Inductive reasoning is used when generating hypotheses, formulating theories, and discovering relationships.  It is essential for scientific discovery.

I. Definition

1. Basic definition of inductive reasoning

"Induction is a major kind of reasoning process in which a conclusion is drawn from particular cases.  It is usually contrasted with deduction, the reasoning process in which the conclusion logically follows from the premises, and in which the conclusion has to be true if the premises are true.  In inductive reasoning, on the contrary, there is no logical movement from premises to conclusion.  The premises constitute good reasons for accepting the conclusion.  The premises in inductive reasoning are usually based on facts or observations.  There is always a possibility, though, that the premises may be true while the conclusion is false, since there is not necessarily a logical relationship between premises and conclusion."  (Grolier's 1994 Multimedia Encyclopedia)

Inductive reasoning is used when generating hypotheses, formulating theories, and discovering relationships.  It is essential for scientific discovery.
(http://www.csun.edu/science/ref/reasoning/inductive_reasoning/inductive_reasoning.html)

2. The definitions of inductive reasoning in research

Induction can be defined as the process whereby regularities or order are detected and, inversely, whereby apparent regularities, seeming generalizations, are disproved or falsified.  This is achieved by finding out, for instance, that all swans observed so far are white or, on the contrary, that at least one single swan has another color.  To put it more generally, one can state that the process of induction takes place by detecting commonalities through a process of comparing.  In this context, comparing means stating similarities and differences.  However, with inductive reasoning it is not enough to compare whole objects globally to each other.  Instead, they have to be compared with respect to their attributes or to the relations held in common.  That is the reason why all inductive reasoning processes are processes of abstract reasoning.  As can be seen in Fig. 1, the end product of an inductive reasoning process is the discovery of a generalization or the disproving of an assumed generalization.  This end product can be achieved by a process of comparison, i.e. by finding out similarity or dissimilarity or both. Similarity and dissimilarity can refer to attributes of objects or to relations holding between objects.  (Klauer, 1996)

II. Simplified examples of inductive reasoning

Question 1：What should be in the final box?

From the 5 pictures we can induce that the first image and the second image appear in turn, so the final box should be option E.

Question 2：What should be in the final box?

From the first 5 pictures we can induce that the square spot moves clockwise and the semicircle and semi-square exchange their position in turn.  So the final box should be option D.

III. Importance of inductive reasoning

Inductive reasoning is considered to consist of the educative ability, that is, the ability to generate the ‘‘new’’ – the productive characteristic of human beings (De Koning, Sijtsma, &Hamers, 2003; Sternberg & Gardner, 1983).  Inductive reasoning is different from deductive reasoning in that deductive inferences draw out conclusions which are implicit in the given information while inductive inferences add information (Klauer, 2001).

Inductive reasoning is a widely used thinking method in our daily life. We regularly make abstract conclusions from limited observations.

IV. Research in inductive reasoning

James J. Watters, Lyn D. English. Children's application of simultaneous and successive processing in inductive and deductive reasoning problems: Implications for developing scientific reasoning skills. Journal of Research in Science Teaching, Volume 32, Issue 7, pages 699–714, September 1995

Constantinos Christou, Eleni Papageorgiou. A framework of mathematics inductive reasoning. Learning and Instruction 17 (2007) 55-66

Karl Josef Klauer. A Process Theory of Inductive Reasoning Tested by the Teaching of Domain-Specific Thinking Strategies. European Journal of Psychology of Education, 1990, Vol. V, 191-206

Susan A. Gelman, Ellen M. Markman. Categories and induction in young children. Cognition, 23 (1986) 183-209.

Karl Josef Klauer, Gary D. Phye. Inductive Reasoning: A Training Approach. Review of Educational Research, March 2008, Vol. 78, No. 1, pp. 85–123

Els de Koning et al. Teaching Inductive Reasoning in Primary Education. Developmental Review 22, 211–241 (2002)

Karl Josef Klauer. Teaching inductive reasoning: some theory and three experimental studies. Learning and instruction. Vol. 6, No. 1. pp. 31-51, 1996