Critical thinking in the context of STEM

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.

Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premises and conclusions express propositions or claims that can be true or false. An important feature of propositions is their internal structure. For example, complex propositions are made up of simpler propositions linked by logical vocabulary like ${\displaystyle \land }$ (and) or ${\displaystyle \to }$ (if...then). Simple propositions also have parts, like "Sunday" or "work" in the example. The truth of a proposition usually depends on the meanings of all of its parts. However, this is not the case for logically true propositions. They are true only because of their logical structure independent of the specific meanings of the individual parts.

A master's degree (from Latin magister) is a postgraduate academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice. A master's degree normally requires previous study at the bachelor's level, either as a separate degree or as part of an integrated course. Within the area studied, master's graduates are expected to possess advanced knowledge of a specialized body of theoretical and applied topics; high order skills in analysis, critical evaluation, or professional application; and the ability to solve complex problems and think rigorously and independently.

An intellectual is a person who engages in critical thinking, research, and reflection about the nature of reality, especially the nature of society and proposed solutions for its normative problems. Coming from the world of culture, either as a creator or as a mediator, the intellectual participates in politics, either to defend a concrete proposition or to denounce an injustice, usually by either rejecting, producing or extending an ideology, and by defending a system of values.

A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites".

In logic, many paradoxes exist that are invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, cannot be easily resolved by making foundational changes in a logical system.

Education is the transmission of knowledge and skills and the development of character traits. Formal education occurs within a structured institutional framework, such as public schools, following a curriculum. Non-formal education also follows a structured approach but occurs outside the formal schooling system, while informal education involves unstructured learning through daily experiences. Formal and non-formal education are categorized into levels, including early childhood education, primary education, secondary education, and tertiary education. Other classifications focus on teaching methods, such as teacher-centered and student-centered education, and on subjects, such as science education, language education, and physical education. Additionally, the term "education" can denote the mental states and qualities of educated individuals and the academic field studying educational phenomena.

The precise definition of education is disputed, and there are disagreements about the aims of education and the extent to which education differs from indoctrination by fostering critical thinking. These disagreements impact how to identify, measure, and enhance various forms of education. Essentially, education socializes children into society by instilling cultural values and norms, equipping them with the skills necessary to become productive members of society. In doing so, it stimulates economic growth and raises awareness of local and global problems. Organized institutions play a significant role in education. For instance, governments establish education policies to determine the timing of school classes, the curriculum, and attendance requirements. International organizations, such as UNESCO, have been influential in promoting primary education for all children.

Informal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements). However, the precise definition of "informal logic" is a matter of some dispute. Ralph H. Johnson and J. Anthony Blair define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation." This definition reflects what had been implicit in their practice and what others were doing in their informal logic texts.

Informal logic is associated with informal fallacies, critical thinking, the thinking skills movement and the interdisciplinary inquiry known as argumentation theory. Frans H. van Eemeren writes that the label "informal logic" covers a "collection of normative approaches to the study of reasoning in ordinary language that remain closer to the practice of argumentation than formal logic."

Science, technology, engineering, and mathematics (STEM) is an umbrella term used to group together the related technical disciplines of science, technology, engineering, and mathematics. It represents a broad and interconnected set of fields that are crucial for innovation and technological advancement. These disciplines are often grouped together because they share a common emphasis on critical thinking, problem-solving, and analytical skills. The term is typically used in the context of education policy or curriculum choices in schools. It has implications for workforce development, national security concerns (as a shortage of STEM-educated citizens can reduce effectiveness in this area), and immigration policy, with regard to admitting foreign students and tech workers.

There is no universal agreement on which disciplines are included in STEM; in particular, whether or not the science in STEM includes social sciences, such as psychology, sociology, economics, and political science. In the United States, these are typically included by the National Science Foundation (NSF), the Department of Labor's O*Net online database for job seekers, and the Department of Homeland Security. In the United Kingdom, the social sciences are categorized separately and are instead grouped with humanities and arts to form another counterpart acronym HASS (humanities, arts, and social sciences), rebranded in 2020 as SHAPE (social sciences, humanities and the arts for people and the economy). Some sources also use HEAL (health, education, administration, and literacy) as the counterpart of STEM.

