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Reasoning

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Updated on Dec 23, 2009

Reasoning has long been a topic of study in logic and philosophy. Logical philosophical approaches are typically concerned with formal and epistemic aspects of reasoning: describing normative models of sound or valid reasoning. However, philosopher David Hume (1711–1776), who produced some of the most influential work on inductive reasoning, recognized the limitations of purely logical accounts of reasoning and noted that psychological processes were vital to a full account of reasoning. Formal or logical approaches to reasoning specify the syntactic form of valid inferences (i.e., those that do not lead to logical contradictions). In contrast, psychological approaches to reasoning explain cognitive performance or how people actually reason. Inferences that are syntactically valid from a logical perspective may be practically uninformative. For example, given the premises (a) Jane is taller than Mary, and (b) Mary is taller than Jill, it would be logically valid to deduce the following inference: Jane is taller than Mary, and Mary is taller than Jill, and Jane is taller than Mary and Jill. However, people are unlikely to make this particular inference from the premises (a) and (b) because it is not parsimonious. Instead, people are far more likely to draw the logically valid and parsimonious conclusion that Jane is taller than Jill.

People's knowledge of the world places pragmatic constraints on how they reason (Brewer & Samarapunga-van, 1991; Giere, 1988; Johnson-Laird, 2006; Cheng, 1997). Classical models of reasoning based on logic or the laws of statistics and probability assume an ideal reasoner, unconstrained by cognitive resources. However, Gigerenzer & Goldstein (1996) argue that people display bounded rationality. Their reasoning is constrained by a number of factors such as the limited capacity of working memory and their cognitive goals (they often reason to find an acceptable solution, not necessarily the “best” solution).

DEFINITION OF REASONING

From a psychological perspective, reasoning may be defined as the set of mental processes used to derive inferences or conclusions from premises. Reasoning helps to generate new knowledge and to organize existing knowledge, rendering it more usable for future mental work. Reasoning is therefore central to many forms of thought such as scientific, critical, and creative thinking, argumentation, problem solving, and decision making. Each of these more complex forms of thought can employ inductive, deductive, and abductive reasoning which are described below.

Induction. Inductive reasoning is ampliative; it generates new knowledge. Inductive reasoning supports inferences but does not guarantee that the inferences are true. Vickers (2006) characterizes inductive reasoning as “contingent” (i.e., dependent on past experiences and observations). There are many forms of inductive reasoning such as enumerative induction and analogical reasoning. The best known form is enumerative induction in which the general properties of a class are inferred from a specific set of empirical observations. For example, upon observing that all the birds in the neighborhood have wings and fly, a person infers that all birds have wings and fly. Generalizations of this kind, though commonplace in human reasoning, are clearly fallible (ostriches and penguins are birds and have wings, but do not fly). The preceding example illustrates a general epistemic problem with inductive inferences, which philosophers refer to as the problem of underdetermination.

Analogical reasoning is another form of inductive reasoning that is important in generating new knowledge. Analogical reasoning involves the transfer of knowledge elements and relationships among knowledge elements (e.g., object properties and property relations such as correlated features) from a well-known domain, a “base,” to an unknown or partially known domain, a “target” (see Gentner, Holyoak, & Koikinov, 2001). For example, the analogy of a biological cell as a factory allows people to transfer knowledge about how a factory works (it has parts that are specialized to perform certain tasks and that operate together to maintain the functioning of the whole) to understand how a cell works. Analogical reasoning is often employed in instruction to help student understand new concepts by analogical transfer from more familiar concepts (Clement, 1993; Baker & Lawson, 2001, Thagard, 2006). Inductive reasoning presumes principles of regularity or continuity in the world that allow the drawing of inferences about new instances from past experience. Induction plays a role in concept formation and concept learning in every domain of knowledge from natural language to science.

