Critical thinking

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Critical_thinking

Critical thinking is the process of analyzing available facts, evidence, observations, and arguments to reach sound conclusions or informed choices. It involves recognizing underlying assumptions, providing justifications for ideas and actions, evaluating these justifications through comparisons with varying perspectives, and assessing their rationality and potential consequences. The goal of critical thinking is to form a judgment through the application of rational, skeptical, and unbiased analyses and evaluations. The use of the phrase critical thinking can be traced to John Dewey, who used the phrase reflective thinking, which depends on the knowledge base of an individual. The excellence of critical thinking in which an individual can engage varies according to it. According to philosopher Richard W. Paul, critical thinking and analysis are competencies that can be learned or trained. The application of critical thinking includes self-directed, self-disciplined, self-monitored, and self-corrective habits of the mind. Critical thinking is not a natural process; it must be induced, and ownership of the process must be taken for successful questioning and reasoning. Critical thinking presupposes a rigorous commitment to overcoming egocentrism and sociocentrism , which leads to a mindful command of effective communication and problem solving.

History

In the West, critical reasoning originated from the teachings of the Greek philosopher Socrates (470–399 BC).

In the classical period (5th c.–4th c. BC) of Ancient Greece, the philosopher Plato (428–347 BC) indicated that the teachings of Socrates (470–399 BC) are the earliest records of what today is called critical thinking. In an early dialogue by Plato,^{[citation needed]} the philosopher Socrates debates several speakers about the ethical matter of the rightness or wrongness of Socrates escaping from prison. Upon consideration, Plato concluded that to escape prison would violate everything he believes to be greater than himself: the laws of Athens and the guiding voice that Socrates claims to hear.

Socrates established the unreliability of authority and authority figures as possessors of knowledge and consequent insight; that for an individual man or woman to lead a good life that is worth living, that person must ask critical questions and possess an interrogative soul, which seeks evidence and then closely examines the available facts, and then follows the implications of the statement under analysis, thereby tracing the implications of thought and action.

As a form of co-operative argumentation, Socratic questioning requires the comparative judgment of facts, which answers then would reveal the person's irrational thinking and lack of verifiable knowledge. Socrates also demonstrated that Authority does not ensure accurate, verifiable knowledge; thus, Socratic questioning analyses beliefs, assumptions, and presumptions, by relying upon evidence and a sound rationale.

In modern times, the phrase critical thinking was coined by Pragmatist philosopher John Dewey in his book How We Think. As a type of intellectualism, the development of critical thinking is a means of critical analysis that applies rationality to develop a critique of the subject matter. According to the Foundation for Critical Thinking, in 1987 the U.S. National Council for Excellence in Critical Thinking defined critical thinking as the "intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action."

Etymology and origin of critical thinking

In the term critical thinking, the word critical, (Grk. κριτικός = kritikos = "critic") derives from the word critic and implies a critique; it identifies the intellectual capacity and the means "of judging", "of judgement", "for judging", and of being "able to discern". The intellectual roots of critical thinking are as ancient as its etymology, traceable, ultimately, to the critical reasoning of the Presocractic philosophers, as well as the teaching practice and vision of Socrates 2,500 years ago who discovered by a method of probing questioning that people could not rationally justify their confident claims to knowledge.

According to the Oxford English Dictionary, the exact term “critical thinking” first appeared in 1815, in the British literary journal The Critical Review, referring to critical analysis in the literary context. The meaning of "critical thinking" gradually evolved and expanded to mean a desirable general thinking skill by the end of the 19th century and early 20th century.

Definitions

Traditionally, critical thinking has been variously defined as follows:

• "The intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action."
• "Disciplined thinking that is clear, rational, open-minded, and informed by evidence"
• "Purposeful, self-regulatory judgment which results in interpretation, analysis, evaluation, and inference, as well as explanation of the evidential, conceptual, methodological, criteriological, or contextual considerations upon which that judgment is based"
• "Includes a commitment to using reason in the formulation of our beliefs"
• The skill and propensity to engage in an activity with reflective scepticism (McPeck, 1981)
• Thinking about one's thinking in a manner designed to organize and clarify, raise the efficiency of, and recognize errors and biases in one's own thinking. Critical thinking is not 'hard' thinking nor is it directed at solving problems (other than 'improving' one's own thinking). Critical thinking is inward-directed with the intent of maximizing the rationality of the thinker. One does not use critical thinking to solve problems—one uses critical thinking to improve one's process of thinking.
• "An appraisal based on careful analytical evaluation"
• "Critical thinking is a type of thinking pattern that requires people to be reflective, and pay attention to decision-making which guides their beliefs and actions. Critical thinking allows people to deduct with more logic, to process sophisticated information and look at various sides of an issue so they can produce more solid conclusions."
• Critical thinking has seven critical features: being inquisitive and curious, being open-minded to different sides, being able to think systematically, being analytical, being persistent to truth, being confident about critical thinking itself, and lastly, being mature.
• Although critical thinking could be defined in several different ways, there is a general agreement in its key component—the desire to reach for a satisfactory result, and this should be achieved by rational thinking and result-driven manner. Halpern thinks that critical thinking firstly involves learned abilities such as problem-solving, calculation and successful probability application. It also includes a tendency to engage the thinking process. In recent times, Stanovich believed that modern IQ testing could hardly measure the ability of critical thinking.
• "Critical thinking is essentially a questioning, challenging approach to knowledge and perceived wisdom. It involves ideas and information from an objective position and then questioning this information in the light of our own values, attitudes and personal philosophy."

Contemporary critical thinking scholars have expanded these traditional definitions to include qualities, concepts, and processes such as creativity, imagination, discovery, reflection, empathy, connecting knowing, feminist theory, subjectivity, ambiguity, and inconclusiveness. Some definitions of critical thinking exclude these subjective practices.

