Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers' perceptions of inductive…

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…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

A cognitive schema is a mechanism which allows an individual to organize her/his experiences in such a way that a new similar experience can easily be recognised and dealt with successfully. Well-structured schemas provide for the knowledge base for subsequent mathematical activities. A new experience can be assimilated into a previously existing…

Humans routinely make inductive generalizations about unobserved features of objects. Previous accounts of inductive reasoning often focus on inferences about a single object or feature: accounts of causal reasoning often focus on a single object with one or more unobserved features, and accounts of property induction often focus on a single…

To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. Six students with each of 3 different multiplicative concepts participated. This paper reports on the 6 students with the most basic multiplicative…

The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…

The spontaneous use of analogies in problem-solving occurs when a subject first spontaneously shifts his attention to a situation (B) which differs in some significant way from an original problem situation (A), and then tries to apply findings from B to A. This paper describes research on the process with 10 scientifically trained subjects…

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…

This study investigated the effects of K. J. Klauer's (1989) inductive reasoning training program of teaching children. Effects of training and the range of transfer of the training were assessed. The subjects were 34 third-grade Dutch children of average ability, matched on age, sex, and IQ. Children from the training condition (N=17) received…

Evaluation of a sequenced inquiry learning task with 20 normally achieving junior high students, 18 students with learning disabilities (LD), and 16 with mild mental retardation (MR) found 75 percent of the normal, 50 percent of the LD, but none of the MR students made the correct induction. LD and MR students were less likely to answer…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…