Deduction. Deduction refers to processes of inference which guarantee logically valid conclusions from a set of premises. In other words, assuming that the premises are correct, the conclusions deduced from these premises must also be correct. Transitive inferences of the kind described earlier (Jane is taller than Mary; Mary is taller than Jill; therefore Jane is taller than Jill) are one form of deductive inference. Deduction is a constituent of many varieties of cognitive performance such as text comprehension, scientific and mathematical reasoning, and argumentation. Deduction also plays an important role in categorical reasoning. If, for example, scientists were to discover the remains of a hitherto unknown animal in permafrost, conduct DNA analysis on the remains and conclude that the animal was a mammal. they could then deduce that this previously unknown species had defining mammalian characteristics (e.g., it gave birth to its young and had body hair). One of the main cognitive functions of deductive reasoning is to organize knowledge in ways that allow one to derive parsimonious conclusions from sets of premises.

Abduction. The term abduction was coined by Charles Peirce (1839–1914) to refer to a third mode of inference that was distinct from induction and deduction and played a crucial role in scientific reasoning and discovery. Adductive reasoning is a form of reasoning in which individuals start by attending to a particular phenomenon and try to construct a hypothesis that best explains their observation. The process is often called inference to the best explanation (Lipton, 1961; Thagard & Shelley, 1997). Many causal inferences are abductive in nature.

An example of abductive reasoning would be an inquiry into a car crash in which investigators try to reconstruct what happened from forensic evidence (e.g., patterns of damage to a car and its surroundings, data from physiological and toxicological exams conducted on the driver and passengers). From the forensic data, they reconstruct the most plausible or likely explanation for the crash.

SCIENTIFIC REASONING

A classic model of scientific reasoning in philosophy is the hypothetico-deductive model developed by Karl Popper (1902–1994) (1959, 1972). This model posits that hypotheses are deduced from theory and empirically verified by conducting tests that attempt to falsify them. Hypotheses that withstand repeated attempts at falsification may be regarded as better corroborated by the existing evidence than those that do not. However, according to Popper (following Hume), no matter how often a hypothesis is corroborated by empirical evidence, there can be no certainty that it is true.

Post-Popperian scholarship suggests that scientific reasoning is multi-faceted and includes inductive, deductive, and abductive reasoning (Giere, 1988). It is perhaps most useful to think of scientific reasoning as an umbrella term that encompasses all forms of inference that further the generation, evaluation, and revision of scientific knowledge. One important source of scholarship on scientific reasoning comes from the area of science studies. Much of this research draws upon the methods and data of historical research to understand how science is done (Conant, 1957; Giere, 1988; Kuhn, 1962; Thagard, 1990). Such studies analyze archival data, including the laboratory notebooks, correspondence, and the publications of scientists. Dunbar, Giere, Knorr-Cetina, and Sahdra and Thagard have undertaken cognitive analyses of the research practices of working scientists. Naturalistic research has highlighted the role of interpretation in scientific reasoning. Laudan (1990) suggests that scientific judgments are often based on pragmatic criteria such as the compatibility of new ideas with those that are considered to be “well founded.”

VARIATIONS IN REASONING ACROSS DISCIPLINES

Naturalistic research suggests that reasoning within different disciplines and sub-disciplines is shaped by the specific conventions of disciplinary practice such as methodological conventions for collecting, analyzing, presenting, and evaluating data (Ericsson, Charness, Hoffman, & Feltovich, 2006; Giere, 1988; Thagard, 2003; Sahdra & Thagard, 2003). Deductive reasoning may play a greater role in disciplines or sub-disciplines with well-developed formal theories; for instance, certain areas of mathematics and physics. Inductive and abductive reasoning may play a greater role in contexts in which different causal patterns can result in similar outcomes (medical diagnosis) or where particular configurations of events are unique and unlikely to be repeated exactly (forensic science). For instance, Wineburg (1998, 1999) argues that history is a discipline with its own unique contextualized patterns of reasoning. It should be noted that most disciplines employ varied forms of reasoning. Although mathematics has historically been characterized as a deductive discipline (Kitcher, 1979; Netz, 2005; Russell, 1903), Kitcher (1985) and Lakatos (1976) suggest that inductive reasoning plays an important role in mathematical thinking.

