2.1 Puzzle-Solving Paradigm
In his seminal book The Structure of Scientific Revolutions about the philosophy that underlies people’s understanding of the world and their use of scientific methods in every sequential historical period, Thomas Kuhn (1962) suggested viewing science as a puzzle-solving practice (p. 36). A certain philosophical configuration is a skeleton, and people build on its DNA to grow their understanding of existence, knowledge, rational arguments, and values as well as the puzzle-solving methods. Such a configuration, or as Kuhn referred to it, paradigm , ‘stands for the entire constellation of beliefs, values, techniques, and so on shared by the members of a given community … it denotes … the concrete puzzle-solutions which, employed as models or examples,’ become ‘a basis for the solution of the remaining puzzles’ (p. 174).
Since the rudimental purpose of education is to develop people’s know-how to survive and progress in their habitual-natural, traditional-cultural and established social milieus , education becomes a direct reflection of the collectively endorsed paradigm , including its established puzzle-solving systems. Typically, education takes its contemporary worldview for granted, framing curricula and teaching practices within the proposed set of assumptions without challenging or interrogating them. According to Kuhn, it is ‘striking’ how little novelty the conventional puzzle-solving traditions produce, either ‘conceptual[ly] or phenomenal[ly]’ (p. 35). In accepting an existing worldview without question, education turns the student into ‘a solver of puzzles, not a tester of paradigms ’ (p. 144).
Because the evolution of a society goes hand-in-hand with the gradual accumulation of facts, empirical observations, technological inventions and the emergence of new theoretical approaches, the validity of once firmly approved assumptions is eventually challenged, causing a paradigm shift. This is often associated with ‘the convergence, amalgamation, or syncretism of originally disparate ideas and practices’ (Bunge 2003, loc. 3885). The original picture in a jigsaw puzzle—a cosmology, a view of the world, and its associated puzzle-solving techniques—its disciplinary symbolisms and operational technologies, becomes more complex, generating new concepts and techniques. Social progress can be envisioned as an inseparable flow of intellectual, social and technological currents, constantly merging, creating new intricate compositions and carving new patterns of thought and operation. Just as movement periodically reaches a state of chaotic overflow, it restructures itself by redesigning the order and instrumentality of the flow.
Moving within this continuity, education is an organic current that transcribes and transmits collectively generated thoughts and practices to the mass-cultivated younger members of society. Using Vygotsky’s (1978) famous concept, education is a dynamic zone of proximal development whereby inexperienced puzzle-solvers are assisted by ‘adult guidance or collaboration with more capable others’ (p. 86). The zone of proximal development is oriented to helping the puzzle-solver grow from operating on the level of imitation to reaching the higher level of independent mental activities (p. 87). The only issue with this approach is the puzzle itself, as every puzzle has ‘the assured existence of a solution’ (Kuhn 1962, p. 36), or as in jigsaw puzzles, one predesigned picture. ‘On the contrary, the really pressing problems, e.g., a cure for cancer or the design of a lasting peace, are often not puzzles at all, largely because they may not have any solution’ (p. 36).
Consequently, the instrumentality of contemporary education rests on the principle of a puzzle-solving methodology that implies a ‘one size fits all’ confirmed solution and established ‘correct’ methods for arriving at it. This further alienates the learner from self-discovery, innovation, the production of alternatives and the search for effective means of social integration. If we return to the metaphor of a society as interflowing intellectual, social, technical currents running together towards progression, we can see that today’s puzzle solving -oriented education is no longer a natural rivulet in a synergetic dance with the others but a heavily restrained channel.
During the turbulent paradigm shift from Newtonian cosmology hypothesised as an ordered, mechanistic clockwork to the fluid and chaotic worldview of the twenty-first century, contemporary education has appeared to be under arrest, sailing on a residual construction of the past and desperately clinging to stability and reassurance. This ‘enslavement to clockwork regularity and chronology’, as Porush (1991, loc. 1558) describes it, continues to saturate the whole fabric of contemporary education. From orderly class bells to standardised drills and testing, benchmarked knowledge and systemic pedagogies reinforce conformity of thinking, which promotes the growth of the dispassionate learner.
It is still a common belief that the laws of exact sciences and the well-established order of things can continue enabling us, humans, to maintain control over nature, social experiences, our wellbeing and each other. This is exemplified in the cultural attitude shared by Galileo (1844) that mathematics is the alphabet used by God to write Nature’s laws (as cited in Doll 1993, loc. 559) and Rutherford’s expression that ‘all science is either physics or stamp collecting’ (1984) (as cited in Doll, loc. 1412). Such a mindset endorses the exclusion of the concepts of self-discovery, arts, natural, cultural and social integration and has caused ‘devastating effects on curriculum’ (loc. 1412). ‘As both Dewey and Piaget have pointed out, it is interaction that form the heart of growth’ (loc. 1412).
The absence of interactions with nature and the social world results in an undeveloped sense of caring for the environment we live in and for the other living beings with whom we share this environment. For short-term profits, we keep damaging our planet, the only home we have. We are happy to buy cheap products while turning a blind eye to the fact that the people who produce them may be exposed to hazardous health conditions, or that they may be children working in physically unbearable surroundings. We ignore the fact that mass production has turned us into monsters who nourish our children with the stress-infused milk from maltreated cows. As teachers, we are too busy cramming our students’ minds with facts and operations, forgetting that among them may be some who are desperately seeking help; who may be driven to a suicide by being bullied under a teacher’s nose; or others who may be becoming so lonely and angry that they take out their frustration on their school community. We have no time for anything that is outside the discipline’s content—we are too overloaded by teaching to a test.
2.2 Sputnik’s Effect on Liberal Education
As societies become more complex in structure and resources, the need of formal or intentional teaching and learning increases. As formal teaching and training grow in extent, there is the danger of creating an undesirable split between the experience gained in more direct associations and what is acquired in school. This danger was never greater than at the present time, on account of the rapid growth in the last centuries of knowledge and technical modes of skills. (Dewey 2015, loc. 484)
The dangerous split of schooling, as Dewey identified at the beginning of the twentieth century, may plough its way through the disregard for social obligations and connectedness to human associations. In this scenario, the cultivation of the consciousness of young people takes a lopsided course in which ‘remote matters’ conveyed and learned through the symbolic systems of academic disciplines become the sole goal of teaching and learning. The acquisition of lingual, mathematical, computer and science literacies, in other words, ‘technical intellectual skills’, without consideration for the ‘formation of a social disposition’ leads to the production of ‘sharps in learning – that is egoistic specialists’ (Dewey 2015, loc. 467).
Today, a hundred years after Dewey’s insightful prognosis, we can clearly observe the split in education between learning abstract symbolic literacies, on the one hand, and students’ innate abilities and interests as well as natural and sociocultural environments, on the other. We can also recognise a strong resistance to acknowledging and modifying this condition of alienation. Cosmetic changes, such as cramming classrooms with modern technology and publishing subject content online, are only convenient new masks covering an old, rigid, mechanistic structure. It can be compared to the famous Henry Ford quote: ‘If I had asked people what they wanted, they would have said faster horses.’ When contemporary education faces the need to re-envision its fundamental architecture, it camouflages it with a narrative that can be summarised by a statement from Florida’s Governor Rick Scott: ‘The liberal education is irrelevant, and technical training is the new path forward. It is the only way, we are told, to ensure that Americans survive in an age defined by technology and shaped by global competition. The stakes could not be higher’ (as cited in Zakaria, March 2015, The Washington Post).
