Texts
- The Problem of Learning
- Problemistics Courseware
- Corso su Problemistica
- Resources Management
- Manuale/Intellettuale
- Campagna/Città
Problemistics - Problémistique - Problemistica
The Art & Craft of Problem Dealing
Concepts
Concepts : definition (Reference Books)
Concepts : definition (Deobold B. Van Dalen)
Concepts : definition (Chava F. Nachmias and David Nachmias)
Concepts : definition (Ayn Rand)
Concepts : definition (Neil Bolton)
Concepts : definition (Richard R. Skemp)
Concepts : definition (Edward E. Smith)
Concepts : definition (J. S. Bruner, J. Goodnow and G. A. Austin)Concepts : classification (Richard R. Skemp)
Concepts : classification (Paul Davidson Reynolds)Concepts : function (Peter Caws)
Concepts : function (Ayn Rand)
Concepts : function (Chava F. Nachmias and David Nachmias)
Concepts : function (Neil Bolton)
Concepts : function (Rita L. Atkinson et alii)
Concepts : function (Edward E. Smith)
Concepts : function (Deobold B. Van Dalen)
Concepts : function (Abraham Kaplan)Concepts : requirements in research (Robert K. Merton)
Concepts : requirements in research (J. Bronowski)
Concepts : concepts and theories (Abraham Kaplan)
Concepts : concepts and facts (Jennifer Trusted)
Concepts : concepts and language (L. S. Vygotsky)
Reference Books
[1974] The American Heritage Dictionary of the English Language
"Concept. An idea, esp. an abstraction drawn from the specific."
[1973] K.T. Collins et alii, Keywords in Education
“Concept. A mental pattern, grouping or structure, arrived at by abstracting common elements from a variety of experiences, and usually expressed in words or symbols. All higher mental processes (reasoning, the use of symbols) depend upon concepts.”
[1981] P. A. Angeles, A Dictionary of Philosophy
"1. A mental impression, a thought, a notion, an idea of any degree of concreteness or abstraction, used in abstract thinking.
2. That which enables the mind to distinguish one thing from another.
3. What is meant (or imaged) by the term used to designate it.
4. Sometimes refers to the universals abstracted from particulars.” (p. 42)
Textbooks
[1962] Deobold B. Van Dalen, Understanding Educational Research. An Introduction McGraw-Hill Book Company, New York, 1979
“A concept is a symbol or term - a class name - that is invented to communicate with others about the similarities or relationships that one has noted.”
“Concepts are products of both abstracting and generalizing.” (Chapter III, p. 43)
[1992, Fourth Edition] Nachmias, Chava Frankfort and Nachmias, David, Research Methods in the Social Sciences
“A concept is an abstraction representing an object, a property of an object, or a certain phenomenon.” (Chapter II, p. 27)
“Concepts are abstracted from sense impressions and are used to convey and transmit perceptions and information.” (Chapter II, p. 28)
[1989] Ayn Rand in Hospers, John (editor), Readings in Introductory Philosophical Analysis
“A ‘concept' is a mental integration of two or more perceptual concretes, which are isolated by a process of abstraction and united by means of a specific definition.”
“It is by organizing his perceptual material into concepts, and his concepts into wider and still wider concepts that man is able to grasp and retain, to identify and integrate an unlimited amount of knowledge, a knowledge extending beyond the immediate perceptions of any given, immediate moment.” (“Value and Rights”, p. 369)
[1977] Bolton, Neil, Concept Formation
“Concepts are the expression of shared meanings, and, in this sense, they are socially constructed. Social cooperation and conventions stabilize concepts because an agreed name can be given to the same experience.” (p. 16)
“A concept may be defined ... as a stable organization in the experience of reality which is achieved through the utilization of rules of relation, and to which can be given a name.” (p. 23)
[1971] Skemp, Richard R., The Psychology of Learning Mathematics
“A concept is a way of processing data which enables the user to bring past experience usefully to bear on the present situation.” (Chapter 2, p. 28)
[1988] Smith, Edward E. in Sternberg, R. J. and Smith, Edward E., The Psychology of Human Thought
“In short, concepts reflect the way we divide the world into classes, and much of what we learn, communicate, and reason about involves relations among these classes.” (Chapter 2, p. 19)
[1966, First Published 1956] Bruner, Jerome S.; Goodnow, J. and Austin, G.A., Study of Thinking
“We ... regard a concept as a network of sign-significate inferences by which one goes beyond a set of observed criterial properties exhibited by an object or event to the class identity of the object or event in question, and thence to additional inferences about other unobserved properties of the object or event.” (Chapter 8, p. 244)
[1971] Skemp, Richard R., The Psychology of Learning Mathematics
“We need now to distinguish between two kinds of concept. Those which are derived from our sensory and motor experiences of the outside world, such as red, motor car, heavy, hot, sweet, will be called primary concepts; and those which are abstracted from other concepts we shall call secondary concepts.” (Chapter 2, p. 25)
[1971] Reynolds, Paul Davidson, A Primer in Theory Construction
“... an abstract concept is not related to any unique spatial (location) or temporal (historical time) setting." [e.g. the temperature]
“If a concept is specific to a particular time or place, then it is considered concrete.”