DEVELOPMENT OF SCIENTIFIC REASONING

Research indicates that some aspects of reasoning develop early, even before the onset of formal schooling or instruction, and may be part of the basic cognitive machinery of humans. There is considerable evidence that people employ forms of inductive and abductive reasoning to construct concepts about the natural world spontaneously, even in the absence of formal instruction in science (Bail-largeon, 2004; Carey, 1985; diSessa, 1993; Hatano & Inagaki, 2004; Vosniadou & Brewer, 1992). Young children can use prior knowledge of causal mechanisms to reason causally in new contexts and to make causal inferences. Brown's 1990 research shows that by the age of 3, children are able to use their causal knowledge about physical mechanisms to select tools of the right shape and material to help them retrieve a physical object. Given a set of tools of the same shape (rakes or hoes) but different materials, the children in Brown's experiments rejected non-rigid or “squishy” tools in favor of those that were made of rigid materials and would pick up the desired objects without bending or breaking.

Children can use category-based induction to infer new biological knowledge. Two-year-olds expect animals that belong to the same category or “kind” to have the same underlying properties (Gelman & Coley, 1991; Lawson & Kalish, 2006). Young children are also able to use analogical reasoning to help them solve novel problems (Goswami, 1989; Holyoak, Junn, & Billman, 1984). Both adults and young children are able to induce causal structures from observed patterns of covariation in data (Cheng, 1997; Glymour, 2001; Sobel, Tennebaum, & Gopnik, 2004). Preshcoolers can use Bayesian knowledge about causal patterns to infer causal structure from data in some circumstances. In experiments, children observe patterns of data in which an outcome C varies as two putative causes A and B are presented either individually or together. For example, they might observe that A alone is followed by C, and A and B together are followed by C, but B alone is not followed by C. Children ages 3 and 4 are able to infer from such patterns that only A and not B causes C (Sobel, Tennebaum, & Gopnik, 2004; Schulz and Gopnik, 2004).

Certain aspects of reasoning develop late and may not be evident even in the thinking of college-educated adults in the absence of specific training. Research shows that complex forms of deductive reasoning such as syllogistic and conditional reasoning start to emerge in the late elementary school years and continue to develop through adolescence (Bara, Bucciarelli, & Johnson-Laird, 1995; Ward & Overton, 1990). One important psychological model of scientific reasoning is Klahr and Dunbar's model which characterizes scientific discovery as the search for hypotheses to account for patterns of relevant evidence. The model posits that during discovery, people simultaneously search in two related spaces, a “hypothesis space” and an “experiment space.” When trying to account for patterns of data, people either invoke hypotheses from prior knowledge or induce them from the data. They then search for an experiment that can help them choose among rival hypotheses. The work of Klahr and his colleagues suggests that adolescents and adults have difficulty with the use of appropriate experimental design and evidence evaluation strategies. For instance, many people do not spontaneously employ a “control of variables” strategy in complex scientific discovery tasks where there are several potential causes that might influence an outcome (Chen & Klahr, 1999; Klahr, 2000).

On tasks that require the interpretation of covariation evidence (for instance, rates of illness among people who have eaten different combinations of foods) research shows that both children and adults often make unwarranted causal inferences from confounded experiments (Kuhn, 1989, 1991; Kuhn & Dean, 2004). Additionally, people reason differently about identical patterns of covariation evidence depending on whether the variables under consideration are believed to be causal or non-causal based on prior knowledge (Kuhn, 1991; Schauble, 1996). These findings parallel earlier work by Kahneman and Tversky (1979) on errors and biases in human reasoning which shows that given the same objective probability data, people's reasoning about probable gains differed from their reasoning about probable losses. Kuhn & Dean (2004, 2005) argue that part of learning to reason scientifically is the ability to generate genuine scientific questions (ones to which the answer is not known) that can be fruitfully addressed by empirical evidence. They point out that in richer and more realistic knowledge building and evaluation contexts, there is considerable variability in reasoning both across individuals (for example, by age and expertise) and within individuals (for instance, across domains and tasks). Thus, one aspect of developing reasoning competence is the range of contexts to which different forms of reasoning can be successfully applied.

