Inductive Reasoning

Inductive reasoning, or induction, refers to inferences from evidence that are more or less plausible; a good inductive inference is likely to be true. In contrast, the conclusions of deductive inferences are guaranteed to be true by the truth of the premises upon which they are based. Deductive inferences occur in mathematical or logical contexts; almost all other judgments involve induction.

Consider a gardener wishing to buy fencing for a square plot 18 feet on a side. Concluding that the perimeter of the plot equals 72 feet is deductive. What it means to be 18 feet on a side is to have a 72 feet perimeter. This deductive inference is an important piece of solving the problem. Ultimately, however, the gardener has to make an inductive judgment about how much fence he or she will need. Constructing a fence always involves some amount of waste and obstructions to be fenced around. In planning a fencing purchase, it is wise not to take the premises as conclusively true; the plot is unlikely to be exactly 18 feet, nor perfectly square. In a mathematics classroom, the problems demand deduction; outside, in the garden, the hard problems demand induction.

Because almost every judgment has some element of induction, the study of induction is a rich and varied enterprise. Questions about the nature and justification of inductive judgments have a long history in philosophy. In psychology and education, there are two major approaches: a focus on form and a focus on content. These perspectives have led to different pictures of the development of induction and different approaches to teaching good inductive practices.

From a formal perspective, induction involves assessment of probability or association. A weather forecaster's statement that “there is a 70% chance of rain tomorrow” reflects the association between current conditions and future rain: On 70% of the days like today, it has rained tomorrow. Statistics and probability theory provide formal means for calculating association and probability (P). Bayes's theorem defines the probability that a hypothesis is true given some data (e.g., that it will rain tomorrow given today's conditions) in terms of the “prior probabilities” of the hypothesis and the data (how likely rain is on any day, how common are today's conditions) and the “likelihood” of the hypothesis—the probability of the data when the hypothesis is true (how often we see today's conditions when it actually does rain the next day).

Probability judgments are a basic element of psychology. Even traditional learning theory (behaviorism) assumes that learners can calculate associations. Animals and infants are able to learn quite complex patterns of probabilities. Whether people's intuitive judgments conform to or violate axioms of probability theory is a major focus of debate. One influential theory is that people reason with heuristics that are efficient and effective given the environments typically encountered. The cognitive abilities underlying valid statistical inference may require particular environmental support (e.g., schooling) or developmental achievements (e.g., Piaget's formal operations). Some psychologists have proposed that people should be explicitly taught good principles of statistical reasoning.

In education, a formal approach to inductive inferences has often focused on teaching the scientific method, such as control of variables in experimentation. More generally, critical thinking is a set of skills for evaluating arguments based on formal principles of logic. Students who learn to construct valid experiments, recognize confounded evidence, uncover assumptions, and avoid contradictions will make better inductive inferences.

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