If there were no more to human intelligence than academic ability, most of human culture would not have happened. There would be no practical science or technology, no business, no arts, no music, no dance, drama, architecture, design, aesthetics, feelings, relationships, emotions, or love … If all you had was academic ability, you wouldn’t have been able to get out of bed this morning. In fact, there wouldn’t have been a bed to get out of. No one could have made one. You could have written about the possibility of one, but not have constructed it. (p. 81)
- (a)
The separation from and deemphasising of liberal education in schooling, which means that most of the sophisticated ethical decisions of the future connected to technology’s invasion of people’s private lives, control of each other, technical intervention in the biology of our physical bodies and the future of the planet as a whole, will be subjected to the decisions of people whose critical thinking skills are extended no further than the operational capacity of symbolic systems related to their technical training. Moving inevitably and in a fast-forward mode towards creating artificial intelligence, would it not be wise for us as humans to emphasise our humanity, to reinforce what we know about our humanness and to better understand ourselves as individuals, so that as non-augmented species, we will not lose our sovereignty and be overpowered by supercomputers?
- (b)
Stressing the restoration of American superpower and its victory in global competition in a time when the paradigm shifts, or borrowing from Gerd Leonhard (2016), ‘megashifts’ (loc. 71), are rapidly altering our very understanding of the term global sounds rather outdated. As a global community, should we not begin thinking about how we can stop competing for power and start working collaboratively before our blind fight for profit and dominance pushes us into a final technological deadlock?
Nevertheless, lawmakers and curriculum designers keep contemporary education away from the turbulence of our time, within the security of the commonly sanctified framework of structures and algorithms. ‘The Industrial Age paradigm of profit and growth at all cost, or some outmoded technological imperative that may have served us well in the 1980’ (Leonhard 2016, p. 7) is still promoted as an assured ‘Moses basket’ set on a tried-and-true stream to a successful career, oblivious to the fact that its course lies through seismic waves of global restructuring.
William Doll (1993) points out that Western education’s tilt towards the adoration of science, math and technology was accelerated by the Cold War and reached its height after the launch of the first artificial Earth satellite, Sputnik, by the Soviet Union in 1957.
At this time, it was believed that professional, scientific knowledge would help us compete with the Russians in space, defeat the communists in Vietnam, eliminate poverty and improve health care at home, and increase the knowledge base of young people. Teaching machines, programmed learning, and a teacher-proof curriculum were the wave of the future, the road to social salvation. (loc. 248)
Sputnik’s outer space triumph ‘alarmed the United States. One of the first reactions was to decide that mathematics teaching must be revamped, so we could regain hegemony over our primary adversary’ (Hacker 2016, p. 102). This approach gave rise to scientific knowing that Donald Schön (1991) identified as ‘technical rationality’, ‘the positivist epistemology of practice’ (p. 31). According to the positivist’s perspective, ‘craft and artistry had no lasting place in rigorous practical knowledge’ (p. 34). Fortunately, the Western world did not need to strive overly hard to equip itself with the technical rationality and scientific expertise in the war against Communism. Ultimately, as Doll notes, Communism ‘collapsed of its own ineptitude’ (loc. 248).
We insist on top-down command-and-control. We micromanage every minute of every lesson plan. Instead of letting a thousand flowers bloom, we replace all flowers with the same lifeless, overtested weed. We take every ounce of bold creativity out of the classroom, replacing it with a soulless march through dull curriculum and test prep decoupled from life skills. We prioritize standardisation and accountability, and don’t seem to notice or care that students lack engagement and purpose. (p. 272)
As a naturalised Australian, living and working in this country, I see how closely this also relates to Australian education. Puzzle-solving abilities based on the operational skills and technical capabilities of a particular discipline and a bank of memorised abstract facts become iconic characteristics in portraying an intelligent individual of our time. Progressively, students are ever more capable of performing within the conditions of algorithms and structures and are less possessive of human idiosyncrasies because those idiosyncrasies may be inconvenient and obstructive to the completion of the task at hand.
As contemporary education proclaims that it is busy cultivating innovators for the future, this inevitably leads to the question: who will these individuals—individuals who are native to digital environments like wound-up ducks in the water—be innovating for? Is not the fundamental purpose of technology to serve humans and to improve their lives? Does it not appear preposterous that through emphasising disciplines for innovating for humans, education pushes away the very core of the equation—humanities?
What then is the purpose of contemporary education?
2.3 Standardised Testing: Cultivating Fearful Puppets and Cheerful Robots
- 1.
Teach students cognitive and social skills.
- 2.
Prepare students to be responsible, contributing citizens.
- 3.
Build character.
- 4.
Help students in the process of self-discovery.
- 5.
Inspire students through the study of humanity’s great works.
- 6.
Prepare students for productive careers (p. 35).
Upon further observation of how students were taught and evaluated, however, the authors concluded that schools’ ‘unequivocal priority’ was ‘to cover meticulously specified content’ (p. 39). As the key priority, the content trumps the listed six points, effectively cast them aside. Why is this so? Chiefly because content-cover provides the most efficient mechanism for taking control of what and how knowledge is delivered to those who will soon take up the country’s governing baton and those who will be subjected to their governing. Standardised testing is a control-loops system, conscientiously designed to manage, direct and regulate population’s knowledge input
output. The bolts of the standardised knowledge input
output testing machine are turned even tighter by the method of evaluating both students’ competence and teachers’ performance in accordance with their students’ tests results. The system is an expertly constructed device of oppression.
Standardised testing is precisely the point of convergence at which Western education merged itself with communist education. In the former Soviet Union, standardised testing was a coercion machine used for cultivating fearful puppets , (which is no less the case under the current Putin regime). In -the Western world, it is a device for the mass production of cheerful robots (Mills 1959, pp. 171–172). Fearful puppets live by obeying instructions from those pulling the strings, and as much as they may find themselves unhappy with the current status quo, when the strings are released, they are incapable of holding themselves together. They are by-products of dictatorial, oppressive cultures such as the former Soviet Union and modern Russia. Cheerful robots, as Henry A. Giroux (2011) describes, are young people who are ‘shamelessly reduced’ to such a status ‘through modes of pedagogy that embrace an instrumental rationality in which matters of justice, values, ethics and power are erased from any notion of teaching and learning’ (p. 3). Their education rears them (at least as it is commonly proclaimed) to be competent employment gainers and experts in recognising and solving puzzles that are straight at hand but not at recognising puzzles as organic elements in the larger network of natural, sociocultural environments. Neither group, each for specific reasons, is equipped with skills for questioning their current state of affairs and having agentic capacity to address the moral and political problems of their time. They are an invention of the standardised testing system of education in which critical attitudes are simply an obstruction to knowledge and citizenry.