THE ROLE OF CONCEPTUAL KNOWLEDGE

As noted earlier, one factor that influences how people reason is the nature of the conceptual base from which they reason. People reason with and about concepts, and one problem in evaluating reasoning is that different individuals may interpret the same situation differently and bring different assumptions to bear in reasoning. Prior knowledge and belief facilitate reasoning in some contexts. The work of Brown (1990) shows that prior knowledge facilitates causal reasoning even in young children. Pragmatic knowledge improves deductive reasoning on conditional reasoning tasks (e.g., tasks of the logical form: If P then Q) for both children and adults (Cheng & Holyoak, 1985; Girotto, Light, & Colbourn, 1988). Samarapungavan (1992) has shown that elementary school children are able to reason scientifically in theory choice tasks if the competing theories are both plausible. For example, given two equally plausible theories, they prefer the theory that is consistent with the available empirical evidence. They also prefer theories that explain a wider range of data to narrower theories.

Prior knowledge and belief can also impede valid reasoning. For example, Kahneman and Tversky (1973) showed that people's predictions about the likelihood of future events were often based not on the actual (known) frequencies with which these events occurred in a target population (the “base rate”) but on other heuristics such as how easily an example of the event came to mind (availability). In the context of scientific investigation tasks, differences in conceptual models lead people to adopt different strategies of investigation and evidence interpretation. When investigating electricity in a simulated microworld (a computer-based dynamic system that simulates how electricity works) called Votlaville, college students with more sophisticated initial causal models of electricity learned more than students with less sophisticated models because they used more fruitful investigative strategies and engaged in better reasoning (Schauble, Glaser, Raghavan, & Reiner, 1992).

SOCIOCULTURAL FACTORS IN REASONING

In contrast to traditional psychological approaches which focus on individual reasoning, sociocultural theories emphasize the socially shared or co-constructed aspects of reasoning (Boyd & Richerson, 2005; Bruner, 1966; Latour & Woolgar, 1986; Knorr-Cetina, 1999; Rogoff, 1990; Vygotsky, 1978). Jean Piaget (1896–1980) (1945) believed that encountering beliefs and opinions that countered one's own in the course of social interaction provided a powerful form of cognitive challenge which impelled a person to reason. The science studies research discussed above illustrates how sociocultural contexts and practices shape and support scientific reasoning in a variety of ways. Individuals learn prototypical forms or patterns of reasoning as they are acculturated into the practices of their discipline. For instance, social scientists become adept in the use of statistical models for reasoning about patterns of evidence. Giere (1988) and Knorr-Cetina (1989) have noted the role of peer discourse, both formal and informal (e.g., peer review, research group discussions), in shaping the reasoning and knowledge of scientists engaged in discovery. Expert reasoning is supported by cultural tools such as charts, laboratory notebooks, and computer programs for statistical analysis or data modeling (Latour, 1990). Such inscriptional tools allow users to externalize and share both the processes and products of reasoning and reduce cognitive load during complex tasks. For example, using computer programs such as SAS to perform multivariate regression reduces the computational burden of reasoning about covariation evidence with large data sets.

INSTRUCTIONAL STRATEGIES

Can good reasoning be developed through instruction? The research suggests that a variety of instructional approaches and strategies can support the development of reasoning in students. In some circumstances, explicit instruction and modeling can help students acquire patterns of reasoning that they are unfamiliar with (Nisbett, Fong, Lehman, & Cheng, 1987). Students who are explicitly taught to use a “control of variables” strategy on scientific reasoning and discovery tasks are more likely to transfer and use this strategy in novel reasoning contexts than students who receive no explicit instruction and are left to discover the strategy on their own (Klahr & Nigam, 2004).

Instructional scaffolding can be used to support and enhance students' reasoning. Adult support and guidance in the form of hints, questions, and prompts during classroom discourse can help students gain awareness and control over their reasoning (Hogan, Nastasi, & Pressley, 2000; Gleason & Schauble, 1999). Cultural tools (especially computer technology) can be used to enhance student thinking and reasoning in the classroom (Polman & Pea, 2001; Roschelle, Pea, Hoadley, & Gordin, 2000).

