Abstract
Positive testing is characteristic of exploratory behavior, yet it seems to be at odds with the aim of information seeking. After all, repeated demonstrations of one’s current hypothesis often produce the same evidence and fail to distinguish it from potential alternatives. Research on the development of scientific reasoning and adult rule learning have both documented and attempted to explain this behavior. The current chapter reviews this prior work and introduces a novel theoretical account—the Search for Invariance (SI) hypothesis—which suggests that producing multiple positive examples serves the goals of causal learning. This hypothesis draws on the interventionist framework of causal reasoning, which suggests that causal learners are concerned with the invariance of candidate hypotheses. In a probabilistic and interdependent causal world, our primary goal is to determine whether, and in what contexts, our causal hypotheses provide accurate foundations for inference and intervention—not to disconfirm their alternatives. By recognizing the central role of invariance in causal learning, the phenomenon of positive testing may be reinterpreted as a rational information-seeking strategy.
What is invariant does not emerge unequivocally except with a flux. The essentials become evident in the context of changing nonessentials.
James Gibson, 1979
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Change history
18 April 2020
In the original version of this book, Chapter 10 was inadvertently published without separation between acknowledgment and the quote in the chapter opening page. This has now been updated in this revised version.
Notes
- 1.
As discussed below, there are many accounts of this behavior, not all of which use the term “PTS.” Additionally, while the term has also been used to describe learners’ motivation for conducting positive tests, we will restrict our use of “PTS” to refer to observable behavior.
- 2.
The exact nature of the relationship between PTS and confirmation bias differs between accounts. PTS is variously suggested to be (a) an instance of (Nickerson, 1998; Wason, 1962), (b) a source of (see Nickerson, 1998 for review), and (c) a departure from confirmation bias (Klayman, 1995; Klayman & Ha, 1987).
- 3.
Wason also created another classic task of hypothesis testing, the Selection Task (1968), which falls outside the scope of the current discussion.
- 4.
While this distinction resembles Schauble et al.’s (1991) notion of “science versus engineering models,” Heyman and Dweck’s (1992) account is agnostic about the immediate goal. You could, therefore, conceivably have either a “learning” or a “performance” goal while following either a “science” or an “engineering” model.
- 5.
See Bramley, Lagnado, and Speekenbrink (2015) for an in-depth treatment of this overlap between expected probability gain and expected utility gain models of intervention.
- 6.
- 7.
In fact, since the scenarios only contained two values for each variable, the HOLD option tests invariance for all possible kinds (though not combinations) of other factors.
- 8.
This is not the only study in the scientific reasoning literature with such ambiguities. Assumptions about parameters—the number of causal variables and whether their effects are independent or interdependent, probabilistic, or deterministic—are regularly made by experimenters but not conveyed to participants or considered when evaluating their behavior. Ongoing work in our lab aims to remove these ambiguities to better assess children’s intuitive experimentation.
- 9.
As a reminder, the “root node” is the starting point for the causal model of the system. Here, the structure is either a common cause (activating component A causes components B and C to activate) or a causal chain (activating A causes B to activate, which causes C to activate, etc.), meaning component A is the root node in both cases.
References
Baron, J., Beattie, J., & Hershey, J. C. (1988). Heuristics and biases in diagnostic reasoning: II. Congruence, information, and certainty. Organizational Behavior and Human Decision Processes, 42(1), 88–110.
Blanchard, T., Vasilyeva, N., & Lombrozo, T. (2018). Stability, breadth and guidance. Philosophical Studies, 175(9), 2263–2283.
Bonawitz, E. B., van Schijndel, T. J. P., Friel, D., & Schulz, L. (2012). Children balance theories and evidence in exploration, explanation, and learning. Cognitive Psychology, 64(4), 215–234. https://doi.org/10.1016/j.cogpsych.2011.12.002
Bramley, N. R., Lagnado, D. A., & Speekenbrink, M. (2015). Conservative forgetful scholars: How people learn causal structure through sequences of interventions. Journal of Experimental Psychology: Learning Memory and Cognition. https://doi.org/10.1037/xlm0000061
Brewer, W. F., & Samarapungavan, A. (1991). Children’s theories vs. scientific theories: Differences in reasoning or differences in knowledge? In R. R. Hoffman & D. S. Palermo (Eds.), Cognition and the symbolic processes: Applied and ecological perspectives (pp. 209–232). Hillsdale, NJ: Erlbaum.