They lived in suburban homes with white picket fences and a brand new Ford or Chevrolet in the driveway. Inside, the modern appliances in the kitchen made the daily task of preparing the family meals more enjoyable for women. Dad enjoyed the morning commute to work in his new car. On the way home, he looked forward to watching the evening news on that brand new black and white television in the living room. The children, after school, played carefree in the neighbourhood and were not expected home for dinner until street lights came on. It is not surprising that […] people would cheerfully embrace this lifestyle.
Sputnik has imparted a sense of urgency and, indeed, at times almost an atmosphere of panic to a searching examination of the techniques, methods, and philosophy which have enabled the Soviet Union to achieve so dramatic a sequence of achievements and, at the same time, have aroused a widespread demand for an equally comprehensive reevaluation of American education. (p. 339)
It seems that many Americans placed their trust in scientific/technological/engineering/mathematical (STEM) education with their nostalgic dream of all-white communities living in identical homes in well cared-for residential areas with beautiful new churches, affluent shopping centres, state-of-the-art modern schools and inviting recreational spaces. With technology on the rise, this lifestyle can be envisioned even more attractively: it is more convenient, more comfortable, and in cutting-edge terms, augmented. Perhaps this is why the slogan ‘Make America Great Again!’ worked such wonders in the 2016 presidential campaign. People are seeking desperately to bring back the image of their ‘true home’.
However, as alluring as this nostalgic picture appears to be, the fact of its fleeting existence is proof of its unsustainability. In a world of constantly changing global dynamics, it is impossible to isolate oneself inside cosy spaces hidden behind socially constructed walls converged to one nationality, economic class, race, or religion. No matter how much STEM-based intelligence people develop through their education, it is no longer possible for them to continue to live in complete obedience to authority, giving high status to special groups in global society and turning a blind eye to the plight of others. Those who are need to be heard and helped will find a way to destroy the most intelligently engineered protective walls and strike at the most sensitive and vulnerable social spots. Thus, instead of building new walls and protecting ourselves with more guns, we must perhaps begin to emphasise understanding ourselves and our relationships with each other. Maybe instead of separating ourselves from those who we think are unsuitable for our company, we must learn to accept our differences and find mutually agreeable solutions.
2.4 The Math Myth
In his book The Math Myth, Andrew Hacker (2016), political scientist, public intellectual and Professor Emeritus at Queens College in New York, developed a compelling argument for STEM as of one of the greatest delusions of our times (p. 12). In juxtaposition with STEM , he proposes another acronym, PATH, which stands for Philosophy, Art, Theology, History, ‘or try your own’ path, as Hacker writes. Leonhard (2016) suggests another integrative acronym to STEM, which is CORE: creativity/compassion, originality, reciprocity/responsibility, and empathy (p. 24).
If our nation is to retain its moral and cultural stature, we must underwrite a million more careers in PATH spheres every year. If we do not, we may continue to lead in affluence, but we will decline as civilisation. (p. 12)
In arguing that viewing math as a linchpin for a successful career and citizenship is a misconception, Hacker draws on two premises from the vast data he gathered in his years of research. The first premise is that people in most occupations, including those considered to be dealing with numbers, such as actuaries, software developers, engineers and system analysists, do not use mathematics to the level it is taught at school.
doctors use only arithmetic in patient care (p. 47);
actuaries confess that the school ‘test covers mathematics that people will never need in their job’ (p. 49);
software designers do not use much of any math ‘except from calculating the tip at lunch’ (p. 52); and
the vast majority of engineers use ‘only eighth-grade mathematics’ (p. 52).
Here is another example of the many voices presented in Hacker’s book: ‘When I meet some of our students after they have graduated and taken engineering jobs, I like to ask them what mathematics they use in their work. The most frequent response: addition, subtraction, multiplication, division,’ (p. 62). In other words, none of the algebra, calculus, differential equations or geometry that is taught at school.
A university graduate meets his professor 15 years after graduation.
- Professor:
I am so glad to see you! You were my best mathematics student! Please tell me if you had a chance to use any of the math skills I have taught you in your everyday life?
- Student:
Yes, professor! Indeed! There was a situation when I used my knowledge of advanced mathematics. Once I was walking down a street and the wind took my hat and landed it into a giant puddle. It was rather an expensive hat and I wanted to get it back, but the puddle was too large and deep. Then, I saw a piece of wire nearby. I bent it in the shape of the integral symbol and used it to pick my hat up from the puddle.
There is always a grain of truth in every joke. In relation to the argument of the Ripples pedagogy, the grain of truth in the joke above is top-notch. The puzzles of real life are often solved not by operational skills acquired from the disciplinary domain but by the rules of a bricoleur , who uses ingenious means to apply the materials and tools at hand (Lévi-Strauss 1962, p. 17). This principle lies at the heart of the Ripples pedagogy, which is modified to state that that it is never either one thing or another but an integration of both. What you know is important, but as Tony Wagner (2012) states: ‘Increasingly in [the] twenty-first century, what you know is far less important than what you can do with what you know,’ (p. 153). One of Wagner’s research participants affirms this: ‘And it is really in the doing – in the probing of the universe, the pursuit of a query – that the real learning takes place,’ (Bottino, as cited in Wagner, p. 167)
Being good at one mental skill does not necessary train the mind to be skilful in other domains. This is one of the most solid findings in psychology, confirmed and reconfirmed. (p. 82)
There appears to be no research whatever that would indicate that the kind of reasoning skills a student is expected to gain from learning algebra would transfer to other domains of thinking or problem solving or critical thinking in general. (p. 83)
I’m waiting to be shown that agility with polynomials produces sharper insights on other topics. Can quod erat demonstrandum, even if exquisitely structured, help us to resolve whether deciding to end pregnancy is taking a life, or if the national interest will be served by invading another country. (p. 82)
In relation to the common belief that mathematics enhances logical thinking, Hacker generates a persuasive assertion of the opposite. A fascinating vignette of his own experience serving as a juror demonstrates how much one can learn about him/herself when they must make decisions from factual and behavioural evidence delivered and produced by others, how much awareness can be raised in making meaning from analysing human interactions and what an excellent exercise it can be to practise logical thinking. ‘And some of these are arguably more valuable to students’ lives than abstract mathematics,’ (p. 96) Hacker concludes.
As stressed earlier, and as will be discussed in greater detail in the following chapters, the core principle of the Ripples pedagogy is pinned to the notion of circularity, in which two linear extremes merge into an operational feedback loop system. This means that the Ripples model does not deny the importance of mathematics and other STEM subjects but proposes to choreograph them with arts and humanities into a dynamic composition of teaching and learning that will produce results beneficial to the future of society and the planet. The depreciation of liberal education blocks aspiration for individual expressions, curtails agentic tendencies and reduces the intrinsic motivation for learning. In other words, instead of cultivating the ability to imagine, or the skills of embodying thoughts into physical representations and concepts, empathy, intuition and innate idiosyncratic abilities—the qualities that make us human—with STEM-focused education, we reduce future generations to acting within restricted structures supported by algorithms. In other words, we are not cultivating all-around abilities in young people to help them take the lead in the future world heavily infused and restructured by technology; rather, we are reducing the development of their minds to the level of symbolic coding, which machines can do and will do exponentially better than humans.
