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Article Excerpt
Learning to recognize and evaluate different patterns of reasoning is important for the development of social understanding, logical and scientific reasoning, critical thinking, and epistemological thought. Realizing that another person has made an inference can help children to assess the other person's knowledge and beliefs, explain the other person's actions, and respond appropriately during social interactions. Awareness of inferential processes also contributes to the development of children's own reasoning and children's evaluation of arguments. Explicit awareness of logic may facilitate sophisticated levels of reasoning (Moshman, 1990). Scientific thinking involves explicit awareness of theories, evidence, and the process of drawing conclusions from evidence (Kuhn & Pearsall, 2000). More generally, to become sophisticated at critical thinking, individuals must recognize that the plausibility of competing opinions may be judged by evaluating the reasoning and evidence on which each opinion is based (e.g., King & Kitchener, 1994; Kuhn, 2001). Advanced levels of epistemological thought include understanding that knowledge is constructed from evidence through subjective processes of inference and interpretation and that knowledge varies in degree of certainty (e.g., King & Kitchener, 1994).
Thus, the concepts of evidence, inference, and certainty are central to epistemological development. Rudimentary recognition of both different patterns of evidence and different levels of certainty begin in early childhood, with understanding of inference appearing by the early elementary school years. Four- and 5-year-old children distinguish determinate and indeterminate evidence between some examples (Fay & Klahr, 1996), and 4-year-olds also distinguish among expressions that connote different degrees of certainty, such as "know," "think," "guess," and "sure" or "must" and "might" (Moore, Bryant, & Furrow, 1989; Moore & Davidge, 1989; Moore, Pure, & Furrow, 1990). By 6 years of age, children begin to recognize inference as a source of knowledge (e.g., Pillow, 1999; Ruffman, 1996; Sodian & Wimmer, 1987). Subsequent integration and refinement of the concepts of evidence, inference, and certainty could facilitate an understanding of the mind as actively constructing knowledge. Schwanenflugel, Fabricius, and Noyes (1996) proposed that a general understanding of constructive processing develops during middle childhood. As part of this understanding, children become increasingly aware that inferential and interpretive activities contribute to knowledge, and children begin to realize that cognitive activities differ in certainty. Likewise, Galotti, Komatsu, and Voelz (1997) suggested that during elementary school, children begin to distinguish among different types of inferences in terms of their strength or certainty.
The present study investigated children's and adults' recognition of differences among inductive inferences, deductive inferences, and guesses. Induction, deduction, and guessing are distinct cognitive activities that are based on different patterns of evidence and are associated with different degrees of certainty. Inductive inferences are generalizations that go beyond experience. They often involve inferring a general pattern from experience with a few instances. Conclusions reached through inductive inference vary in likelihood or plausibility but are not logically necessary. Deductive inferences involve integrating information from two or more premises to reach a novel conclusion based on logical relations among the premises. A deductive inference is valid when the conclusion must be true if the premises are true. In contrast to inductive and deductive inferences, guesses are conjectures that may be arbitrary and are not necessarily based on knowledge. Distinguishing among deduction, induction, and guessing and also recognizing variations in inductive strength would represent an important advance beyond the basic understanding that inferences occur. Appreciation of these distinctions could facilitate understanding of knowledge as constructed through diverse processes and the ability to critically evaluate conclusions based on different patterns of evidence and reasoning.
Adults can evaluate either the deductive correctness or the inductive strength of an argument (Rips, 2001). Rips's participants gave different response patterns depending on whether they were instructed to judge the deductive validity or the inductive plausibility of a set of arguments. Furthermore, when instructed to judge inductive plausibility, participants in Rips's study rated some arguments as inductively stronger than others, indicating that adults recognize variations in inductive strength. Thus, in addition to distinguishing between deduction and induction, adults recognize that inductive inferences vary in plausibility.
Previous studies suggest that children gradually come to appreciate differences among deduction, induction, and guessing. Johnson and Wellman (1980) found that first- and third-grade children used "know" more than "guess" when they had inferred an object's location, suggesting that children recognize that inferences are more certain than guesses. Pillow, Hill, Boyce, and Stein (2000) found that most 8- and 9-year-olds rated another person's deductive inferences as more certain than guesses and also explained the other person's knowledge by referring to the person's exposure to premise information following deduction but not following guesses. In contrast, most 4-, 5-, and 6-year-olds did not distinguish deduction from guessing. Pillow (2002) asked children to evaluate their own certainty following deductive inferences, inductive inferences, and guesses. Six- to 7-year-olds rated both deductive and inductive inferences as more certain than pure guesses (answers based on no information), and 8- to 9-year-olds also rated deductive inferences as more certain than inductive inferences. Only adults rated inductive inferences as more certain than informed guesses (an answer with a 50% chance of being correct).
The goal of the present study was to provide a more detailed description of the development of children's understanding of inference during middle childhood. In particular, we sought to assess more fully children's understanding of inductive inferences. We examined (a) age differences in children's evaluation of the certainty of conclusions based on deduction, induction, and guessing; (b) children's evaluation of inductive inferences varying in strength; and (c) children's and adults' coordination of a particular sample of evidence with information about the frequency of alternative outcomes in a larger population when evaluating inferences and guesses. Previous studies have either focused on the contrast between deduction and guessing or presented just one example of induction. We compared children's and adults' evaluations of both strong and weak inductions with their evaluations of deductive inferences and guesses concerning the color of a hidden toy. Inclusion of strong and weak inductions is important because variation in strength is a central feature of induction and because it allows fuller assessment of children's recognition of induction as distinct from both deduction and guessing. Stronger induction might be more difficult to distinguish from deduction in terms of certainty but easier to distinguish from guessing. A weaker induction might be easier to distinguish from deduction but more difficult to distinguish from guessing. In fact, Galotti et al. (1997) found that when presented with fairly weak inductive arguments, kindergarten children rated themselves as less confident in inductive conclusions than deductive conclusions. Similarly, the certainty of guesses may depend on the extent to which they are based on information. Therefore, we presented examples of induction and guessing based on varying levels of evidence.
Previous studies have presented a sample of evidence and asked children to evaluate inferences derived from that sample. However, inferences are not necessarily based solely on an isolated sample of evidence. When making or evaluating inferences or guesses, children and adults may draw upon general knowledge in addition to a particular set of premises or sample of evidence. Consideration of general base rate information often is useful for evaluating conclusions based on induction or guessing. Therefore, we examined children's and adults' coordination of a sample of evidence concerning a hidden toy's color with additional information about the general likelihood of alternative colors. Although adults often overlook base rate information (e.g., Kahneman & Tversky, 1973), adults do make use of such information in some circumstances (Krynski & Tenenbaum, 2007), and children as young as 4 years of age have been found to take account of base rate information to reason about the relation between a sample of items and larger populations (Denison, Konopczynski,...
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