1. According to Scriven and Paul (1987), "Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action." This definition is endorsed by Harvey Siegel, Peter Facione, and Deanna Kuhn.
2. According to Ennis' definition, critical thinking requires a lot of attention and brain function. When a critical thinking approach is applied to education, it helps the student's brain function better and understand texts differently.
3. Different fields of study may require different types of critical thinking. Critical thinking provides more angles and perspectives upon the same material.

Logic and rationality

Main article: Logic and rationality

The study of logical argumentation is relevant to the study of critical thinking. Logic is concerned with the analysis of arguments, including the appraisal of their correctness or incorrectness. In the field of epistemology, critical thinking is considered to be logically correct thinking, which allows for differentiation between logically true and logically false statements.

In "First wave" logical thinking, the thinker is removed from the train of thought, and the analysis of connections between concepts or points in thought is ostensibly free of any bias. In his essay Beyond Logicism in Critical Thinking Kerry S. Walters describes this ideology thus: "A logistic approach to critical thinking conveys the message to students that thinking is legitimate only when it conforms to the procedures of informal (and, to a lesser extent, formal) logic and that the good thinker necessarily aims for styles of examination and appraisal that are analytical, abstract, universal, and objective. This model of thinking has become so entrenched in conventional academic wisdom that many educators accept it as canon". Such principles are concomitant with the increasing dependence on a quantitative understanding of the world.

In the "second wave" of critical thinking, authors consciously moved away from the logocentric mode of critical thinking characteristic of the "first wave". Although many scholars began to take a less exclusive view of what constitutes critical thinking, rationality and logic remain widely accepted as essential bases for critical thinking. Walters argues that exclusive logicism, in the first-wave sense, is based on "the unwarranted assumption that good thinking is reducible to logical thinking".

Deduction, abduction and induction

Main article: Logical reasoning

Argument terminology used in logic

There are three types of logical reasoning. Informally, two kinds of logical reasoning can be distinguished in addition to formal deduction, which are induction and abduction.

Deduction

• Deduction is the conclusion drawn from the structure of an argument's premises, by use of rules of inference formally those of propositional calculus. For example: X is human and all humans have a face, so X has a face.

Induction

• Induction is drawing a conclusion from a pattern that is guaranteed by the strictness of the structure to which it applies. For example: The sum of even integers is even. Let ${\displaystyle x,y,z\in \mathbb{Z}}$ then ${\displaystyle 2x,2y,2z}$ are even by definition. If ${\displaystyle x+y=z}$, then ${\displaystyle 2x+2y=2(x+y)=2z}$, which is even; so summing two even numbers results in an even number.

Abduction

• Abduction is drawing a conclusion using a heuristic that is likely, but not inevitable given some foreknowledge. For example: I observe sheep in a field, and they appear white from my viewing angle, so sheep are white. Contrast with the deductive statement: Some sheep are white on at least one side.

Critical thinking and rationality

Kerry S. Walters, an emeritus philosophy professor from Gettysburg College, argues that rationality demands more than just logical or traditional methods of problem solving and analysis or what he calls the "calculus of justification" but also considers "cognitive acts such as imagination, conceptual creativity, intuition and insight". These "functions" are focused on discovery, on more abstract processes instead of linear, rules-based approaches to problem-solving. The linear and non-sequential mind must both be engaged in the rational mind.

The ability to critically analyze an argument—to dissect its structure and components, including its thesis and reasons—is essential. But so is the ability to be flexible and consider non-traditional alternatives and perspectives. These complementary functions allow critical thinking to be a practice that encompasses imagination and intuition in cooperation with traditional modes of deductive inquiry.

Functions

The list of core critical thinking skills includes observation, interpretation, analysis, inference, evaluation, explanation, and metacognition. According to Reynolds (2011), an individual or group engaged in a strong way of critical thinking gives due consideration to establish for instance:

• Evidence through reality
• Context skills to isolate the problem from context
• Relevant criteria for making the judgment well
• Applicable methods or techniques for forming the judgment
• Applicable theoretical constructs for understanding the problem and the question at hand

In addition to possessing strong critical-thinking skills, one must be disposed to engage problems and decisions using those skills. Critical thinking employs not only logic but broad intellectual criteria such as clarity, credibility, accuracy, precision, relevance, depth, breadth, significance, and fairness.

Critical thinking calls for the ability to:

• Recognize problems, to find workable means for meeting those problems
• Understand the importance of prioritization and order of precedence in problem-solving
• Gather and marshal pertinent (relevant) information
• Recognize unstated assumptions and values
• Comprehend and use language with accuracy, clarity, and discernment
• Interpret data, to appraise evidence and evaluate arguments
• Recognize the existence (or non-existence) of logical relationships between propositions
• Draw warranted conclusions and generalizations
• Put to test the conclusions and generalizations at which one arrives
• Reconstruct one's patterns of beliefs on the basis of wider experience
• Render accurate judgments about specific things and qualities in everyday life

In sum:

"A persistent effort to examine any belief or supposed form of knowledge in the light of the evidence that supports or refutes it and the further conclusions to which it tends."

Critical thinking is significant in the learning process of internalization, in the construction of basic ideas, principles, and theories inherent in content. And critical thinking is significant in the learning process of application, whereby those ideas, principles, and theories are implemented effectively as they become relevant in learners' lives.

In professional fields

Critical thinking is an important element of all professional fields and academic disciplines (by referencing their respective sets of permissible questions, evidence sources, criteria, etc.). Within the framework of scientific skepticism, the process of critical thinking involves the careful acquisition and interpretation of information and use of it to reach a well-justified conclusion. The concepts and principles of critical thinking can be applied to any context or case but only by reflecting upon the nature of that application. Critical thinking forms, therefore, a system of related, and overlapping, modes of thought such as anthropological thinking, sociological thinking, historical thinking, political thinking, psychological thinking, philosophical thinking, mathematical thinking, chemical thinking, biological thinking, ecological thinking, legal thinking, ethical thinking, musical thinking, thinking like a painter, sculptor, nurse, engineer, business person, etc. In other words, though critical-thinking principles are universal, their application to disciplines requires a process of reflective contextualization. Psychology offerings, for example, have included courses such as Critical Thinking about the Paranormal, in which students are subjected to a series of cold readings and tested on their belief of the "psychic", who is eventually announced to be a fake. In short, critical thinking is considered important for enabling a professional in any field to analyze, evaluate, explain, and restructure thinking, thereby ensuring the act of thinking without false belief.

