Advertisement

Simulation in children’s conscious recursive reasoning

  • M. Bucciarelli
  • R. Mackiewicz
  • S. S. Khemlani
  • P. N. Johnson-Laird
Article
  • 28 Downloads

Abstract

When do children acquire the ability to understand recursion—that is, repeated loops of actions, as in cookery recipes or computer programs? Hitherto, studies have focused either on unconscious recursions in language and vision or on the difficulty of conscious recursions—even for adults—when learning to program. In contrast, we examined 10- to 11-year-old fifth-graders’ ability to deduce the consequences of loops of actions in informal algorithms and to create such algorithms for themselves. In our experiments, the children tackled problems requiring the rearrangement of cars on a toy railway with a single track and a siding—an environment that in principle allows for the execution of any algorithm—that is, it has the power of a universal Turing machine. The children were not allowed to move the cars, so each problem’s solution called for them to envision the movements of cars on the track. We describe a theory of recursive thinking, which is based on kinematic simulations and which we have implemented in a computer program embodying mental models of the cars and track. Experiment 1 tested children’s ability to deduce rearrangements of the cars in a train from descriptions of algorithms containing a single loop of actions. Experiment 2 assessed children’s spontaneous creation of similar sorts of algorithms. The results showed that fifth-grade children with no training in computer programming have systematic abilities to deduce from and to create informal recursive algorithms.

