimented with 26-hour days (Gleick, 1987).

While chaotic systems are inherently unpredictable, they are not random. If systems or elements of a system are witnessed to be behaving in an unusual manner with surprising results, the behaviour is frequently attributed to randomness. When this element of randomness is extrapolated to the context of human behaviour, it is most often termed luck. Random behaviour is akin to a coin toss or a lottery, the future results of which cannot be predicted by whatever volume of past information is available. The information about lottery numbers which have won in the past 100 years for a particular lottery cannot be presented in a linear regression model, however sophisticated, in order to predict the number of the next year’s winning lottery ticket. The lottery represents a random system, while a school does not, even though at times the complexities of school systems present such systems as pseudo-random systems. In contrast to random systems, deterministic systems are those where the outcome is determined by a chain of unbroken prior occurrences (Oestreicher, 2007). Chaotic systems are deterministic systems where the outcome is not predictable. Predictability and determinism are divergent concepts, as Werndl (2016) posited: “deterministic systems can be unpredictable in many ways.” Chaotic systems are found to behave in a way that can be described as deterministic chaos. Deterministic chaos describes the system as being inherently unpredictable but deterministic in nature.

The formal application of chaos theory to analyze school systems is of relatively recent origin; however, researchers and educators have, at various points of time, described schools as complex and unpredictable organizations (Blumberg, 1989; Blair, 1993; Sergiovanni et al., 1992).

Cunningham (2001), in his study on chaos and complexity in the context of education, proposed three basic conditions for a system to be termed chaotic. These conditions were that the system should operate in a nonlinear manner; that the system should be iterative in nature, wherein the output of one cycle would present itself as the input for the next cycle (outputs of one class are the inputs for the next higher class in school systems) and the system should exhibit sensitivity to initial conditions. School systems eminently comply with these conditions and thus are generally accepted to be chaotic by nature.

A school represents chaos, complexity and nonlinearity in many forms. It is posited that the complexities of systems increase with an increase in the number of entities or agents. The complexities of school life are accentuated many-fold by the large number of entities in such school systems as well as the unique nature of each such entity. The exponential increase in the number of interdependencies, connections, interactions and inflexions which present themselves at every moment of a school day enhances the complexity of the system. In an attempt to create comforting and manageable systems, the entities involved often oversimplify school systems to construct illusory predictable models wherein academic inputs are provided to students and outcomes are expected to be directly proportional to the ability of the children to process those inputs. It is with this input-process-output system in mind that schools create conforming principles, strict mechanistic organizational models and an unforgiving environment for learners. Most parents view schools as magical factories wherein raw and clueless children are fed into one end and suave, educated and all-knowing adults walk out of the other after an “education process” is duly completed within a pre-determined period of time. It is this fallacy that the schools are ready to promote in order to inflate their importance and oblige parental aspiration. The reality is that parents will never admit their children to a school which honestly communicates the fact that its wards’ future in that school is unpredictable and the children would just form a part of the chaotic system. Ironically, this visible show of control over the destiny of children forms the basis of a number of disasters that schools tend to inflict upon children.

The chaotic nature of school systems creates the potential for relatively innocuous and small incidents causing life-defining changes in a child’s life. A simple case study involving a six-year-old child named Ravi might illustrate the argument. Ravi does not like mathematics, and, as is common with children of Ravi’s age, the dislike for the subject has its roots within an abject dislike for the teacher. Ravi’s dislike for the mathematics teacher is not the result of a whimsical and idiopathic attribution of distaste but finds its reason within a specific cause: an act of rudeness of the teacher towards the child. The child was previously interested in mathematics but started showing disinterest and phobia for the subject arising from the dislike for the teacher. Consequently, Ravi began to ignore the mathematics lessons in class; thus, his performance in mathematics fell below the average levels for that class. Mathematics is a linear subject, something akin to a railway track, and if there is a gap in the learning, it has to be filled before further learning can take place. As long as the child dislikes the mathematics teacher, that gap keeps widening, thus creating a void which will eventually take time and effort to fill. The dislike for mathematics has other related behavioural implications; the child begins to suffer from performance anxiety when he realizes that he is performing below the academic levels of his classmates, leading to a further drop in performance. The dismal performance in mathematics takes a toll on his confidence which results in a generalized indifference to academic performance and compromised social skills. Ravi is forced to repeat the class, which in turn complicates the situation further. This child, however, is a normal child with an IQ that can be considered above the average levels for the class. The teacher, for his part, forgets that small incident and does not take it seriously enough to follow up with a word of empathy for the child. Thus, unknowingly, he ends up destroying what could have been a perfectly good academic career. The situation can result in far-reaching consequences which may affect Ravi’s adult life. In his adulthood, Ravi might nurture the same fears and biases against mathematics (or mathematicians) and may not encourage his children to take that subject or may even try to overcompensate for his lack of success in mathematics by trying to force it on his children. That may lead to a secondary cycle of events which have the potential to destroy more lives. If one were to conduct a recursive study of the events that occurred on that fateful day in January (when the teacher was rude to Ravi), one would notice that there was a general election at hand, and the ruling government had provided incentives to farmers through fertilizer subsidies. The subsidies resulted in an overwhelming production of wheat, which in turn led to an influx of rats, one of which discovered food within the wires of a local electric transformer which was the main source of electric supply to the mathematics teacher’s house. The resultant power cut led to a nonfunctional water heater, and thus the mathematics teacher had to endure a cold bath before commuting to work. The cold winter bath had turned him irritable, and he had uncharacteristically snapped rudely at the child. The case exhibits a classic instance of the butterfly effect at work in school – the parable of the nail and the lost battle at work in real life:

For want of a nail the shoe was lost.

For want of a shoe the horse was lost.

For want of a horse the rider was lost.

For want of a rider the message was lost.

For want of a message the battle was lost.

For want of a battle the kingdom was lost.

And all for the want of a horseshoe nail.

(Plummer, 2017)

It would be absurd to generalize this predicament and issue a prophylactic caveat to all mathematics teachers through an advisory that they are to keep a solar water heater ready when elections are round the corner. Such an advisory would not contribute to the reduction of math phobia among children. While...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Dedication
• Contents
• List of figures
• Acknowledgements
• Introduction
• Part 1 Nature and characteristics
• Part 2 Behavioural dimensions
• Part 3 Operational dimensions
• Part 4 Outcomes
• Part 5 Summation
• Index