Carey, S. (1985). Conceptual change in childhood. The MIT series in learning development and conceptual change. Cambridge, MA: MIT Press. https://doi.org/10.1016/S0016-6995(85)80176-5
Carey, S., Evans, R., Honda, M., Jay, E., & Unger, C. (1989). ‘An experiment is when you try it and see if it works’: A study of grade 7 students’ understanding of the construction of scientific knowledge. International Journal of Science Education, 11(5), 514–529. https://doi.org/10.1080/0950069890110504
Coenen, A., Nelson, J. D., & Gureckis, T. M. (2018). Asking the right questions about the psychology of human inquiry: Nine open challenges. Psychonomic Bulletin & Review, 1–41. https://doi.org/10.3758/s13423-018-1470-5
Coenen, A., Rehder, B., & Gureckis, T. M. (2015). Strategies to intervene on causal systems are adaptively selected. Cognitive Psychology, 79, 102–133.
Cook, C., Goodman, N. D., & Schulz, L. E. (2011). Where science starts: Spontaneous experiments in preschoolers’ exploratory play. Cognition, 120(3), 341–349. https://doi.org/10.1016/j.cognition.2011.03.003
Croker, S., & Buchanan, H. (2011). Scientific reasoning in a real-world context: The effect of prior belief and outcome on children’s hypothesis-testing strategies. British Journal of Developmental Psychology, 29(3), 409–424.
Devine, P. G., Hirt, E. R., & Gehrke, E. M. (1990). Diagnostic and confirmation strategies in trait hypothesis testing. Journal of Personality and Social Psychology, 58(6), 952.
Dunbar, K., & Klahr, D. (1989). Developmental differences in scientific discovery processes. In D. Klahr & K. Kotovsky (Eds.), Complex information: the impact of Herbert A. Simon (pp. 109–143). Hillsdale, NJ: L. Erlbaum Associates. https://doi.org/10.1109/cipe.2004.1428147
Einhorn, H. J., & Hogarth, R. M. (1978). Confidence in judgment: Persistence of the illusion of validity. Psychological Review, 85(5), 395.
Friedman, M. (1974). Explanation and scientific understanding. The Journal of Philosophy, 71(1), 5–19.
Friedrich, J. (1993). Primary error detection and minimization (PEDMIN) strategies in social cognition: A reinterpretation of confirmation bias phenomena. Psychological Review, 100(2), 298.
Gelman, S. A., Star, J. R., & Flukes, J. (2002). Children’s use of generics in inductive inferences. Journal of Cognition and Development, 3(2), 179–199.
Gerstenberg, T., Goodman, N., Lagnado, D. A., & Tenenbaum, J. (2014). From counterfactual simulation to causal judgment. Proceedings of the annual meeting of the Cognitive Science Society (Vol. 36).
Gerstenberg, T., Peterson, M. F., Goodman, N. D., Lagnado, D. A., & Tenenbaum, J. B. (2017). Eye-tracking causality. Psychological Science, 28(12), 1731–1744.
Gibson, J. J. (1979). The ecological approach to visual perception. Boston, MA: Houghton Mifflin.
Gopnik, A. (1998). Explanation as orgasm. Minds and Machines, 8(1), 101–118. https://doi.org/10.1023/A:1008290415597
Gopnik, A. (2000). Explanation as orgasm and the drive for causal knowledge: The function, evolution, and phenomenology of the theory formation system. In Explanation and cognition (pp. 299–323). Cambridge, MA: The MIT Press.
Gopnik, A., & Meltzoff, A. N. (1997). Words, thoughts, and theories. Learning, development, and conceptual change. Cambridge, MA: MIT Press. https://doi.org/10.1057/9781137322746
Gopnik, A., & Walker, C. M. (2013). Considering counterfactuals: The relationship between causal learning and pretend play. American Journal of Play, 6, 15–28.
Gorman, M. E., & Gorman, M. E. (1984). A comparison of disconfirmatory, confirmatory and control strategies on Wason’s 2–4–6 task. The Quarterly Journal of Experimental Psychology, 36(4), 629–648.
Gweon, H., & Schulz, L. E. (2008). Stretching to learn: Ambiguous evidence and variability in preschoolers exploratory play. Proceedings of the 30th annual meeting of the Cognitive Science Society.
Heyman, G. D., & Dweck, C. S. (1992). Achievement goals and intrinsic motivation: Their relation and their role in adaptive motivation. Motivation and Emotion, 16(3), 231–247.
Hitchcock, C. (2012). Portable causal dependence: A tale of consilience. Philosophy of Science, 79(5), 942–951. https://doi.org/10.1086/667899
Icard, T. F., Kominsky, J. F., & Knobe, J. (2017). Normality and actual causal strength. Cognition, 161, 80–93.
Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence: An essay on the construction of formal operational structures. New York: Basic Books.
Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: A theory of meaning, pragmatics, and inference. Psychological Review, 109(4), 646.
Johnston, A. M., Sheskin, M., Johnson, S. G. B., & Keil, F. C. (2018). Preferences for explanation generality develop early in biology but not physics. Child Development, 89(4), 1110–1119.
Karmiloff-Smith, A. (1988). The child is a theoretician, not inductivist. Mind and Language, 3, 183–195.
Kendler, K. S. (2005). “A gene for…”: The nature of gene action in psychiatric disorders. American Journal of Psychiatry, 162(7), 1243–1252.
Kitcher, P. (1981). Explanatory unification. Philosophy of Science, 48(4), 507–531.
Klahr, D., & Chen, Z. (2003). Overcoming the positive-capture strategy in young children: Learning about indeterminacy. Child Development, 74(5), 1275–1296.
Klahr, D., & Dunbar, K. (1988). Dual space search during scientific reasoning. Cognitive Science, 12(1), 1–48.
Klahr, D., Fay, A. L., & Dunbar, K. (1993). Heuristics for scientific experimentation: A developmental study. Cognitive Psychology, 25(1), 111–146. https://doi.org/10.1006/cogp.1993.1003
Klayman, J. (1995). Varieties of confirmation bias. In D. L. Medin, J. R. Busemeyer, & R. Hastie (Eds.), The psychology of learning and motivation: Decision making from the perspective of cognitive psychology. New York: Academic.
Klayman, J., & Ha, Y.-W. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94(2), 211.
Kuhn, D. (1989). Children and adults as intuitive scientists. Psychological Review. https://doi.org/10.1037/0033-295X.96.4.674
Kuhn, D., Amsel, E., O’Loughlin, M., Schauble, L., Leadbeater, B., & Yotive, W. (1988). The development of scientific thinking skills. San Diego, CA: Academic Press.
Kuhn, D., & Angelev, J. (1976). An experimental study of the development of formal operational thought. Child Development, 697–706.
Kuhn, D., & Brannock, J. (1977). Development of the isolation of variables scheme in experimental and “natural experiment” contexts. Developmental Psychology, 13(1), 9.
Kuhn, D., & Phelps, E. (1982). The development of problem-solving strategies. Advances in Child Development and Behavior, 17(C), 1–44. https://doi.org/10.1016/S0065-2407(08)60356-0
Lapidow, E., & Walker, C. M. (2019). Does the intuitive scientist conduct informative experiments?: Children’s early ability to select and learn from their own interventions. 41st annual meeting of the Cognitive Science Society.
Lewis, D. (1974). Causation. The Journal of Philosophy, 70(17), 556–567.
Lombrozo, T., & Carey, S. (2006). Functional explanation and the function of explanation. Cognition, 99(2), 167–204. https://doi.org/10.1016/j.cognition.2004.12.009
Mackie, J. L. (1974). The cement of the universe: A study of causation. Oxford: Clarendon Press.
Mahoney, M. J., & DeMonbreun, B. G. (1977). Psychology of the scientist: An analysis of problem-solving bias. Cognitive Therapy and Research, 1(3), 229–238.
McCormack, T., Bramley, N. R., Frosch, C., Patrick, F., & Lagnado, D. A. (2016). Children’s use of interventions to learn causal structure. Journal of Experimental Child Psychology. https://doi.org/10.1016/j.jecp.2015.06.017
McKenzie, C. R. M. (2004). Hypothesis testing and evaluation. In D. Koehler & N. Harvey (Eds.), Blackwell handbook of judgment and decision making (pp. 200–219). Oxford: Blackwell.
McKenzie, C. R. M., & Mikkelsen, L. A. (2000). The psychological side of Hempel’s paradox of confirmation. Psychonomic Bulletin & Review, 7(2), 360–366.
Meng, Y., Bramley, N. R., & Xu, F. (2018). Children’s causal interventions combine discrimination and confirmation. Proceedings of the 40th annual conference of the Cognitive Science Society.
Morris, A., Phillips, J. S., Icard, T. F., Knobe, J., Gerstenberg, T., & Cushman, F. (2018). Causal judgments approximate the effectiveness of future interventions. https://doi.org/10.31234/osf.io/nq53z
Navarro, D. J., & Perfors, A. F. (2011). Hypothesis generation, sparse categories, and the positive test strategy. Psychological Review, 118(1), 120.
Nickerson, R. S. (1998). Confirmation bias: A ubiquitous phenomenon in many guises. Review of General Psychology, 2(2), 175–220.
Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101(4), 608.
Pearl, J., & Bareinboim, E. (2011). Transportability of causal and statistical relations: A formal approach. Twenty-fifth AAAI conference on Artificial Intelligence.