STEM
’s hegemony provokes further the alienation of students from natural and sociocultural environments and their own selves, which according to Mills’ description, places society in great danger.The advent of the alienated man […] is a major theme of the human condition in the contemporary epoch and of all studies worthy of the name […] The society in which this man, this cheerful robot , flourishes is the antithesis of the free society – or in the literal and plain meaning of the world, of democratic society. (pp. 171–172)
If we truly see education as a stronghold of reasonableness where the next generation is being equipped with skills and capabilities to build not a profit-based and power–corrupted but a fair, humanistic society, we must stop playing the cheerful robots/fearful puppets’ game. In the worlds of Leonhard, ‘the future cannot be created based on blind optimism or paralysing fear’ (2016, loc. 44).
2.5 Divergence and Convergence
As discussed extensively throughout the following chapters, the Ripples pedagogy is built on a systemic view of the world. This means that its operational mechanism is based on the continuous interactions of individuals with their natural, cultural and social systems in the mode of rippling circularities. An isolated learning unit is envisioned as a ripplework around an established attractor, or the intended purpose. To frame a specific learning unit within a larger rippling system, we must know what circularities usually constitute this ripplework.
Drawing two opposite ends together, e.g., divergence
convergence, the Ripples model forms its core circularity. Put into circular dynamics, these two aspects, divergence
convergence, trigger each other’s movements through ongoing feedback loops. For novelty to emerge, however, the circularity dynamics must be affected by the interactions with other rippling systems, such as technology, cultural aspects, individual tendencies and interests, a given context as well as chance.
Adhering to the principle of forming circularities by joining the opposite ends of a continuum, we can observe the emergence of such ‘ripples’ as, for example, individual idiosyncrasies
collective structures; predetermined circumstances
free individual or collective will; given conditions
emergence of a
chance
; nature
technology; cultural traditions
global integration, science
humanities and so on.
In relation to the process of knowing, the Ripples model emphasises a divergence
convergence ripple. This can be explained using a visual illusion example, such as perspective. According to the principles of perspective, the objects that are closer to a viewer appear bigger, brighter and with more details than those that recede in the distance. If perception is extended beyond the visual into a more divergent representation, it can be noted that we perceive the objects that are close to us in the totality of their existence. We can smell them; upon touching them, we can feel their surface; if they are edible, we can taste them; we can feel the temperature and other particulars of their surroundings that allow the objects to maintain their certain physical states. In other words, we develop a unified and rather complex qualitative experience as a result of our direct observation or physical interaction with the objects in their immediate environment. This knowing of objects through a subjective experience, referred to by Edelman and Tononi (2013) as qualia, is private and ‘cannot be communicated directly through scientific theory that by its nature, is public and intersubjective’ (p. 14).
Making meaning of the divergently experienced qualia may appear to be overwhelming, ambiguous or even confusing. To this end, people invented a number of abstract semiotic systems. To convey the qualia of experience is verbal language; to determine objects’ relations to space, movements, quantity and other possible numerical manipulations is the language of mathematics; to identify and manage objects’ states of matter and behaviour in space and time is the language of physics; to understand, decompose and recreate objects’ compounds, structures and properties is the language of chemistry; and to instruct objects to act and represent is the language of computational coding. In short, each discipline took care of examining and manipulating specific properties of the physical objects and their behaviours. The divergence of the life experience was reduced from superfluous sensory unity into pure abstract symbolic systems of specialised disciplinary meaning-making. The more culture advances, as Dewey (2015) argues, the more data is converted and stored in symbols. ‘There is the standing danger that the material of formal instruction will be merely the subject matter of the schools, isolated from the subject matter of life-experience’ (loc. 458).
Vygotsky’s (1934) illustration of the chemical reduction ‘of water into hydrogen and oxygen, neither of which possesses the property of the whole and which possesses properties not present in the whole’ (p. 84), can be taken as an example. The subject of water as a composition of hydrogen and oxygen is observed as an abstract symbolic entity, present in the external existence that has no personal association with the learner.
[…] does not affirm himself but denies himself. The student only feels himself outside his learning, and his learning feels outside himself. He is at home when he is not learning (in a sense of formal education) and when he is learning he is not at home. His learning is therefore not voluntary, but coerced; it is forced learning […] Its alien character emerges clearly in the fact that as soon as no physical or other compulsion exists, learning is shunned like the plaque. (loc. 1312)
As emphasised, the term ‘learning’ inserted in the above quotation refers to formal education, and the term ‘home’ implies a complex body of personal associations and individual experiences. Accordingly, when students learn from everyday life experience, that is, informally, they are ‘at home’. They construct their knowledge building based on their innate abilities, special interests, deep-seated curiosity, empathy, intuition, concerns and necessities. They are authentically connected to their ‘lifeworld’ (Kalantzis and Cope 2012, p. 137). According to Kalantzis and Cope’s diagnosis, one of the biggest issues in formal learning is ‘the distance between lifeworld experience and the culture and discourse of formal learning (education)’ (p. 138). One of the ways to achieve the reconnection, Sir Ken Robinson (2009) argues, is to create learning conditions in which students can discover their element, ‘the place where things we love to do and the things we are good at come together’ (loc. 176) and learn from building on this.
The Ripples pedagogy
suggests an approach
to reconnection in which the knower constructs their knowledge from being at home and from being in his/her element through a continual divergence
convergence
rippling. This implies that learning occurs through the process of exploring divergent lifeworlds and the qualia of transforming experiences into multimodal symbolic system(s) according to the personal distinctive cognitive appeal.
Alternatively stated, a divergence
convergence
ripple is a rotational force that causes the readjustment of academic content in a given area with respect to volume and topics, and its synchronisation with a student’s personal psychological needs; that is the element. Moving the focus continuously to and fro between divergent context and its representation and manipulation through convergent systems of symbols assists in mastering skills of the personally unique knowledge construction and its application to real life situations. This is essential because with life around us changing at an aggressive speed, the capacity to adapt to constantly altering circumstances by using the what-I-am-good-at principle, combined with the relevant disciplinary knowledge, will soon become one of the most important survival skills.
2.6 Individual Curiosity
Conventional Wisdom Ripple: Leonardo, Isaac, Albert and Steve
In this section, I draw extensively on Walter Isaacson’s three biographical masterpieces written about Albert Einstein (2007), Steve Jobs (2011), and Leonardo Da Vinci (2017). By piecing together historical and personal facts with a philosophical approach, Isaacson assembles a complex jigsaw puzzle of narratives of these outstanding individuals’ lives in near-virtual-reality. Through Isaacson’s mastery, the biographies are interwoven with the reader’s experience in such a way that the reader begins to recognise how he/she can realise their own potential, hear their own stories retold anew, and see their own contribution to society as valuable and desired. Isaacson’s biographies can be taken as an example of how the pieces of a predetermined jigsaw puzzle can be reassembled in a novel and most inspiring way.