However, even with knowledge of the methods of logical inquiry and reasoning, mistakes occur, and due to a thinker's inability to apply the methodology consistently, and because of overruling character traits such as egocentrism. Critical thinking includes identification of prejudice, bias, propaganda, self-deception, distortion, misinformation, etc. Given research in cognitive psychology, some educators believe that schools should focus on teaching their students critical-thinking skills and cultivation of intellectual traits.

Habits or traits of the mind

The habits of mind that characterize a person strongly disposed toward critical thinking include a desire to follow reason and evidence wherever they may lead, a systematic approach to problem-solving, inquisitiveness, even-handedness, and confidence in reasoning.

According to a definition analysis by Kompf & Bond (2001), critical thinking involves problem-solving, decision making, metacognition, rationality, rational thinking, reasoning, knowledge, intelligence and also a moral component such as reflective thinking. Critical thinkers therefore need to have reached a level of maturity in their development, possess a certain attitude as well as a set of taught skills.

There is a postulation by some writers that the tendencies from habits of mind should be thought as virtues to demonstrate the characteristics of a critical thinker. These intellectual virtues are ethical qualities that encourage motivation to think in particular ways towards specific circumstances. However, these virtues have also been criticized by skeptics who argue that the evidence is lacking for a specific mental basis underpinning critical thinking.

Teaching critical thinking

John Dewey is one of many educational leaders who recognized that a curriculum aimed at building thinking skills would benefit the individual learner, the community, and democracy.

In a 2014 meta-analysis, researchers reviewed 341 quasi- or true-experimental studies of teaching critical thinking, all of which used some form of standardized critical-thinking measure. The authors describe the various methodological approaches and attempt to categorize differing assessment tools, which include standardized tests (and second-source measures), tests developed by teachers, tests developed by researchers, and tests developed by teachers who also serve the role as the researcher. The results emphasized the need for exposing students to real-world problems and the importance of encouraging open dialogue within a supportive environment. Effective strategies for teaching critical thinking are thought to be possible in a wide variety of educational settings. One attempt to assess the humanities' role in teaching critical thinking and reducing belief in pseudoscientific claims was made at North Carolina State University. Some success was noted and the researchers emphasized the value of the humanities in providing the skills to evaluate current events and qualitative data in context.

Historically, the teaching of critical thinking focused only on logical procedures such as formal and informal logic. This emphasized to students that good thinking is equivalent to logical thinking. However, a second wave of critical thinking, urges educators to value conventional techniques, meanwhile expanding what it means to be a critical thinker. In 1994, Kerry Walters compiled a conglomeration of sources surpassing this logical restriction to include many different authors' research regarding connected knowing, empathy, gender-sensitive ideals, collaboration, world views, intellectual autonomy, morality and enlightenment. These concepts invite students to incorporate their own perspectives and experiences into their thinking. Scott Lilienfeld notes that there is some evidence to suggest that basic critical-thinking skills might be successfully taught to children at a younger age than previously thought.

In the English and Welsh school systems, Critical Thinking is offered as a subject that 16- to 18-year-olds can take as an A-Level.

Well-educated citizens

See also: Citizenship education (subject)

In 1995, a meta-analysis of the literature on teaching effectiveness in higher education noted concerns that higher education was failing to meet society's requirements for well-educated citizens. It concluded that although faculty may aspire to develop students' thinking skills, in practice they have tended to aim at facts and concepts utilizing lowest levels of cognition, rather than developing intellect or values.

Critical thinking is also considered important for human rights education for toleration. The Declaration of Principles on Tolerance adopted by UNESCO in 1995 affirms that "education for tolerance could aim at countering factors that lead to fear and exclusion of others, and could help young people to develop capacities for independent judgement, critical thinking and ethical reasoning".

Assessment of critical thinking

Under the OCR exam board, students can sit two exam papers for the Advanced Subsidiary: "Credibility of Evidence" and "Assessing and Developing Argument". The full Advanced GCE is now available: in addition to the two Advanced Subsidiary units, candidates sit the two papers "Resolution of Dilemmas" and "Critical Reasoning". The A-level tests candidates on their ability to think critically about, and analyze, arguments on their deductive or inductive validity, as well as producing their own arguments. It also tests their ability to analyze certain related topics such as credibility and ethical decision-making. However, due to its comparative lack of subject content, many universities do not accept it as a main A-level for admissions. Nevertheless, the Advanced Subsidiary is often useful in developing reasoning skills, and the full Advanced GCE is useful for degree courses in politics, philosophy, history or theology, providing the skills required for critical analysis that are useful, for example, in biblical study.

There used to also be an Advanced Extension Award offered in Critical Thinking in the UK, open to any A-level student regardless of whether they have the Critical Thinking A-level. Cambridge International Examinations have an A-level in Thinking Skills.

From 2008, Assessment and Qualifications Alliance has also been offering an A-level Critical Thinking specification. OCR exam board have also modified theirs for 2008. Many examinations for university entrance set by universities, on top of A-level examinations, also include a critical-thinking component, such as the LNAT, the UKCAT, the BioMedical Admissions Test and the Thinking Skills Assessment.

In Qatar, critical thinking was offered by Al-Bairaq - an outreach, non-traditional educational program that targeted high school students and focussed on a curriculum based on STEM fields. The idea behind this was to offer high school students the opportunity to connect with the research environment in the Center for Advanced Materials (CAM) at Qatar University. Faculty members train and mentor the students and help develop and enhance their critical thinking, problem-solving, and teamwork skills.