Popper, K. R. (1959). The logic of scientific discovery. Physics Today. https://doi.org/10.1063/1.3060577
Redhead, M. (1987). Incompleteness, nonlocality, and realism: A prolegomenon to the philosophy of quantum mechanics. Oxford: Clarendon Press.
Saffran, J. R., Aslin, R. N., & Newport, E. L. (1996). Statistical learning by 8-month-old infants. Science, 274(5294), 1926–1928. https://doi.org/10.1126/science.274.5294.1926
Saffran, J. R., Johnson, E. K., Aslin, R. N., & Newport, E. L. (1999). Statistical learning of tone sequences by human infants and adults. Cognition. https://doi.org/10.1016/S0010-0277(98)00075-4
Schauble, L. (1990). Belief revision in children: The role of prior knowledge and strategies for generating evidence. Journal of Experimental Child Psychology, 49(1), 31–57. https://doi.org/10.1016/0022-0965(90)90048-D
Schauble, L., Glaser, R., Duschl, R. A., Schulze, S., & John, J. (1995). Students’ understanding of the objectives and procedures of experimentation in the science classroom. The Journal of the Learning Sciences, 4(2), 131–166.
Schauble, L., Klopfer, L. E., & Raghavan, K. (1991). Students’ transition from an engineering model to a science model of experimentation. Journal of Research in Science Teaching, 28(9), 859–882. https://doi.org/10.1002/tea.3660280910
Schulz, L. E. (2012). The origins of inquiry: Inductive inference and exploration in early childhood. Trends in Cognitive Sciences. https://doi.org/10.1016/j.tics.2012.06.004
Schulz, L. E., & Bonawitz, E. B. (2007). Serious fun: Preschoolers engage in more exploratory play when evidence is confounded. Developmental Psychology. https://doi.org/10.1037/0012-1649.43.4.1045
Schulz, L. E., Standing, H. R., & Bonawitz, E. B. (2008). Word, thought, and deed: The role of object categories in children’s inductive inferences and exploratory play. Developmental Psychology. https://doi.org/10.1037/0012-1649.44.5.1266
Schwartz, B. (1982). Reinforcement-induced behavioral stereotypy: How not to teach people to discover rules. Journal of Experimental Psychology: General, 111(1), 23.
Siegler, R. S., & Liebert, R. M. (1975). Acquisition of formal scientific reasoning by 10-and 13-year-olds: Designing a factorial experiment. Developmental Psychology, 11(3), 401.
Siler, S. A., & Klahr, D. (2012). Detecting, classifying, and remediating: Children’s explicit and implicit misconceptions about experimental design. Psychology of Science: Implicit and Explicit Processes. https://doi.org/10.1093/acprof:oso/9780199753628.003.0007
Siler, S. A., Klahr, D., & Price, N. (2013). Investigating the mechanisms of learning from a constrained preparation for future learning activity. Instructional Science, 41(1), 191–216.
Skov, R. B., & Sherman, S. J. (1986). Information-gathering processes: Diagnosticity, hypothesis-confirmatory strategies, and perceived hypothesis confirmation. Journal of Experimental Social Psychology, 22(2), 93–121.
Sloman, S. A. (2005). Causal models : How people think about the world and its alternatives. Oxford, NY: Oxford University Press.
Sloman, S. A., & Lagnado, D. A. (2005). Do We “do”? Cognitive Science, 29(1), 5–39. https://doi.org/10.1207/s15516709cog2901_2
Sloman, S. A., & Lagnado, D. A. (2015). Causality in thought. Annual Review of Psychology, 66, 223–247.
Sodian, B., Zaitchik, D., & Carey, S. (1991). Young children’s differentiation of hypothetical beliefs from evidence. Child Development, 62(4), 753–766.
Strevens, M. (2009). Depth: An account of scientific explanation. Cambridge, MA: Harvard University Press.
Tschirgi, J. E. (1980). Sensible reasoning: A hypothesis about hypotheses. Child Development, 51(1), 1–10. https://doi.org/10.2307/1129583
Tukey, D. D. (1986). A philosophical and empirical analysis of subjects’ modes of inquiry in Wason’s 2–4–6 task. The Quarterly Journal of Experimental Psychology Section A, 38(1), 5–33.
Tweney, R. D., Doherty, M. E., Worner, W. J., Pliske, D. B., Mynatt, C. R., Gross, K. A., et al. (1980). Strategies of rule discovery in an inference task. Quarterly Journal of Experimental Psychology, 32(1), 109–123.