Indoctrination is the process of inculcating (teaching by repeated instruction) a person or people into an ideology, often avoiding critical analysis. It can refer to a general process of socialization. The term often implies forms of brainwashing or disagreeable forms of socialization. However, it can refer to both positive and negative forms of cultural transmission, and some academics consider it an integral element of education.

The precise boundary between education and indoctrination is contested. The concept originally referred to education, but after World War I, the term took on a pejorative meaning akin to brainwashing or propaganda. Some distinguish indoctrination from education on the basis that the indoctrinated person is expected not to question or critically examine the doctrine they have learned. As such the term may be used pejoratively or as a buzz word, often in the context of political opinions, theology, religious dogma or anti-religious convictions.

Intelligence has been defined in many ways: the capacity for abstraction, logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity, critical thinking, and problem-solving. It can be described as the ability to perceive or infer information and to retain it as knowledge to be applied to adaptive behaviors within an environment or context.

The term rose to prominence during the early 1900s. Most psychologists believe that intelligence can be divided into various domains or competencies.

Cognitive skills are skills of the mind, as opposed to other types of skills such as motor skills, social skills or life skills. Cognitive skills include literacy, self-reflection, logical reasoning, abstract thinking, critical thinking, introspection and mental arithmetic. Cognitive skills vary in processing complexity, and can range from more fundamental processes such as perception and various memory functions, to more sophisticated processes such as decision making, problem solving and metacognition.

An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes all the key components of the argument, traditionally called the conclusion and the premises, also called contention and reasons. Argument maps can also show co-premises, objections, counterarguments, rebuttals, inferences, and lemmas. There are different styles of argument map but they are often functionally equivalent and represent an argument's individual claims and the relationships between them.

Argument maps are commonly used in the context of teaching and applying critical thinking. The purpose of mapping is to uncover the logical structure of arguments, identify unstated assumptions, evaluate the support an argument offers for a conclusion, and aid understanding of debates. Argument maps are often designed to support deliberation of issues, ideas and arguments in wicked problems.

The philosophy of education is the branch of applied philosophy that investigates the nature of education as well as its aims and problems. It also examines the concepts and presuppositions of education theories. It is an interdisciplinary field that draws inspiration from various disciplines both within and outside philosophy, like ethics, political philosophy, psychology, and sociology. Many of its theories focus specifically on education in schools but it also encompasses other forms of education. Its theories are often divided into descriptive theories, which provide a value-neutral description of what education is, and normative theories, which investigate how education should be practiced.

A great variety of topics is discussed in the philosophy of education. Some studies provide a conceptual analysis of the fundamental concepts of education. Others center around the aims or purpose of education, like passing on knowledge and the development of the abilities of good reasoning, judging, and acting. An influential discussion concerning the epistemic aims of education is whether education should focus mainly on the transmission of true beliefs or rather on the abilities to reason and arrive at new knowledge. In this context, many theorists emphasize the importance of critical thinking in contrast to indoctrination. Another debate about the aims of education is whether the primary beneficiary is the student or the society to which the student belongs.

A research university or a research-intensive university is a university that is committed to research as a central part of its mission. They are "the key sites of knowledge production", along with "intergenerational knowledge transfer and the certification of new knowledge" through the awarding of doctoral degrees, and continue to be "the very center of scientific productivity". They can be public or private, and often have well-known brand names.

Undergraduate courses at many research universities are often academic rather than vocational and may not prepare students for particular careers, but many employers value degrees from research universities because they teach fundamental life skills such as critical thinking. Globally, research universities are overwhelmingly public institutions, while some countries like the United States and Japan also have well-known private research institutions.