Once or twice, opening my Amazon Kindle, I wished I could see a new title from Isaacson, a biography of Isaac Newton. Unfortunately, however, this was never the case. Therefore, integrating facts and concepts around Newton’s life, I rely on the brilliantly crafted works of two other authors, Sarah Dry (2014) and John Chambers (2018), as well as the material produced by Hourly History (2017).
The purpose of this section is to use examples from the lives of four influential individuals to illustrate the second essential circularity of the Ripples approach to learning, which is
individual curiosity
conventional wisdom. Da Vinci, Newton, Einstein and Jobs lived in different historical periods, but what made their times similar were the paradigmatic shifts that shook the formations of established knowledge and the giving way of dominant social structures to new understanding and beliefs. The fifteenth century of Da Vinci was a time of technological, social and cultural renaissance. The seventeenth century of Newton is marked by the English Civil War but also by the Scientific Revolution and profound cultural growth. The beginning of the twentieth century saturated collective thought with the spirit of avant-gardism, accompanied by breaking the boundaries of classical norms and an assertion of unconventional wisdom. The end of twentieth and the beginning of the twenty-first centuries will be collectively remembered as a period of Digital Revolution that strove for creative scientific innovations.
Da Vinci, Newton, Einstein and Jobs were prominent figures in their times of change and cardinal contributors to the changes taking place around them. Stephan Klein (2010) writes that Leonardo’s most precious legacy was not so much his art—21 famous paintings and hundreds of thousands drawing and sketches—but his new mode of thinking, ‘which can serve as a source of inspiration today more than ever’ (loc. 147). Namely, it was his ability to invent the world of the future through passionate and thorough observations of the world around him. Regarding Newton’s legacy, Chambers (2018) writes, ‘The world from which Newton departed in 1727 was substantially different from the world into which he was born, and he himself accounted for much of the difference,’ (loc. 79). Edmund Halley, the first editor of Newton’s Principia, upon presenting the book to Queen Anne told her: ‘All science can be divided into two halves. The first is everything up to Newton. The second is Newton’ (as cited in Chambers 2018, loc. 71). Similarly, Einstein is described by Isaacson (2007) as ‘a paramount icon of our age’ whose story is ‘a testament to the connection between creativity and freedom, reflects the triumphs and tumults of the modern era’ (p. 6). Illustrating Jobs’ contribution to technological progress, Isaacson (2011) writes that his ‘passion and ferocious drive revolutionised six industries: personal computers, animated movies, music, phones, tablet computing, and digital publishing’ (loc. 344).
conventional wisdom (CCI
CW) ripple of such intensity that using Jobs’ words, it ‘made a ding in the universe’ (p. 102). To examine the nature of this circularity in relation to these outstanding individuals, let us begin with an extract from Isaacson’s work on Einstein (2007):Near the end of his life, Einstein was asked by the New York State Education Department what school should emphasise. ‘In teaching history,’ he replied, ‘there should be extensive discussion of personalities who benefited mankind through independence of character and judgment’. (p. 6)
From what he said, we can surmise that Einstein associated the evolution of society with the contributions of those who were capable of taking an independent stance in questioning conventional wisdom. There are some rare individuals among us who are curious enough to move away from the traditional vantage point and start examining common truths from a different angle and in a new light. As they generate sufficient evidence to give them a certain level of confidence, they challenge existing beliefs. Einstein was one of these individuals, who had the ‘brashness needed to scrub away the layers of conventional wisdom that were obscuring the cracks in the foundation of physics, and his visual imagination allowed him to make conceptual leaps that eluded more traditional thinkers,’ (p. 92). In this quote, Isaacson demonstrates an eloquent visual imagination of his own to assist us in seeing clearly how Einstein’s imagination helped him to alter the existing worldview.
Einstein was brash but that alone would not be enough to undertake such a colossal endeavour as ‘to scrub away’ the scientific camouflage that had been knitted tightly through centuries by a multitude of people and was deeply embedded in the collective psyche. To do this, he also needed to be strongly equipped with a deep knowledge of the symbolic domains of physics and mathematics. However, even that was not enough, as Isaacson stated; what distinguished Einstein from other ‘more traditional thinkers’ was his capacity for visual imagination. In view of this, a fascinating link can be made to Einstein’s education that deserves emphasis in the context of this text.
[…] it made me clearly realize how much superior an education based on free action and personal responsibility is to one relying on outward authority.
[…] In Aarau I made my first rather childish experiments in thinking that had a direct bearing on the Special Theory. (as cited in Isaacson 2007, p. 26)
Over the years, he would picture in his mind such things as lightning strikes and moving trains, accelerating elevators and falling painters, two-dimensional blind beetles crawling on curved branches, as well as a variety of contraptions designed to pinpoint, as least in theory, the location and velocity of speeding electrons. (p. 26)
Einstein’s genius was fuelled first by his intense and self-governing desire to understand things. As he put it, he had ‘no special talents, I am only passionately curious’. He wondered childishly about the things that ‘the ordinary adult never bothers his head about’ (as cited in Isaacson 2007, p. 548). His curiosity motivated him to master the symbolic systems of the domains of his interest; he was not, however, doing well in ‘literature, French, zoology, botany, and politics’ (p. 25) and he ‘needed to do remedial work in chemistry’ (p. 29). In other words, Einstein’s curiosity, and his immense desire to learn, had a convergent character pulled into focus by his very specific interests. In addition, yet, to achieve his out-of-this-world results, Einstein mastered harmonising his mind with the universal ‘mysterious tune, intoned in the distance by an invisible player’ (p. 391) by means of visual imagining and playing his violin. As he wrote, ‘I am enough of an artist to draw freely on my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world’ (p. 387). On playing a violin duet, Einstein earned the admiration of the second violinist for his ‘enchanting tone and incomparable rhythm’. ‘Do you count the beats?’ his partner asked. ‘Heavens no, it’s in my blood,’ Einstein replied (p. 29).
It appears that the convergence
divergence circularity, in Einstein’s case, was synchronised with a
focused curiosity
cosmic tuning in which he was breaking through the limitations of the world and flowing into a consonance with the vastness and richness of the universe. One of his contemporaries wrote that ‘Music, Nature and God became intermingled in him in a complex of feeling, a moral unity, the trace of which never vanished’ (p. 14).
Get the master of arithmetic to show you how to square a triangle […]
Ask Giannino the Bombardier about how the tower of Ferrara is walled […]
Get the master of hydraulics to tell you how to repair a lock, canal and mill in the Lombard manner […]
Observe the goose’s foot: if it were always open or always closed the creature would not be able to make any kind of movement […]
Why the fish in the water is swifter than the bird in the air when it ought to be contrary since the water is heavier and thicker than the air? […]
Describe the tongue of the woodpecker […] (p. 5).
‘Who on earth would decide one day, for no apparent reason, that he wanted to know what the tongue of a woodpecker looks like? How would you even find out?’ (p. 5) Isaacson wonders in bewilderment and in awe.