Valanides, N., Papageorgiou, M., & Angeli, C. (2014). Scientific investigations of elementary school children. Journal of Science Education and Technology, 23(1), 26–36. https://doi.org/10.1007/s10956-013-9448-6
van Schijndel, T. J. P., Visser, I., van Bers, B. M. C. W., & Raijmakers, M. E. J. (2015). Preschoolers perform more informative experiments after observing theory-violating evidence. Journal of Experimental Child Psychology, 131, 104–119. https://doi.org/10.1016/j.jecp.2014.11.008
Vasilyeva, N., Blanchard, T., & Lombrozo, T. (2018). Stable causal relationships are better causal relationships. Cognitive Science, 42(4), 1265–1296.
Vogel, R., & Annau, Z. (1973). An operant discrimination task allowing variability of reinforced response patterning 1. Journal of the Experimental Analysis of Behavior, 20(1), 1–6.
Walker, C. M., Lombrozo, T., Legare, C. H., & Gopnik, A. (2014). Explaining prompts children to privilege inductively rich properties. Cognition, 133(2), 343–357. https://doi.org/10.1016/j.cognition.2014.07.008
Wason, P. C. (1960). On the failure to eliminate hypotheses in a conceptual task. Quarterly Journal of Experimental Psychology, 12(3), 129–140.
Wason, P. C. (1962). Reply to wetherick. Quarterly Journal of Experimental Psychology, 14(4), 250.
Wason, P. C. (1968). Reasoning about a rule. Quarterly Journal of Experimental Psychology, 20(3), 273–281.
Wason, P. C., & Johnson-Laird, P. N. (1972). Psychology of reasoning: Structure and content (Vol. 86). Cambridge, MA: Harvard University Press.
Wells, G. L., & Gavanski, I. (1989). Mental simulation of causality. Journal of Personality and Social Psychology, 56(2), 161.
Weslake, B. (2010). Explanatory depth. Philosophy of Science, 77(2), 273–294.
Wetherick, N. E. (1962). Eliminative and enumerative behaviour in a conceptual task. Quarterly Journal of Experimental Psychology, 14(4), 246–249.
Woodward, J. (1997). Explanation, invariance, and intervention. Philosophy of Science, 64, S26–S41.
Woodward, J. (2003). Making things happen: A theory of causal explanation. New York: Oxford University Press.
Woodward, J. (2006). Sensitive and insensitive causation. The Philosophical Review, 115(1), 1–50.
Woodward, J. (2010). Causation in biology: Stability, specificity, and the choice of levels of explanation. Biology and Philosophy, 25(3), 287–318.
Wu, R., Gopnik, A., Richardson, D. C., & Kirkham, N. Z. (2011). Infants learn about objects from statistics and people. Developmental Psychology, 47(5), 1220–1229. https://doi.org/10.1037/a0024023
Yang, S. C., Vong, W. K., Yu, Y., & Shafto, P. (2019). A unifying computational framework for teaching and active learning. Topics in Cognitive Science, 11, 316–337.
Ylikoski, P., & Kuorikoski, J. (2010). Dissecting explanatory power. Philosophical Studies, 148(2), 201–219.
Yoon, E. J., MacDonald, K., Asaba, M., Gweon, H., & Frank, M. C. (2018). Balancing informational and social goals in active learning. Proceedings of the 40th annual meeting of the Cognitive Science Society.
Zimmerman, C. (2000). The development of scientific reasoning skills. Developmental Review, 20(1), 99–149. https://doi.org/10.1006/drev.1999.0497
Zimmerman, C. (2007). The development of scientific thinking skills in elementary and middle school. Developmental Review, 27(2), 172–223. https://doi.org/10.1016/j.dr.2006.12.001
Zimmerman, C., & Glaser, R. (2001). Testing positive versus negative claims: A preliminary investigation of the role of cover story on the assessment of experimental design skills. CSE Technical Report.
Zimmerman, C., & Klahr, D. (2018). Development of scientific thinking. In J. Wixted (Ed.), Stevens’ handbook of experimental psychology and cognitive neuroscience (4th ed., pp. 1–25). New York: Wiley. https://doi.org/10.1002/9781119170174.epcn407
Acknowledgement
This research was supported by funding from the National Defense Science and Engineering Graduate Fellowship awarded to EL. We would like to thank Gail Heyman and Craig McKenzie for their insights, discussion, and feedback on these ideas.
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Lapidow, E., Walker, C.M. (2020). The Search for Invariance: Repeated Positive Testing Serves the Goals of Causal Learning. In: Childers, J. (eds) Language and Concept Acquisition from Infancy Through Childhood. Springer, Cham. https://doi.org/10.1007/978-3-030-35594-4_10
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