This chapter illustrates the main warning signals that could help us to detect the flaws of an explanation in physics: internal contradiction (two examples); direct contradiction of a law of physics (one example); indirect contradiction of a law of physics (one example); logical incompleteness of an explanation (three examples); overgeneralization…

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…

Although discussions about inductive reasoning can be traced back thousands of years (Fitelson 2011), the implementation of the Standards for Mathematical Practice (SMP) within the Common Core State Standards (CCSSI 2010) is generating renewed attention to how students learn mathematics. The third SMP, "Construct viable arguments and critique…

The production of verbal operants not previously taught is an important aspect of language productivity. For Skinner, new mands, tacts, and autoclitics result from the recombination of verbal operants. The relation between these mands, tacts, and autoclitics is what linguists call "analogy," a grammatical pattern that serves as a foundation on…

Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…

The article deals with issues concerning the abductive-inductive reasoning of 42 preservice elementary majors on patterns that consist of figural and numerical cues. We discuss: ways in which the participants develop generalizations about classes of abstract objects; abductive processes they exhibit which support their induction leading to a…

Induction, properly understood, is not merely a game, nor is it a gimmick, nor is it an artificial way of explaining an element of reasoning. Proper understanding of inductive reasoning--and the various types of reasoning that the authors term inductive--enables the student to evaluate critically other people's writing and enhances the composition…

Researchers have regarded inductive reasoning as one of the seven primary mental abilities that account for human intelligent behaviours. Researchers have also shown that inductive reasoning ability is one of the best predictors for academic performance. Modelling of inductive reasoning is therefore an important issue for providing adaptivity in…

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…

Analogy is widely considered to be an important mechanism of scientific thinking and a source of creative insight in theory development. In this paper the implicit constraints that determine analogical soundness are considered. It first examines the constraints that govern analogical reasoning as it is predicted today. The scientific uses of…

The tendency to generalize from specific experiences leading to new, more abstract concepts is a natural aspect of human thought. Generalizations are the end result of an inductive process that begins with the identification of similarities in seemingly disparate situations. It is the existence of such generalizations that makes it possible for us…