Research of critical thinking

After undertaking research in schools, Edward M. Glaser proposed in 1941 that the ability to think critically involves three elements:

1. An attitude of being disposed to consider in a thoughtful way the problems and subjects that come within the range of one's experiences
2. Knowledge of the methods of logical inquiry and reasoning
3. Some skill in applying those methods.

The Critical Thinking project at Human Science Lab, London, is involved in the scientific study of all major educational systems in prevalence today to assess how the systems are working to promote or impede critical thinking.

Contemporary cognitive psychology regards human reasoning as a complex process that is both reactive and reflective. This presents a problem that is detailed as a division of a critical mind in juxtaposition to sensory data and memory.

The psychological theory disposes of the absolute nature of the rational mind, in reference to conditions, abstract problems and discursive limitations. Where the relationship between critical-thinking skills and critical-thinking dispositions is an empirical question, the ability to attain causal domination exists, for which Socrates was known to be largely disposed against as the practice of Sophistry. Accounting for a measure of "critical-thinking dispositions" is the California Measure of Mental Motivation and the California Critical Thinking Dispositions Inventory. The Critical Thinking Toolkit is an alternative measure that examines student beliefs and attitudes about critical thinking.

Online communication

The advent and rising popularity of online courses have prompted some to ask if computer-mediated communication promotes, hinders, or has no effect on the amount and quality of critical thinking in a course (relative to face-to-face communication). There is some evidence to suggest a fourth, more nuanced possibility: that online communication may promote some aspects of critical thinking but hinder others. For example, Guiller et al. (2008) found that, relative to face-to-face discourse, online discourse featured more justifications, while face-to-face discourse featured more instances of students expanding on what others had said. The increase in justifications may be due to the asynchronous nature of online discussions, while the increase in expanding comments may be due to the spontaneity of 'real-time' discussion. Newman et al. (1995) showed similar differential effects. They found that while online communications boasted more important statements and linking of ideas, it lacked novelty. The authors suggest that this may be due to difficulties participating in a brainstorming-style activity in an asynchronous environment. Rather, the asynchrony may promote users to put forth "considered, thought out contributions".

Researchers assessing critical thinking in online discussion forums often employ a technique called Content Analysis, where the text of online discourse (or the transcription of face-to-face discourse) is systematically coded for different kinds of statements relating to critical thinking. For example, a statement might be coded as "Discuss ambiguities to clear them up" or "Welcoming outside knowledge" as positive indicators of critical thinking. Conversely, statements reflecting poor critical thinking may be labeled as "Sticking to prejudice or assumptions" or "Squashing attempts to bring in outside knowledge". The frequency of these codes in online communication and face-to-face discourse can be compared to draw conclusions about the quality of critical thinking.

Searching for evidence of critical thinking in discourse has roots in a definition of critical thinking put forth by Kuhn (1991), which emphasizes the social nature of discussion and knowledge construction. There is limited research on the role of social experience in critical thinking development, but there is some evidence to suggest it is an important factor. For example, research has shown that three- to four-year-old children can discern, to some extent, the differential credibility and expertise of individuals. Further evidence for the impact of social experience on the development of critical-thinking skills comes from work that found that 6- to 7-year-olds from China have similar levels of skepticism to 10- and 11-year-olds in the United States. If the development of critical-thinking skills was solely due to maturation, it is unlikely we would see such dramatic differences across cultures.

Autodidacticism

From Wikipedia, the free encyclopedia

Autodidacticism (also autodidactism) or self-education (also self-learning, self-study, and self-teaching) is the practice of education without the guidance of teachers. Autodidacts are self-taught people who learn a subject through self-study. Autodidacticism may involve, complement, or be an alternative to formal education. Formal education itself may have a hidden curriculum that requires self-study for the uninitiated.

Generally, autodidacts choose the subject they will study, their studying material, and the studying rhythm and time. Autodidacts may or may not have formal education, and their study may be either a complement or an alternative to formal education. Many notable contributions have been made by autodidacts.

The self-learning curriculum is infinite. One may seek out alternative pathways in education and use these to gain competency; self-study may meet some prerequisite-curricula criteria for experiential education or apprenticeship.

Self-education techniques can include reading educational books or websites, watching educational videos and listening to educational audio recordings, or by visiting infoshops. One uses some space as a learning space, where one uses critical thinking to develop study skills within the broader learning environment until they've reached an academic comfort zone.

Terminology

The term autodidact has its roots in the Ancient Greek words αὐτός (autós, lit. 'self') and διδακτικός (didaktikos, lit. 'teaching'). The related term didacticism defines an artistic philosophy of education.

Various terms are used to describe self-education. One such is heutagogy, coined in 2000 by Stewart Hase and Chris Kenyon of Southern Cross University in Australia; others are self-directed learning and self-determined learning. In the heutagogy paradigm, a learner should be at the centre of their own learning. A truly self-determined learning approach also sees the heutagogic learner exploring different approaches to knowledge in order to learn; there is an element of experimentation underpinned by a personal curiosity.

Andragogy "strive[s] for autonomy and self-direction in learning", while Heutagogy "identif[ies] the potential to learn from novel experiences as a matter of course [...] manage their own learning". Ubuntugogy is a type of cosmopolitanism that has a collectivist ethics of awareness concerning the African diaspora.

Tadao Ando, a famous architect from Japan since the 20th century.

Autodidacticism is sometimes a complement of modern formal education. As a complement to formal education, students would be encouraged to do more independent work.

Before the twentieth century, only a small minority of people received an advanced academic education. As stated by Joseph Whitworth in his influential report on industry and innovators dated from 1853, literacy rates were higher in the United States than in England. However, even in the U.S., most children were not completing high school. High school education was necessary to become a teacher. In modern times, a larger percentage of those completing high school also attended college, usually to pursue a professional degree, such as law or medicine, or a divinity degree.

Collegiate teaching was based on the classics (Latin, philosophy, ancient history, theology) until the early nineteenth century. There were few if any institutions of higher learning offering studies in engineering or science before 1800. Institutions such as the Royal Society did much to promote scientific learning, including public lectures. In England, there were also itinerant lecturers offering their service, typically for a fee.

