When we "think like a computer scientist," we are able to systematically solve problems in different fields, create software applications that support various needs, and design artefacts that model complex systems. Abstraction is a soft skill embedded in all those endeavours, being a main cornerstone of computational thinking. Our…

This is an article about abstraction, generalization, and the beauty of mathematics. We claim that abstraction and generalization in of itself may very well be a beauty of the human mind. The fact that we humans continue to explore and expand mathematics is truly beautiful and remarkable. Many years ago, our ancestors understood that seven stones,…

As a programmer when solving a problem, a number of conscious and unconscious cognitive operations are being performed. Problem-solving is a gradual and cyclic activity; as the mind is adjusting the problem to its schemas formed by its previous experiences, the programmer gets closer and closer to understanding and defining the problem. The…

Abilities in scientific thinking and reasoning have been emphasized as core areas of initiatives, such as the Next Generation Science Standards or the College Board Standards for College Success in Science, which focus on the skills the future will demand of today's students. Although there is rich literature on studies of how these abilities…

The social studies curriculum travels through time and space and is bigger on the inside than it is on the outside. To an outsider, the social studies curriculum is a single line on a program of studies, 45 minutes of a student's school day. Those on the inside, however, know that the field covers history, geography, civics, economics, and much…

Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

This paper describes the methods and techniques called Conceptual Analysis (CA), a rigorous procedure to generate (without involuntary omissions and repetitions) knowledge bases for the development of knowledge-based systems. An introduction is given of CA and how it can be used to produce knowledge bases. A discussion is presented on what is…

The Philosophy for Children Program was introduced to a class of deaf fifth graders as an instructional approach for reasoning skills. The program is intended to develop analytic skills required for intellectual functioning (including concept development, generalization, inference making, question formulation, and analogies). The program's major…

This paper describes Topdown Conceptual Analysis (TCA) and how it can be used to produce the knowledge base for the development of courseware. Some of the prerequisites and basic theories behind TCA are explained. In discussing what is meant by learning and teaching a concept, an explanation is given of how a complex concept can be taught in terms…

Defines a generalization as "a descriptive statement of broad application indicating a relationship between two or more concepts." Argues that successful teaching about generalizations can only occur when students understand the relationship between concepts and facts. Discusses four issues and four approaches related to teaching…