In addition to specific strategies to foster reasoning, many educators have discussed the general characteristics of learning environments that support habits of thought and reasoning. These include the use of knowledge-rich, challenging, and open-ended instructional tasks, such as those used in project-based, problem-based, and inquiry learning, that provide the students with affordances to reason (Barron, Schwartz, Vye, & Moore, 1998; Chinn & Malhotra, 2001; Duschl, 2000; Haskill, 2001, Hammer & Elby, 2002; Magnusson, & Palinscar, 1995; Penner, Lehrer, & Schauble, 1998). More generally, fostering a culture of communication in which children are encouraged to talk to one another, argue about ideas, explain concepts, and share their discoveries supports the development of reasoning (Bruner, 1996; Polman & Pea, 2001; Roth, 2005).

BIBLIOGRAPHY

Baker, W. P., & Lawson, A. E., (2001). Complex instructional analogies and theoretical concept acquisition in college genetics. Science Education, 85(6), 665–683.

Baillargeon, R. (2004). Infants' reasoning about hidden objects: evidence for event-general and event-specific expectations. Developmental Science, 7(4), 391–414.

Bara, G. B., Bucciarelli, M., & Johnson-Laird, P. N. (1995). Development of syllogistic reasoning. American Journal of Psychology, 108(2), 157–193.

Barron, B. J. S., Schwartz, D. L., Vye, N. J., & Moore, A. (1998). Doing with understanding: Lessons from research on problem-and project-based learning. Journal of the Learning Sciences, 7(3&4), 271–311.

Boyd, R., & Richerson, P. J. (2005). The origin and evolution of cultures. Oxford, England: Oxford University Press.

Brewer, W. F., & Samarapungavan, A. (1991). Children's theories versus scientific theories: Differences in reasoning or differences in knowledge? In R. R Hoffman & D. S. Palermo (Eds.), Cognition and the symbolic processes: Vol. 3. Applied and ecological perspectives (pp. 209–232). Hillsdale, NJ: Erlbaum.

Brown, A. L. (1990). Domain-specific principles affect learning and transfer in children. Cognitive Science, 14(1), 107–133.

Bruner, J. (1996). The culture of education. Cambridge, MA: Harvard University Press.

Carey, S. (1985). Conceptual change in childhood. Cambridge, MA: MIT Press.

Chen, Z., & Klahr, D. (1999). All other things being equal: the acquisition and transfer of the control of variables strategy. Child Development, 70(5), 1098–1120.

Cheng, P. W. (1997). From covariation to causation: A causal power theory. Psychological Review, 104, 367–405.

Cheng, P. W., & Holyoak, K. J. (1985). Pragmatic reasoning schemas. Cognitive Psychology, 17, 391–416.

Chinn, C. A., & Malhotra, B. A. (2001). Epistemologically authentic inquiry in schools: A theoretical framework for evaluating inquiry tasks. Science Education, 86, 175–218).

Clement, J. (1993). Using bridging analogies and anchoring intuitions to deal with students' misconceptions in physics. Journal of Research in Science Teaching, 30(10), 1241–1257.

Conant, J. B. (1957). The overthrow of the phlogiston theory. The chemical revolution of 1775–1789. In J. B. Conant & L. K. Nash (Eds.), Harvard case histories in experimental science (pp. 67–115). Cambridge, MA: Harvard University Press.

diSessa, A. (1993). Towards an epistemology of physics. Cognition and instruction, 10, 105–225.

Dunbar, K. (1995). How scientists really reason: Scientific reasoning in real-world laboratories. In R.J. Sternberg, & J. Davidson (Eds.), Mechanisms of insight (pp. 365–395). Cambridge MA: MIT Press.

Duschl, R. (2000). Making the nature of science explicit. In R. Millar, J. Osborne & J. Leach (Eds.), Improving Science Education (pp. 185–206). Philadelphia: Open University Press.

Ericsson, C. A., Charness, N., Hoffman, R. R., Feltovich, J. P. (Eds.) (2006). The Cambridge handbook of expertise and expert performance. Cambridge, England: Cambridge University Press.