Prior to the nineteenth century, there were many important inventors working as millwrights or mechanics who, typically, had received an elementary education and served an apprenticeship. Mechanics, instrument makers and surveyors had various mathematics training. James Watt was a surveyor and instrument maker and is described as being "largely self-educated". Watt, like some other autodidacts of the time, became a Fellow of the Royal Society and a member of the Lunar Society. In the eighteenth century these societies often gave public lectures and were instrumental in teaching chemistry and other sciences with industrial applications which were neglected by traditional universities. Academies also arose to provide scientific and technical training.

Years of schooling in the United States began to increase sharply in the early twentieth century. This phenomenon was seemingly related to increasing mechanization displacing child labor. The automated glass bottle-making machine is said to have done more for education than child labor laws because boys were no longer needed to assist. However, the number of boys employed in this particular industry was not that large; it was mechanization in several sectors of industry that displaced child labor toward education. For males in the U.S. born 1886–90, years of school averaged 7.86, while for those born in 1926–30, years of school averaged 11.46.

One of the most recent trends in education is that the classroom environment should cater towards students' individual needs, goals, and interests. This model adopts the idea of inquiry-based learning where students are presented with scenarios to identify their own research, questions and knowledge regarding the area. As a form of discovery learning, students in today's classrooms are being provided with more opportunity to "experience and interact" with knowledge, which has its roots in autodidacticism.

Successful self-teaching can require self-discipline and reflective capability. Some research suggests that the ability to regulate one's own learning may need to be modeled to some students so that they become active learners, while others learn dynamically via a process outside conscious control. To interact with the environment, a framework has been identified to determine the components of any learning system: a reward function, incremental action value functions and action selection methods. Rewards work best in motivating learning when they are specifically chosen on an individual student basis. New knowledge must be incorporated into previously existing information as its value is to be assessed. Ultimately, these scaffolding techniques, as described by Vygotsky (1978) and problem solving methods are a result of dynamic decision making.

In his book Deschooling Society, philosopher Ivan Illich strongly criticized 20th-century educational culture and the institutionalization of knowledge and learning - arguing that institutional schooling as such is an irretrievably flawed model of education - advocating instead ad-hoc co-operative networks through which autodidacts could find others interested in teaching themselves a given skill or about a given topic, supporting one another by pooling resources, materials, and knowledge.

Secular and modern societies have given foundations for new systems of education and new kinds of autodidacts. As Internet access has become more widespread the World Wide Web (explored using search engines such as Google) in general, and websites such as Wikipedia (including parts of it that were included in a book or referenced in a reading list), YouTube, Udemy, Udacity and Khan Academy in particular, have developed as learning centers for many people to actively and freely learn together. Organizations like The Alliance for Self-Directed Education (ASDE) have been formed to publicize and provide guidance for self-directed education. Entrepreneurs like Henry Ford, Steve Jobs, and Bill Gates are considered influential self-teachers.

History

The first philosophical claim supporting an autodidactic program to the study of nature and God was in the philosophical novel Hayy ibn Yaqdhan (Alive son of the Vigilant), whose titular hero is considered the archetypal autodidact. The story is a medieval autodidactic utopia, a philosophical treatise in a literary form, which was written by the Andalusian philosopher Ibn Tufail in the 1160s in Marrakesh. It is a story about a feral boy, an autodidact prodigy who masters nature through instruments and reason, discovers laws of nature by practical exploration and experiments, and gains summum bonum through a mystical mediation and communion with God. The hero rises from his initial state of tabula rasa to a mystical or direct experience of God after passing through the necessary natural experiences. The focal point of the story is that human reason, unaided by society and its conventions or by religion, can achieve scientific knowledge, preparing the way to the mystical or highest form of human knowledge.

Commonly translated as "The Self-Taught Philosopher" or "The Improvement of Human Reason", Ibn-Tufayl's story Hayy Ibn-Yaqzan inspired debates about autodidacticism in a range of historical fields from classical Islamic philosophy through Renaissance humanism and the European Enlightenment. In his book Reading Hayy Ibn-Yaqzan: a Cross-Cultural History of Autodidacticism, Avner Ben-Zaken showed how the text traveled from late medieval Andalusia to early modern Europe and demonstrated the intricate ways in which autodidacticism was contested in and adapted to diverse cultural settings.

Autodidacticism apparently intertwined with struggles over Sufism in twelfth-century Marrakesh; controversies about the role of philosophy in pedagogy in fourteenth-century Barcelona; quarrels concerning astrology in Renaissance Florence in which Pico della Mirandola pleads for autodidacticism against the strong authority of intellectual establishment notions of predestination; and debates pertaining to experimentalism in seventeenth-century Oxford. Pleas for autodidacticism echoed not only within close philosophical discussions; they surfaced in struggles for control between individuals and establishments.

In the story of Black American self-education, Heather Andrea Williams presents a historical account to examine Black American's relationship to literacy during slavery, the Civil War and the first decades of freedom. Many of the personal accounts tell of individuals who have had to teach themselves due to racial discrimination in education.

Future role

The role of self-directed learning continues to be investigated in learning approaches, along with other important goals of education, such as content knowledge, epistemic practices and collaboration. As colleges and universities offer distance learning degree programs and secondary schools provide cyber school options for K–12 students, technology provides numerous resources that enable individuals to have a self-directed learning experience. Several studies show these programs function most effectively when the "teacher" or facilitator is a full owner of virtual space to encourage a broad range of experiences to come together in an online format. This allows self-directed learning to encompass both a chosen path of information inquiry, self-regulation methods and reflective discussion among experts as well as novices in a given area. Furthermore, massive open online courses (MOOCs) make autodidacticism easier and thus more common.

A 2016 Stack Overflow poll reported that due to the rise of autodidacticism, 69.1% of software developers appear to be self-taught.