[e.g. the temperature in Paris the 14 of July 1998] (Chapter 3, p. 49)
[1965] Caws, Peter, The Philosophy of Science
“The concept ... is a functional entity; we know what it does (identification, recognition, and representation).” (Part I, Chapter 4, p. 27)
[1989] Ayn Rand in Hospers, John (editor), Readings in Introductory Philosophical Analysis
“It is by organizing his perceptual material into concepts, and his concepts into wider and still wider concepts that man is able to grasp and retain, to identify and integrate an unlimited amount of knowledge, a knowledge extending beyond the immediate perceptions of any given, immediate moment.” (“Value and Rights”, p. 369)
[1992, Fourth Edition] Nachmias, Chava Frankfort and Nachmias, David, Research Methods in the Social Sciences
“Concepts serve a number of important functions in social science research.”
- “First and foremost, they are the foundation of communication. Without a set of agreed-on concepts, intersubjective communication is impossible.”
- “Second, concepts introduce a perspective, a way of looking at empirical
phenomena.”
- “Third, concepts are means for classification and generalization.”
- “Fourth, concepts serve as components of theories and thus of explanations and predictions.” (Chapter II, pp. 28-29)
[1977] Bolton, Neil, Concept Formation
“... the organization of reality and the development of concepts are correlative processes, two aspects of a single whole: our concepts develop as we organize the environment to which we respond, and we organize our environment through developing our concepts.” (p. 20)
[1987, Ninth Edition] Atkinson, Rita L. et alii, Introduction to Psychology
“Concepts are our means of dividing the world into manageable units.” (Chapter 9, p. 281)
[1988] Smith, Edward E. in Sternberg, R. J. and Smith, Edward E., The Psychology of Human Thought
“From a psychological perspective, concepts are mental representations of classes, and their most salient function is to promote cognitive economy.
By partitioning the world into classes, we decrease the amount of information we must perceive, learn, remember, communicate, and reason about.”
“Another important function of concepts is that they enable us to go beyond the information given. When we come across an object, say a wolf, we have direct knowledge only of its appearance. It is essential that we go beyond appearances and bring to bear another knowledge that we have. Such as our belief that wolves can bite and inflict severe injury.”
"Concepts, then, are recognition device; they serve as entry points into our knowledge stores and provide us with expectations that we can use to guide our actions.” “A third important function of concepts is that they can be combined to form complex concepts and thoughts.” (Chapter 2, pp. 19-20)
[1962] Deobold B. Van Dalen, Understanding Educational Research. An Introduction McGraw-Hill Book Company, New York, 1979
“Concepts convey considerable compact information to scientists and make it easier for scientists to manipulate facts and to communicate findings.” (Chapter 3, p. 57)
[1964] Kaplan, Abraham, The Conduct of Inquiry
“Whether a concept is useful depends on the use we want to put it to; but there is always the additional question whether things so conceptualized will lend themselves to that use. And this is the scientific question.” (p. 51)
“Concepts ... mark out the paths by which we may move most freely in logical space. They identify nodes or junctions in the network of relationships, termini at which we can halt while preserving the maximum range of choice as to where to go next.” (p. 52)
“The function of scientific concepts is to mark the categories which will tell us more about our subject matter that any other categorial sets.” (p. 52)
[1968] Merton, Robert K., Social Theory and Social Structure
“Empirical research exerts pressure for clear concepts.”
“For a basic requirement of research is that the concepts, the variables, be defined with sufficient clarity to enable the research to proceed.” (Part 1 - Chapter 5, pp. 168-169)
[1956] Bronowski, J., Science and Human Values
"... science ... is a system of concepts : the place of experience is to test and correct the concept.
The test is : Will the concept work ?
Does it give an unforced unity to the experience of men ?
Does the concept make life orderly, not by edict but in fact ?” (Chapter 2, p. 55)
[1964] Kaplan, Abraham, The Conduct of Inquiry
“... concept formation and theory formation in science go hand in hand.” (p. 52)
“Every conceptualization involves us in an inductive risk. The concepts in terms of which we pose our scientific questions limit the range of admissible answers.” (p. 53)
“The appropriate conceptualization of the problem already prefigures its solution.” “In consequence, we are caught up in a paradox, one which might be called the paradox of conceptualization . The proper concepts are needed to formulate a good theory, but we need a good theory to arrive at the proper concepts.” (p. 53)
“... the paradox is resolved by a process of approximation: the better our concepts, the better the theory we can formulate with them, and in turn, the better the concepts available for the next improved theory.” (p. 54)
[1987] Trusted, Jennifer, Inquiry and Understanding
"We seek explanations in order to satisfy curiosity and gain knowledge and understanding, and in doing this we also come to criticise current concepts and the current body of knowledge.
Modifications of our concepts entail modifications of our facts, modification of our view of the world.” (Chapter 2, p. 21)
[1996] Vygotsky, L. S., Thought and Language, First Published 1934
"Real concepts are impossible without words and thinking in concepts does not exist beyond verbal thinking." (Chapter 5, p. 107)
"A concept emerges only when the abstracted traits are synthesized anew, and the resulting abstract synthesis becomes the main instrument of thought. The decisive role in this process ... is played by the word, deliberately used to direct all the subprocesses of advanced concept formation." (Chapter 5, p. 139)
“... the process leading to concept formation develop along two main lines. The first is complex formation: the child unites diverse objects in groups under a common ‘family name’. The second line of development is the formation of ‘potential concepts’, based on singling out certain common attributes. In both, the use of the word is an integral part of the developing process, and the word maintains its guiding function in the formation of genuine concepts, to which these processes lead.” (Chapter 5, pp. 144-145)