Gelman, S. A., & Coley, J. D. (1991). The importance of knowing a dodo is a bird: Categories and inference in 2-year-old children. Developmental Psychology, 26, 796–804.

Gentner, D., Holyoak, K.J., & Koikinov, B. N. (Eds.) (2001). The analogical mind. Cambridge, MA: MIT Press.

Giere, R. (1988). Explaining science: A cognitive approach. Chicago: University of Chicago Press.

Gigerenzer, D., & Goldstein, D. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103(4), 650–669.

Girotto, V., Light, P., & Colbourn, C. (1988). Pragmatic reasoning schemas and conditional reasoning in children. Quarterly Journal of Experimental Psychology, 40A(3), 469–482.

Gleason, M. E., & Schauble, L. (1999). Parents' assistance of their children's scientific reasoning. Cognition & Instruction, 17(4), 343–378.

Glymour, C. (2001). The mind's arrows: Bayes nets and graphical causal models in psychology. Cambridge, MA: MIT Press.

Goswami, U. (1989). Relational complexity and the development of analogical reasoning. Cognitive Development, 4, 251–268.

Hammer, D., & Elby, A. (2002). On the form of a personal epistemology. In B. K. Hofer & P. R. Pintrich, (Eds.), Personal epistemology: The psychology of beliefs about knowledge and knowing (pp 169–190). Mahwah, NJ: Erlbaum.

Haskill, R. E. (2001). Transfer of learning. Cognition, instruction, & reasoning. New York: Academic Press.

Hatano. G., & Inagaki, K. (1994). Young children's naïve theory of biology. Cognition, 50, 171–188.

Hogan, K., Nastasi, B. K., Pressley, M. (2000). Discourse patterns and collaborative scientific reasoning in peer and teacher-guided discussions. Cognition & Instruction, 17(4), 379–432.

Johnson-Laird, P. N. (2006). How we reason. Oxford, England: Oxford University Press.

Kahneman, D., & Tversky, A. (1973). On the psychology of prediction. Psychological Review, 80, 237–251.

Kahneman, D., & Tversky, A. (1979) Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), 263–292.

Kitcher, P. (1979). Frege's epistemology. The Philosophical Review, 88(2), 235–262.

Kitcher, P. (1985). The nature of mathematical knowledge. Oxford, England: Oxford University Press.

Klahr, D. (2000). Exploring science: The cognition and development of discovery processes. Cambridge, MA: MIT Press.

Klahr, D., & Dunbar, K. (1988). Dual space search during scientific reasoning. Cognitive Science, 12(1), 1–48.

Klahr, D., & Nigam, M. (2004). The equivalence of learning paths in early science instruction, Psychological Science, 15(10), 661–667.

Knorr-Cetina, K. K. (1999). Epistemic cultures. How the sciences make knowledge. Cambridge, MA: Harvard University Press.

Kuhn, D. (1989). Children and adults as intuitive scientists. Psychological Review, 96, 674–689.

Kuhn, D. (1991). The skills of argument. Cambridge, MA: MIT Press.

Kuhn, D., & Dean, D. (2004). Connecting scientific reasoning and causal inference. Journal of Cognition and Development, 5(2), 261–288.

Kuhn, D., & Dean, D. (2005). Is developing scientific thinking all about learning to control variables? Psychological Science, 16(11), 866–870.

Kuhn, T. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.

Lakatos, I. (1976). A renaissance of empiricism in recent philosophy of mathematics. The British Journal for the Philosophy of Science, 27(3), 201–223.

Latour, B. (1990). Drawing things together. Representation in scientific practice. Cambridge, MA: MIT Press.

Latour, B., & Woolgar, S. (1986). Laboratory life: the construction of scientific facts. Princeton, NJ: Princeton University Press.

Laudan, L. (1990). Science and relativism: Some key controversies in the philosophy of science. Chicago: Chicago University Press.

Lawson, C. A., & Kalish, C. W. (2006). Inductive inferences across time and identity: Are category members more like than single individuals? Journal of Cognition and Development, 7(2), 233–252.