Let us imagine for a moment that a student of the present time, in a contemporary school, brings to his/her teacher a similar list of things about which he/she is eager to learn. What would be the reaction of the teacher? Naturally, different teachers would react differently, but it would not be surprising if the list formed a cause for concern for most of them, particularly with regard to the student’s unusual and exceedingly extravagant divergence in the scope of interests. Psychological and behavioural therapies might even be suggested to help the student learn how to restrain his/her curiosity; similarly, testing for attention deficit disorder or medication that can effectively ‘converge’ the focus of his/her interests into the ‘right’ channel might be considered.
In 2011, 3.5 million American children were taking medications for ADHD (attention deficit hyperactivity disorder). In the UK the number rose from 92,000 in 1997 to 786,000 in 2012. The original aim had been to treat attention disorders, but today completely healthy kids take such medication to improve their performance and live up to the growing expectations of teachers and parents. Many object to this development and agree that the problem lies with the education system rather with the children. (p. 45)
In this connection, the words of Steve Jobs in relation to his school authority come to mind: ‘They came close to really beating any curiosity out of me,’ (Isaacson 2011, p. 10) by making ‘me memorise stupid stuff rather than stimulating me’ (p. 11). Jobs also recalls: ‘I was kind of bored […] so I occupied myself by getting into trouble’ (p. 10). The same thing happened to him later in college. ‘I had no idea what I wanted to do with my life and no idea how college was going to help me figure it out. And here I was spending all of the money my parents had saved their entire life. So, I decided to drop out and trust that it would all work out okay,’ said Jobs in his famous address at Stanford (p. 36). In other words, an education focused on memorizing the convergent symbolic systems of academic disciplines without allowing divergent explorations in areas of personal interest stifled Jobs’ inquisitive mind that was hungrily searching for creative application.
Leonardo da Vinci, by contrast, having not been exposed to any formal education ‘liked to boast that because he was not formally educated, he had to learn from his own experiences instead’ (Isaacson 2017, p. 170). Da Vinci wrote: ‘He who has access to the fountain does not go to the water-jar’ (p. 170). Elaborating on this analogy, it should be stressed that Da Vinci by no means dismissed the importance of the ‘water-jar’, the content of which can be viewed as a distilled substance of the water in a fountain—a convergence of the whole into a manageable, concise abstract system of its symbolic representation and operation. In the context of Da Vinci’s approach, the fountain analogy should be treated as an inverse method of modern education. His first step was to ‘consult experience,’ and then, ‘with reasoning show why such experience is bound to operate in such a way’ (p. 173). He used his curiosity as a catalyst leading him to established knowledge. With visualisation and drawing as his most efficient natural tools to record his empirical studies and embody his thoughts, Da Vinci capitalised on them to connect the dots and link experience with theory. Moving between experiencing the object in its medium divergently, as a whole, and converging this experience into an abstract symbolic understanding, we can see Da Vinci’s divergence
convergence ripple. This method made him an avant-garde thinker of his time, leading to the modern, theory
experiment approach in research practices (p. 175), which unfortunately is not used sufficiently as a strategy for learning in schools.
Similar to Da Vinci, Newton left a colossal archival legacy, ‘containing well over five million words in his own writing’ (Dry 2014, p. 4). These papers comprised extensive records of his work in diverse areas, including theology, philosophy, mystics, prophecy, mechanics, optics, chronology and history, as well as alchemical investigations. For two centuries, the papers were hidden from the public eye as their disclosure ‘threatened to undermine not just Newton’s reputation but, some felt, that of science itself’ (p. 4). Looking through the lens of the Ripples approach, the material discovered in the papers can be seen as divergent components of Newton’s ‘ripples of knowing’. Einstein referred to them as Newton’s private method of discovery, ‘the formative development of his work in physics […] so-called, mental workshop (geistige Werstatt)’ (p. 172). According to Einstein, this was ‘in no way evidence of dangerous obsession […] but the evidence of a mind at work on the way to creation’ (p. 172). As Dry explains, ‘Rather than revealing the substructure upon which Newton built his philosophy or the process of his most rational thought, the very looseness and foulness of the archive, its population of drafts and redrafts, reveals a mind always changing,’ (p. 216).
In the words of one of the scholars studying Newton’s manuscripts, the papers illustrate ‘a holistic view of the man in which his theology and natural philosophy are seen as equally important elements of the same grand unified project, the restoration of man’s original pristine knowledge of God and the world’ (Chambers 2018, loc. 106).
making models of windmills (including one with a mouse on a treadmill turning the mill and grinding wheat); of watermills that he placed in streams; of four-foot-high water clock that still told the right time years after he went to Cambridge – of paper lanterns, kites with candles attached, sundials […] He also drew, decorating “his whole room with pictures of his own making, [of king’s heads,] birds, beasts, men, ships & mathematical schemes, & very well designed” (loc. 150), [inhibiting] a world of “forms, forces, and spirits some real and some imagined” – a world that helped him form the uncanny faculty of intuition that […] helped Newton arrive at truth before he’d worked out the mathematics that would lead him there. (loc. 139)
Newton scholars agree that ‘he did well at school only when pushed’ (loc. 161) and yet being at home in his element, he did not need any pushing. Once more, we can see an example of natural curiosity as a motivational force behind heuristic knowing, which led to the search for and acquisition of exact, algorithmic knowing in the form of converged abstract systems. Independently, Newton read Plato, Aristotle, Descartes, Kepler and Galileo and ‘in his third year of college, he began to create his own mathematics’ (loc. 180). Manuel argues that Newton had ‘a compelling drive to find order and design in what appeared to be chaos, to distil from vast, inchoate mass of materials a few basic principles that would embrace the whole and define the relationships of its component parts’ (as cited in Dry, p. 199).
[…] to myself I seem to have been only like a boy playing on the seashore, and diverting myself now and then in finding a smoother pebble or prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me. (as cited in Hourly History 2017, loc. 422)
In this analogy, we can find Newton’s visualisation of his divergence
convergence mode of inquiry. It is based on the idea of a free and curious mind indulging itself like a little boy playing at the edge of the great unknown, connecting the dots that reveal themselves through strata of mystery and converging those connections into patterns of the pebbles or shells that are found on the shore.
As charming as it is to visualise, it is difficult to imagine this mode of learning being easily implemented in a traditional classroom, mainly because it does not go well with the concept of a rigid structure that dominates traditional pedagogies. The metaphors of the fountain and jug, ocean and pebbles are too idealistic for standardised learning. Their implementation can be messy and lead to unsatisfactory tests result. Additionally, we must be realistic—the students in our classrooms are not Newtons. That does not mean, however, that they are not curious within their own areas of interest and in their own, unique ways. If cherished and nurtured, students’ curiosity can help them to find their individual element and learn from the expanding intrinsic motivation. Unfortunately, formal schooling blocks the view of ‘the ocean of truth’—the ‘great unknown’, that lies in front of each individual student—and relegates them to studying already patterned pebbles and shells. They must memorise the number of lines, names of the dots and retain the arrangements of patterns in their minds. That is, what the students will be tested on and that is what will earn them marks and grades. That is, what we call modern education.