Notable individuals

Main article: List of autodidacts

Some notable autodidacts can be broadly grouped in the following interdisciplinary areas:

• Artists and authors
• Actors, musicians, and other artists
• Architects
• Engineers, inventors and software developers (Computer programmers)
• Scientists, historians, and educators

Democratization of knowledge

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Democratization_of_knowledge 

The democratization of knowledge is the acquisition and spread of knowledge amongst a wider part of the population, not just elite groups such as clergy, professionals, or academia. Mass literacy, the printing press, public libraries, television, and modern information technology such as the Internet have played a key role, as they provide the masses with open access to information through a variety of means.

History

Main article: Information Age

Literate and illiterate world population between 1800 and 2016

Wide dissemination of knowledge is inseparable from the spread of literacy.

The Information Age is a historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during the Industrial Revolution, to an economy centered on information technology.

Digitization efforts by Google Books have been pointed to as an example of the democratization of knowledge, but Malte Herwig in Der Spiegel raised concerns that the virtual monopoly Google has in the search market, combined with Google's hiding of the details of its search algorithms, could undermine this move towards democratization.

Google Scholar (and similar scholarly search services) and Sci-Hub (and similar scholarly shadow libraries) have also been pointed to as examples of democratization of knowledge.

Open Library's and HathiTrust's digitization efforts and their use of the controlled digital lending model are also examples of democratization of knowledge.

After the most powerful search engine, Google, and the most viewed online encyclopedia, Wikipedia, the most viewed information-based website is the Encyclopædia Britannica.

Large language models like ChatGPT or Google Gemini have also been shown as examples of democratization of knowledge.

Role of libraries

An article written in 2005 by the editors of Reference & User Services Quarterly calls the library the greatest force for the democratization of knowledge or information. It continues to say that public libraries in particular are inextricably linked with the history and evolution of the United States, but school library media centers, college and university libraries, and special libraries have all also been influential in their support for democracy. Libraries play an essential role in the democratization of knowledge and information by providing communities with the resources and tools to find information free of charge. Democratic access to knowledge has also been co-opted to mean providing information in a variety of formats, which essentially means electronic and digital formats for use by library patrons. Public libraries help further the democratization of information by guaranteeing freedom of access to information, by providing an unbiased variety of information sources and access to government services, as well as the promotion of democracy and active citizenship.

Dan Cohen, the founding executive director of the Digital Public Library of America, writes that democratic access to knowledge is a profound idea that requires constant tending and revitalization. In 2004, a World Social Forum and International workshop was held entitled "Democratization of Information: Focus on Libraries". The focus of the forum was to bring awareness to the social, technological, and financial challenges facing libraries dealing with the democratization of information. Social challenges included globalization and the digital divide, technological challenges included information sources, and financial challenges constituted shrinking budgets and manpower. Longtime Free Library of Philadelphia director Elliot Shelkrot said that "Democracy depends on an informed population. And where can people get all the information they need? —At the Library."

Symmetry (physics)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Symmetry_(physics) 

The symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.

A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group).

These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems.

Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all frames of reference, which is described in special relativity by a group of transformations of the spacetime known as the Poincaré group. Another important example is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations, which is an important idea in general relativity.

As a kind of invariance

Invariance is specified mathematically by transformations that leave some property (e.g. quantity) unchanged. This idea can apply to basic real-world observations. For example, temperature may be homogeneous throughout a room. Since the temperature does not depend on the position of an observer within the room, we say that the temperature is invariant under a shift in an observer's position within the room.

Similarly, a uniform sphere rotated about its center will appear exactly as it did before the rotation. The sphere is said to exhibit spherical symmetry. A rotation about any axis of the sphere will preserve the shape of its surface from any given vantage point.

Invariance in force

The above ideas lead to the useful idea of invariance when discussing observed physical symmetry; this can be applied to symmetries in forces as well.

For example, an electric field due to an electrically charged wire of infinite length is said to exhibit cylindrical symmetry, because the electric field strength at a given distance r from the wire will have the same magnitude at each point on the surface of a cylinder (whose axis is the wire) with radius r. Rotating the wire about its own axis does not change its position or charge density, hence it will preserve the field. The field strength at a rotated position is the same. This is not true in general for an arbitrary system of charges.

In Newton's theory of mechanics, given two bodies, each with mass m, starting at the origin and moving along the x-axis in opposite directions, one with speed v₁ and the other with speed v₂ the total kinetic energy of the system (as calculated from an observer at the origin) is ⁠1/2⁠m(v₁² + v₂²) and remains the same if the velocities are interchanged. The total kinetic energy is preserved under a reflection in the y-axis.

The last example above illustrates another way of expressing symmetries, namely through the equations that describe some aspect of the physical system. The above example shows that the total kinetic energy will be the same if v₁ and v₂ are interchanged.

Local and global

Symmetries may be broadly classified as global or local. A global symmetry is one that keeps a property invariant for a transformation that is applied simultaneously at all points of spacetime, whereas a local symmetry is one that keeps a property invariant when a possibly different symmetry transformation is applied at each point of spacetime; specifically a local symmetry transformation is parameterised by the spacetime coordinates, whereas a global symmetry is not. This implies that a global symmetry is also a local symmetry. Local symmetries play an important role in physics as they form the basis for gauge theories.

Continuous

The two examples of rotational symmetry described above – spherical and cylindrical – are each instances of continuous symmetry. These are characterised by invariance following a continuous change in the geometry of the system. For example, the wire may be rotated through any angle about its axis and the field strength will be the same on a given cylinder. Mathematically, continuous symmetries are described by transformations that change continuously as a function of their parameterization. An important subclass of continuous symmetries in physics are spacetime symmetries.

Spacetime

Main article: Spacetime symmetries

Continuous spacetime symmetries are symmetries involving transformations of space and time. These may be further classified as spatial symmetries, involving only the spatial geometry associated with a physical system; temporal symmetries, involving only changes in time; or spatio-temporal symmetries, involving changes in both space and time.