Lipton. P. (1961). Inference to the best explanation. New York: Routledge.

Magnusson, S. J., & Palinscar, A. S. (1995). The learning environment as a site for science education reform. Theory Into Practice, 34(1), 43–59.

Netz, R. (2005). The shaping of deduction in Greek mathematics. A study in cognitive history. Cambridge, England: Cambridge University Press.

Nisbett, R. E., Fong, G. T., Lehman, D. R., & Cheng, P. W. (1987). Teaching reasoning. Science, 238(4827), 628–631.

Penner, D., Lehrer, R., & Schauble, L. (1998). From physical models to biomechanics: A design-based modeling approach. Journal of the Learning Sciences, 7(3–4), 429–449.

Piaget, J. (1945). Sociological studies. New York: Routledge.

Polman, J. L., & Pea, R. D. (2001). Transformative communication as a cultural tool for guiding inquiry science. Science Education, 85(3), 223–238.

Popper, K. (1959). The logic of scientific discovery. New York: Basic.

Popper, K. (1972). Objective knowledge. Oxford, England: Oxford University Press.

Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development in social context. New York: Oxford University Press.

Roschelle, J. M., Pea, R., D., Hoadley, C. M., Gordin, D. N. (2000). Changing how and what children learn in school with computer-based technologies. The Future of Children, 10(2), 76–102.

Roth, W. M. (2005). Talking science: Language and learning in science. Lanham, MD: Rowman & Littlefield.

Russell, B. (1903). The principles of mathematics. London, England: Cambridge University Press.

Sahdra, B., & Thagard, P. (2003). Procedural knowledge in molecular biology. Philosophical Psychology, 16, 477–498.

Samarapungavan, A. (1992). Children's judgments in theory choice tasks: Scientific rationality in childhood. Cognition, 45(1), 1–32.

Schauble, L. (1996). The development of scientific reasoning in knowledge rich contexts. Developmental Psychology, 32(1), 102–119.

Schauble, L., Glaser, R., Ragahavan, K., & Reiner, M. (1992). The integration of knowledge and experimentation strategies in understanding a physical system. Applied Cognitive Psychology, 6(4), 321–343.

Schulz, L. E., & Gopnik. A. (2004). Causal learning across domains. Developmental Psychology, 40(2), 162–176.

Simon, H. A. (1997). Models of bounded rationality. Cambridge, MA: MIT Press.

Sobel, D., Tennebaum, J., B., & Gopnik, A. (2004). Children's causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers. Cognitive Science, 28(3), 303–333.

Thagard, P. (1990). The conceptual structure of the chemical revolution. Philosophy of Science, 57, 183–209.

Thagard, P. (1993). Explanatory coherence. Cambridge, MA: MIT Press.

Thagard, P. (2003). Pathways to biomedical discovery. Philosophy of Science, 70, 235–254.

Thagard, P. (2006). Analogy, Explanation, & Education. Journal of Research in Science Teaching, 29(6), 537–544.

Thagard, P., & Shelley, C. P. (1997). Abductive reasoning: Logic, visual thinking, and coherence. In M.L. D. Chiara, K. Doets, D. Mundici, & J. van Benthem (Eds.), Logic and scientific methods (pp. 413–427). Dordrecht: Kluwer.

Vickers, J. (2006). The Problem of Induction. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy, Retrieved April 16, 2008, from http://plato.stanford.edu/entries/induction-problem/.

Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24(4), 535–585.

Vygotsky, L. (1978). Mind in society. The development of higher psychological processes (M. Cole., V. John-Steiner, S. Scribner, & E. Souberman, Eds.). Cambridge, MA: Harvard University Press.

Ward, S. L., & Overton, W. F. (1990). Semantic familiarity, relevance, and the development of deductive reasoning. Developmental Psychology, 26(3), 488–493.

Wineburg, S. (1998). Historical Thinking and Other Unnatural Acts. Phi Delta Kappan, 80(7), 488–99.

Wineburg, S. (1999). Reading Abraham Lincoln: An expert/expert study in the interpretation of historical texts. Cognitive Science, 22(3), 319–346.

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