From this point of view, it is not surprising that, ‘Bill Gates, Mark Zuckerberg, Steve Jobs, Michael Dell, Dean Kamen, Paul Allen, and many other brilliant innovators had to drop out of college to pursues their new ideas,’ (Wagner 2012, p. 64).
[…] their schooling was interfering with their education. According to Jobs, the course that he did take in college that had the most impact on the design of the first Apple Macintosh computer was not a STEM-related course at all – it was a course in calligraphy! (p. 64)
I always thought of myself as a humanities person as a kid, but I liked electronics […] Then, I read something that one of my heroes, Edwin Land of Polaroid, said about the importance of people who could stand at the intersection of humanities and science, and I decided that’s what I wanted to do. (as cited in Isaacson, loc. 342)
It’s in Apple’s DNA that technology alone is not enough. We believe that its technology married with humanities that yields us the result that makes our heart sing. (p. 485)
By contrast, years of schooling aligned with the transmission of regulated academic material deprives students of their
diversive curiosity
engendered by a passion for their individual objects of interest. A case in point is STEM
education, which is heavily oriented towards construction of positivistic, objective knowledge. By considering liberal education and aesthetic dimensions as superfluous, ‘perhaps pleasing but neither [a] necessary nor indispensable’ (Vecchi 2010, p. 15) part of individual growth, STEM is detached from the exercise of curiosity. As a delivery machine for convergent symbolic systems, modern education deprives its students of the chance to give their curiosity a lead role in the exploration of the wonders of the universe, recognition of real-life problems and discovery of their own element. Elaborating further, this provokes a decline of purpose and engenders the atrophy of a desire to make difference. In the language of the Ripples pedagogy, with the disappearance of an individual curiosity component, the individual curiosity
conventional wisdom circularity is reduced to the conventional wisdom, unchallenged. This means that the cheerful robots and fearful puppets get along in life causing no disruptions, ‘no dings in the universe’, susceptible to the machines’ growing intelligence and ability to take full control of the world.
2.7 Convergence Points
This chapter introduced the highly seismic landscape of contemporary society where a paradigmatic shift has led to profound adjustments and restructuring in all areas of present-day life. The chapter argued that despite finding itself in the midst of an extreme social and cultural tremor, modern education has asserted itself as a bedrock of traditional values and remained a closed system. Using some superficially effective technological cover-ups, education has protected its rigid configuration built on the infrastructure of standardised testing that underlies all associations and proceedings in the contemporary business of schooling. It has preserved the established system as the most convenient and effective mode of control, keeping its grip on delivering the content and methods of teaching academic disciplines. Instead of reconsidering its foundational principles to adapt to the exponential reconstructions of the worldview, world organisation and communication, education remains dedicated to the old ‘puzzle-solving’ conventions.
It takes artists, musicians, and psychologists working side by side with engineers to build products as elegant as the iPad. […] My advice to my students – and to my own children – is to study what interests them the most; to excel in fields in which they have the most passion and ability; to change the world in their own way and on their own terms. (p. 191)
Additionally, acquiring more algorithmic ‘education and skills will not necessarily offer effective protection against job automation in the future,’ as Martin Ford (2015, loc. 172) argues. In fact, the concepts of ‘a job-as-we-know-it today’ and the money–occupation relationship (Leonhard 2016, p. 49) are facing a radical transformation. Thus, when we so confidently guarantee our students their future employment by making a certain area of study compulsory, how can we be sure that we are giving them the right direction if we ourselves are entering uncharted territory?
One thing we do know, however, is that the territory is densely penetrated by algorithms and machines that are becoming exponentially better and better at responding to and operating with those algorithms. Human entanglement with machines has become commonplace in all areas of modern life. In this entanglement, as much as it is categorically essential to be a proficient technology user, on the one hand, it is absolutely critical to be adept in distinguishing the human side—androrithms—of these interactions, on the other. As the androrithms of this entanglement, we who are non-digitised, non-automated, non-virtualised, non-augmented and non-robotised (yet) but yielding progressively to the rapidly expanding technology, it is crucial for us to know more about our own humanness to maintain our sovereignty.
The Ripples pedagogy suggests considering the two fundamental ‘ripples’ for knowledge construction that assist in the evaluation and maintenance of human autonomy in the human
machines enmeshment They are the divergence
convergence
and individual curiosity
conventional wisdom circularities.
The divergent aspect is seen as the ability to view an object or concept in its totality within the medium of its existence, to observe it from various perspectives and identify a facet about which an individual student is most passionate. The convergent component is about linking the dots in the identified facet with the symbolic system of the discipline or cross-disciplines within which learning takes place. Focusing learning strategies solely on the convergent side of this circularity takes students away ‘from home’ by placing them in an estranged area that might be of little interest to them. It also alienates students from discovering and maturing in their ‘element’ —their innate abilities and skills, as well as the capacity to apply them to real-life situations.
The individual curiosity
conventional wisdom circularity is considered through the examples taken from the lives and works of four outstanding historical personalities: Leonardo da Vinci, Isaac Newton, Albert Einstein and Steve Jobs. Using examples from these great people’s lives, the chapter illustrates that without the ability to challenge conventional wisdom, education is doomed to produce
fearful puppets
and
cheerful robots
. Individual curiosity
can be sustained by providing a learning environment of being ‘at home’
and in ‘the element’
. Such a
heuristic
approach facilitates the conditions for intrinsic motivation that determine the areas of algorithmic knowledge to be integrated into the learning project and appropriated by the student(s). The individual curiosity together with the generated knowledge provides a student with the confidence necessary to question common concepts.