• Time translation: A physical system may have the same features over a certain interval of time Δt; this is expressed mathematically as invariance under the transformation t → t + a for any real parameters t and t + a in the interval. For example, in classical mechanics, a particle solely acted upon by gravity will have gravitational potential energy mgh when suspended from a height h above the Earth's surface. Assuming no change in the height of the particle, this will be the total gravitational potential energy of the particle at all times. In other words, by considering the state of the particle at some time t₀ and also at t₀ + a, the particle's total gravitational potential energy will be preserved.
• Spatial translation: These spatial symmetries are represented by transformations of the form r→ → r→ + a→ and describe those situations where a property of the system does not change with a continuous change in location. For example, the temperature in a room may be independent of where the thermometer is located in the room.
• Spatial rotation: These spatial symmetries are classified as proper rotations and improper rotations. The former are just the 'ordinary' rotations; mathematically, they are represented by square matrices with unit determinant. The latter are represented by square matrices with determinant −1 and consist of a proper rotation combined with a spatial reflection (inversion). For example, a sphere has proper rotational symmetry. Other types of spatial rotations are described in the article Rotation symmetry.
• Poincaré transformations: These are spatio-temporal symmetries which preserve distances in Minkowski spacetime, i.e. they are isometries of Minkowski space. They are studied primarily in special relativity. Those isometries that leave the origin fixed are called Lorentz transformations and give rise to the symmetry known as Lorentz covariance.
• Projective symmetries: These are spatio-temporal symmetries which preserve the geodesic structure of spacetime. They may be defined on any smooth manifold, but find many applications in the study of exact solutions in general relativity.
• Inversion transformations: These are spatio-temporal symmetries which generalise Poincaré transformations to include other conformal one-to-one transformations on the space-time coordinates. Lengths are not invariant under inversion transformations but there is a cross-ratio on four points that is invariant.

Mathematically, spacetime symmetries are usually described by smooth vector fields on a smooth manifold. The underlying local diffeomorphisms associated with the vector fields correspond more directly to the physical symmetries, but the vector fields themselves are more often used when classifying the symmetries of the physical system.

Some of the most important vector fields are Killing vector fields which are those spacetime symmetries that preserve the underlying metric structure of a manifold. In rough terms, Killing vector fields preserve the distance between any two points of the manifold and often go by the name of isometries.

Discrete

Main article: Discrete symmetry

A discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type of 'swapping', these swaps usually being called reflections or interchanges.

• Time reversal: Many laws of physics describe real phenomena when the direction of time is reversed. Mathematically, this is represented by the transformation, ${\displaystyle t\to -t}$. For example, Newton's second law of motion still holds if, in the equation ${\displaystyle F=m\ddot{r}}$, ${\displaystyle t}$ is replaced by ${\displaystyle -t}$. This may be illustrated by recording the motion of an object thrown up vertically (neglecting air resistance) and then playing it back. The object will follow the same parabolic trajectory through the air, whether the recording is played normally or in reverse. Thus, position is symmetric with respect to the instant that the object is at its maximum height.
• Spatial inversion: These are represented by transformations of the form ${\displaystyle \overrightarrow{r}\to -\overrightarrow{r}}$ and indicate an invariance property of a system when the coordinates are 'inverted'. Stated another way, these are symmetries between a certain object and its mirror image.
• Glide reflection: These are represented by a composition of a translation and a reflection. These symmetries occur in some crystals and in some planar symmetries, known as wallpaper symmetries.

C, P, and T

Main article: Wu experiment

The Standard Model of particle physics has three related natural near-symmetries. These state that the universe in which we live should be indistinguishable from one where a certain type of change is introduced.

• C-symmetry (charge symmetry), a universe where every particle is replaced with its antiparticle.
• P-symmetry (parity symmetry), a universe where everything is mirrored along the three physical axes. This excludes weak interactions as demonstrated by Chien-Shiung Wu.

• T-symmetry (time reversal symmetry), a universe where the direction of time is reversed. T-symmetry is counterintuitive (the future and the past are not symmetrical) but explained by the fact that the Standard Model describes local properties, not global ones like entropy. To properly reverse the direction of time, one would have to put the Big Bang and the resulting low-entropy state in the "future". Since we perceive the "past" ("future") as having lower (higher) entropy than the present, the inhabitants of this hypothetical time-reversed universe would perceive the future in the same way as we perceive the past, and vice versa.

These symmetries are near-symmetries because each is broken in the present-day universe. However, the Standard Model predicts that the combination of the three (that is, the simultaneous application of all three transformations) must be a symmetry, called CPT symmetry. CP violation, the violation of the combination of C- and P-symmetry, is necessary for the presence of significant amounts of baryonic matter in the universe. CP violation is a fruitful area of current research in particle physics.

Supersymmetry

Main article: Supersymmetry

A type of symmetry known as supersymmetry has been used to try to make theoretical advances in the Standard Model. Supersymmetry is based on the idea that there is another physical symmetry beyond those already developed in the Standard Model, specifically a symmetry between bosons and fermions. Supersymmetry asserts that each type of boson has, as a supersymmetric partner, a fermion, called a superpartner, and vice versa. Supersymmetry has not yet been experimentally verified: no known particle has the correct properties to be a superpartner of any other known particle. Currently LHC is preparing for a run which tests supersymmetry.

Generalized symmetries

See also: Non-invertible symmetry

Generalized symmetries encompass a number of recently recognized generalizations of the concept of a global symmetry. These include higher form symmetries, higher group symmetries, non-invertible symmetries, and subsystem symmetries.

Mathematics of physical symmetry

Main article: Symmetry group

See also: Symmetry in quantum mechanics and Symmetries in general relativity

The transformations describing physical symmetries typically form a mathematical group. Group theory is an important area of mathematics for physicists.

Continuous symmetries are specified mathematically by continuous groups (called Lie groups). Many physical symmetries are isometries and are specified by symmetry groups. Sometimes this term is used for more general types of symmetries. The set of all proper rotations (about any angle) through any axis of a sphere form a Lie group called the special orthogonal group SO(3). (The '3' refers to the three-dimensional space of an ordinary sphere.) Thus, the symmetry group of the sphere with proper rotations is SO(3). Any rotation preserves distances on the surface of the ball. The set of all Lorentz transformations form a group called the Lorentz group (this may be generalised to the Poincaré group).

Discrete groups describe discrete symmetries. For example, the symmetries of an equilateral triangle are characterized by the symmetric group S₃.

A type of physical theory based on local symmetries is called a gauge theory and the symmetries natural to such a theory are called gauge symmetries. Gauge symmetries in the Standard Model, used to describe three of the fundamental interactions, are based on the SU(3) × SU(2) × U(1) group. (Roughly speaking, the symmetries of the SU(3) group describe the strong force, the SU(2) group describes the weak interaction and the U(1) group describes the electromagnetic force.)

Also, the reduction by symmetry of the energy functional under the action by a group and spontaneous symmetry breaking of transformations of symmetric groups appear to elucidate topics in particle physics (for example, the unification of electromagnetism and the weak force in physical cosmology).

Conservation laws and symmetry

Main article: Noether's theorem

The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. The theorem states that each continuous symmetry of a physical system implies that some physical property of that system is conserved. Conversely, each conserved quantity has a corresponding symmetry. For example, spatial translation symmetry (i.e. homogeneity of space) gives rise to conservation of (linear) momentum, and temporal translation symmetry (i.e. homogeneity of time) gives rise to conservation of energy.

The following table summarizes some fundamental symmetries and the associated conserved quantity.

Class	Invariance	Conserved quantity
Proper orthochronous Poincaré symmetry	translation in time (homogeneity)	energy E
	translation in space (homogeneity)	linear momentum p
	rotation in space (isotropy)	angular momentum L = r × p
	Lorentz-boost (isotropy)	boost 3-vector N = tp − Er
Discrete symmetry	P, coordinate inversion	spatial parity
	C, charge conjugation	charge parity
	T, time reversal	time parity
	CPT	product of parities
Internal symmetry (independent of spacetime coordinates)	U(1) transformation	electric charge
	U(1) transformation	lepton generation number
	U(1) transformation	hypercharge
	U(1)Y transformation	weak hypercharge
	U(2) [ U(1) × SU(2) ]	electroweak force
	SU(2) transformation	isospin
	SU(2)L transformation	weak isospin
	P × SU(2)	G-parity
	SU(3) "winding number"	baryon number
	SU(3) transformation	quark color
	SU(3) (approximate)	quark flavor
	U(1) × SU(2) × SU(3)	Standard Model

Mathematics

Continuous symmetries in physics preserve transformations. One can specify a symmetry by showing how a very small transformation affects various particle fields. The commutator of two of these infinitesimal transformations is equivalent to a third infinitesimal transformation of the same kind hence they form a Lie algebra.

A general coordinate transformation described as the general field ${\displaystyle h(x)}$ (also known as a diffeomorphism) has the infinitesimal effect on a scalar ${\displaystyle \varphi (x)}$, spinor ${\displaystyle \psi (x)}$ or vector field ${\displaystyle A(x)}$ that can be expressed (using the Einstein summation convention):

${\displaystyle \delta \varphi (x)=h^{\mu }(x){\mathrm{\partial }}_{\mu }\varphi (x)}$

${\displaystyle \delta {\psi }^{\alpha }(x)=h^{\mu }(x){\mathrm{\partial }}_{\mu }{\psi }^{\alpha }(x)+{\mathrm{\partial }}_{\mu }{h}_{\nu }(x){\sigma }_{\mu \nu }^{\alpha \beta }{\psi }^{\beta }(x)}$

${\displaystyle \delta A_{\mu }(x)=h^{\nu }(x){\mathrm{\partial }}_{\nu }{A}_{\mu }(x)+A_{\nu }(x){\mathrm{\partial }}_{\mu }{h}^{\nu }(x)}$

Without gravity only the Poincaré symmetries are preserved which restricts ${\displaystyle h(x)}$ to be of the form:

${\displaystyle h^{\mu }(x)=M^{\mu \nu }{x}_{\nu }+P^{\mu }}$

where M is an antisymmetric matrix (giving the Lorentz and rotational symmetries) and P is a general vector (giving the translational symmetries). Other symmetries affect multiple fields simultaneously. For example, local gauge transformations apply to both a vector and spinor field:

${\displaystyle \delta {\psi }^{\alpha }(x)=\lambda (x).{\tau }^{\alpha \beta }{\psi }^{\beta }(x)}$

${\displaystyle \delta A_{\mu }(x)={\mathrm{\partial }}_{\mu }\lambda (x),}$

where ${\displaystyle \tau }$ are generators of a particular Lie group. So far the transformations on the right have only included fields of the same type. Supersymmetries are defined according to how the mix fields of different types.

Another symmetry which is part of some theories of physics and not in others is scale invariance which involve Weyl transformations of the following kind:

${\displaystyle \delta \varphi (x)=\mathrm{\Omega }(x)\varphi (x)}$

If the fields have this symmetry then it can be shown that the field theory is almost certainly conformally invariant also. This means that in the absence of gravity h(x) would restricted to the form:

${\displaystyle h^{\mu }(x)=M^{\mu \nu }{x}_{\nu }+P^{\mu }+D{x}_{\mu }+K^{\mu }|x{|}^2-2K^{\nu }{x}_{\nu }{x}_{\mu },}$

with D generating scale transformations and K generating special conformal transformations. For example, N = 4 supersymmetric Yang–Mills theory has this symmetry while general relativity does not although other theories of gravity such as conformal gravity do. The 'action' of a field theory is an invariant under all the symmetries of the theory. Much of modern theoretical physics is to do with speculating on the various symmetries the Universe may have and finding the invariants to construct field theories as models.

In string theories, since a string can be decomposed into an infinite number of particle fields, the symmetries on the string world sheet is equivalent to special transformations which mix an infinite number of fields.