convergence
and individual curiosity
conventional wisdom circularities in terms of their foundational capacity to assist in the cultivation of free thinkers, who are aware of their individual strengths and adept in knowing how to apply their potential to life outside the classroom, who are intelligent critical and ethical evaluators, responsible for the future of the world.Key Terms | |
|---|---|
Algorithmic learning | – Puzzle-solving by following a prescribed methodology |
Being ‘at home’ | – Learning in an environment that is conducive to a student feeling free to act on their diversive curiosity |
Being in ‘the element ’ | – Learning by being engaged in doing things that one loves to do and building on the things that one is good at |
Bricoleur | – The knower uses ingenious means to apply the materials and tools at hand |
Cheerful robot s | – Concept of C. Wright Mills (1959) referring to the individual who has lost their ‘capacity and will to reason; it also affects his chances and capacity to act as free man’ (p. 170) |
Divergence
| – Oscillations between explorations within diverse areas of interest and making connections for the pursuit of directed inquiry |
Diversive curiosity | – Eagerness to know novel things, to explore unknown territories, to discover unusual methods of doing things based on the individual interests |
Epistemic curiosity | – Inquisitiveness that guides the pursuit of knowledge |
Fearful puppets | – People who avoid taking risks and instead learn by seeking to escape punishment |
Focused curiosity
| – Finding a precise answer to a problem by studying it well, as well as applying the techniques of visual imagination, drawing, playing or listening to music or any other artistic activity to tune oneself with the harmony of the universe, as Einstein did |
Heuristic learning | – Learning by discovery |
Individual curiosity
| – Oscillations between diverse explorations based on individual interests and a juxtaposition of the results of these explorations with the collectively constructed concepts |
Paradigm | – A collectively accepted set of intellectual conceptualisations, theories and scientific practices characterised by a certain historical period |
Puzzle-solving | – A common strategy established by a certain paradigm in searching for an answer to a problem |
STEM | – A contemporary trend in education with an intensified focus on algorithmic learning across the disciplines of science, technology, engineering and mathematics. It advocates critical and creative thinking in the project-based learning, but at the same time, it gives preference to STEM disciplines at the expense of arts and humanities |
2.8 DOING
KNOWING: The Ripples Pedagogy in Practice
2.8.1 Learning Task One: The Newtonian Knower
[…] pluses and minuses, apples and oranges, anything you please – can be used to express or signify messages. (William Friedman 1963, p. 31)
The above quote is derived from a lecture of an esteemed pioneer in the application of scientific principles to cryptology, William Friedman (1892–1969). In this quote, Friedman refers to Sir Francis Bacon’s (1561–1626) methods of ciphering. ‘Bacon was, in fact, the inventor of the binary code that forms the basis of modern electronic digital computers,’ Friedman said (p. 31).
In this task, I suggest drawing links from disparate concepts and analogies to explore such circularities as:
puzzle-solving
mystery-discerning;
algorithmic
heuristic methods of knowledge gathering; divergence
convergence and
individual curiosity
conventional wisdom.
Let us put ourselves in the shoes of the Newton’s boy playing on a seashore. He is at the edge of his immediate physical reality embodied in waves, sand, pebbles and shells and the mystery of the ocean, the great unknown truth. Newton describes himself as a boy who, while playing, finds pebbles and shells that were not found by other people before. In his seashore analogy, Newton proposes the notion that The Great Unknown, the divergent, reveals its elements through the convergent codes that are readily available in physical reality to those who are looking to decipher them. Those people who decode the messages from The Great Unknown examine them and make meaning from them through the lens of the existing paradigm. They embody the derived meaning in symbols and concepts of their own construction in congruence with the existing ones. Thus, a great database of the collectively generated knowledge coded in various symbolic systems and conceptualised in accordance with academic domains is continuously being formed. On the one hand we have The Great Unknown, the universe in its totality including its micro- and macrodimensions, and on the other, we have a vast collection of man-made abstract systems of Coded Knowledge (CK), algorithms and facts representing the discovered aspects of The Great Unknown (TGU).
Working with the components of circularities presented above, we can say that if we focus on studying only from CK, we break the circularities, reducing them to one segment and turning them into disconnected curved lines: conventional wisdom, convergence to the symbols; puzzle-solving and algorithmic methods of learning, that is, > studying the disciplinary symbols and their functionality > adhering to the given instructions > arriving at the expected result. In the language of the Ripples pedagogy, such an approach is alienated learning, in which students are separated from the observation of the objects of their interest in their immediate environments, and students’ psychological inclinations and social needs are not taken into consideration.
The Ripples model suggests placing an individual student’s preferences in terms of interests and abilities in the centre of the learning unit.
Materials and Equipment:
Mobile recording devices such as digital tablets or mobile phones;
Empty lunch box-type plastic container for collecting diverse samples from nature that draw students’ personal interest; and
Drinking water, snacks, hats, insect repellents—at the teacher’s discretion.
Computer with PowerPoint software installed;
Scanner;
Printer;
Drawing materials: paper and coloured pencils; and
Craft and construction materials: scissors, glue, coloured paper.
- 1.
In your own words and in language appropriate to the year level, introduce the students to the concept of the Newtonian Knower.
- 2.
The surrounding for a field trip can be anything that is aligned with the topic of intended study where objects can be observed in their totality as parts of a larger system—The Great Unknown (TGU). Although an environment, natural or social, may appear to be well-known, there are many grey areas that can still be discovered and learned about. Thus, TGU can be the seashore, the bush, a river bank, a street in the city, an outdoor space on the school ground or even the present classroom.
- 3.
Students are given time to work independently and divergently to take photos of various objects in their surroundings. They must type brief and simple notes and questions about their observations in their mobile devices’ Notes app. Asking questions is a sophisticated and essential skill in practising curiosity and nurturing humanness. During the field trip, students may not be ready to form deep-level thinking questions as they are engaged in ‘grasping’ fragments from the environment, isolating them into captured frames according to their interests. This is a time for exercising diversive curiosity. It is essential to keep up the excitement about what the students are observing and discovering, but it is also important to record the mind flashes that occur as responses to what is experienced, even if these are explained in a primitive or naïve way. This can be defined as anchoring qualia, the state of mind at the time of a certain experience.
- 4.
Ask the students to make short recordings of sounds they hear, as well as to video-record short snippets of movements showing the interactions of various objects in the environment. These activities should also be annotated in the Notes app.
- 5.
Back in the classroom, the students are asked to start working with their generated divergent data by transferring it into PowerPoint. This software is suggested for this task because it is easy to perform image manipulations, write annotations in separate text-boxes, insert audio and video files, and create flexible compositions of multimodal elements as presentations at any time. It is also suitable for use as a personal developmental folio of a learning process as it facilitates a notebook style that can resemble the notebooks of Newton or Da Vinci. Because it is easy to alter the sizes of images and fit text-boxes between and around objects, it is suggested to assemble the data in categories, not one image per page, but to create relational organisations of the images, sounds and videos with their annotations and analytical notes. It is suggested to generate approximately three or four pages of the gathered data.
- 6.
The next stage of the process is referred to as an epistemic curiosity module. It is the process of distilling an essence from what has been collected, converging it with what appears to be the most interesting. This is done by asking deep-level thinking questions, manipulating and reorganising images, and making observational drawings like Da Vinci and Newton. The remarkable thing about observational drawing is the engagement in a different type of observation. It reveals the kind of special relationship between elements that is not noticeable at first glance. The purpose of the drawing activity is not to produce pretty pictures but an intent study of ‘coded messages from the environment expressed in the observed object’. Students scan the drawings or take photos of them and place them in their developmental folios.
- 7.
Divide the class into groups of five or less and ask students to present their ideas and questions to their groups. Ask the groups to assess each other’s developmental process with regard their individual diversive curiosity and the convergent questions that they posed for themselves to investigate certain areas of their interest.
- 8.
The students continue working towards answering their questions by consulting collective pools of knowledge on the Internet, posing questions on their social media sites, joining websites established by the groups of interest and taking interviews. They record their activities in their folios.
- 9.
As a result of the synthesis of the collected data, students develop embodiments of their ideas with the use of physical materials or other modes of expression, which can be conceptual models, engineering constructions, spatial arrangements, audio compositions, animations and so on.
- 10.
The final production along with the developmental folio explaining how the students have arrived at their conclusive results—which may well be another question—is presented to the group for an assessment.