Keywords

Recursion Informal algorithms Deduction Abduction Kinematic simulations 

References

  1. Aamodt-Leeper, G., Creswell, C., McGurk, R., & Skuse, D. H. (2001). Individual differences in cognitive planning on the Tower of Hanoi task: Neuropsychological maturity or measurement error? Journal of Child Psychology and Psychiatry, 42, 551–556.CrossRefPubMedGoogle Scholar
  2. Anzai, Y., & Uesato, Y. (1982). Learning recursive procedures by middleschool children. In Proceedings of the Fourth Annual Conference of the Cognitive Science Society (pp. 100–102). Hillsdale: Erlbaum.Google Scholar
  3. Bauer, M. I., & Johnson-Laird, P. N. (1993). How diagrams can improve reasoning. Psychological Science, 4, 372–378.  https://doi.org/10.1111/j.1467-9280.1993.tb00584.x CrossRefGoogle Scholar
  4. Berwick, R. C., Pietroski, P., Yankama, B., & Chomsky, N. (2011). Poverty of the stimulus revisited. Cognitive Science, 35, 1207–1242.CrossRefPubMedGoogle Scholar
  5. Bona, M. (2012). Combinatorics of permutations (2nd). Boca Raton: Taylor & Francis.CrossRefGoogle Scholar
  6. Brooks, R. (1991). Intelligence without representation. Artificial Intelligence, 47, 139–160.CrossRefGoogle Scholar
  7. Bucciarelli, M., Mackiewicz, R., Khemlani, S. S., & Johnson-Laird, P. N. (2016). Children’s creation of algorithms: Simulations and gestures. Journal of Cognitive Psychology, 28, 297–318.CrossRefGoogle Scholar
  8. Caeyenberghts, K., Wilson, P. H., van Roon, D., Swinnen, S. P., & Smits-Engelsman, B. C. M. (2009). Increasing convergence between imagined and executed movement across development: Evidence for the emergence of movement representations. Developmental Science, 12, 474–483.CrossRefGoogle Scholar
  9. Chan Mow, I. (2008). Issues and difficulties in teaching novice computer programming. In M. Iskander (Ed.), Innovative techniques in instruction technology, e-learning, e-assessment (pp. 199–204). New York: Springer.Google Scholar
  10. Cherubini, P., & Johnson-Laird, P. N. (2004). Does everyone love everyone? The psychology of iterative reasoning Thinking & Reasoning, 10, 31–53.CrossRefGoogle Scholar
  11. Corballis, M. C. (2011). The recursive mind: The origins of human language, thought, and civilization. Princeton: Princeton University Press.Google Scholar
  12. Dicheva, D., & Close, J. (1996). Mental models of recursion. Journal of Educational Computing Research, 14, 1–23.CrossRefGoogle Scholar
  13. Enderton, H. B. (2010). Computability theory: An introduction to recursion theory. San Diego: Academic Press.Google Scholar
  14. Hauser, M. D., Chomsky, N., & Fitch, W. T. (2002). The faculty of language: What is it, who has it, and how did it evolve? Science, 298, 1569–1579.  https://doi.org/10.1126/science.298.5598.1569 CrossRefPubMedGoogle Scholar
  15. Hegarty, M. (2004). Mechanical reasoning by mental simulation. Trends in Cognitive Sciences, 8, 280–285.CrossRefPubMedGoogle Scholar
  16. Hopcroft, J. E., & Ullman, J. S. (1979). Introduction to automata theory, languages, and computation (1st). Boston: Addison-Wesley.Google Scholar
  17. Jackendoff, R., & Pinker, S. (2005). The nature of the language faculty and its implications for evolution of language (Reply to Fitch, Hauser, and Chomsky). Cognition, 97, 211–225.CrossRefGoogle Scholar
  18. Jahn, G., Knauff, M., & Johnson-Laird, P. N. (2007). Preferred mental models in reasoning about spatial relations. Memory & Cognition, 35, 2075–2086.CrossRefGoogle Scholar
  19. Johnson-Laird, P. N. (1983). Mental models: Towards a cognitive science of language, inference, and consciousness. Cambridge: Harvard University Press.Google Scholar
  20. Johnson-Laird, P. N. (2006). How we reason. Oxford: Oxford University Press.Google Scholar
  21. Keen, R. (2011). The development of problem solving in young children: A critical cognitive skill. Annual Review of Psychology, 62, 1–21.CrossRefPubMedGoogle Scholar
  22. Khemlani, S., Goodwin, G. P., & Johnson-Laird, P. N. (2015). Causal relations from kinematic simulations. In D. C. Noelle, R. Dale, A. S. Warlaumont, J. Yoshimi, T. Matlock, C. D. Jennings, & P. P. Maglio (Eds.), Proceedings of the 37th Annual Conference of the Cognitive Science Society (pp. 1075–1080). Austin: Cognitive Science Society.Google Scholar
  23. Khemlani, S. S., & Johnson-Laird, P. N. (2013). The processes of inference. Argument & Computation, 4, 4–20.CrossRefGoogle Scholar
  24. Khemlani, S. S., Mackiewicz, R., Bucciarelli, M., & Johnson-Laird, P. N. (2013). Kinematic mental simulations in abduction and deduction Proceedings of the National Academy of Sciences, 110, 16766–16771.Google Scholar
  25. Knauff, M., Fangmeier, T., Ruff, C. C., & Johnson-Laird, P. N. (2003). Reasoning, models, and images: Behavioral measures and cortical activity. Journal of Cognitive Neuroscience, 15, 559–573.CrossRefPubMedGoogle Scholar
  26. Kuhn, D. (2013). Reasoning. In P. D. Zelazo (Ed.), The Oxford handbook of developmental psychology (pp. 744–764). Oxford: Oxford University Press.Google Scholar
  27. Kurland, D. M., & Pea, R. D. (1985). Children’s mental models of recursive Logo programs. Journal of Educational Computing Research, 1, 235–243.CrossRefGoogle Scholar
  28. Li, M., & Vitányi, P. (1997). An introduction to Kolmogorov complexity and its applications (2nd). New York: Springer.CrossRefGoogle Scholar
  29. Martins, M., Mursic, Z., Oh, J., & Fitch, W. T. (2015). Representing visual recursion does not require verbal or motor resources. Cognitive Psychology, 77, 20–41.CrossRefGoogle Scholar
  30. Martins, M. D., Laaha, S., Freiberger, E. M., Choi, S., & Fitch, W. T. (2014). How children perceive fractals: Hierarchical self-similarity and cognitive development. Cognition, 133, 10–24.CrossRefPubMedPubMedCentralGoogle Scholar
  31. Mayer, R. E. (2013). Teaching and learning computer programming: Multiple research perspectives. London: Routledge.Google Scholar
  32. Miller, P. H., Kessel, F. S., & Flavell, J. H. (1970). Thinking about people thinking about people thinking about . . . : A study of social cognitive development. Child Development, 41, 613–623.Google Scholar
  33. Oaksford, M., & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning. New York: Oxford University Press.CrossRefGoogle Scholar
  34. Papert, S. (1980). Mindstorms. New York: Basic Books.Google Scholar
  35. Pylyshyn, Z. (2003). Return of the mental image: Are there really pictures in the brain? Trends in Cognitive Sciences, 7, 113–118.  https://doi.org/10.1016/S1364-6613(03)00003-2 CrossRefPubMedGoogle Scholar
  36. Resnick, M. (1994). Turtles, termites, and traffic jams: Explorations in massively parallel microworlds. Cambridge: MIT Press.Google Scholar
  37. Rips, L. J. (1994). The psychology of proof. Cambridge: MIT Press.Google Scholar
  38. Roeper, T. (2009). The minimalist microscope: How and where interface principles guide acquisition. In J. Chandlee, M. Franchini, S. Lord, & G. M. Rheiner (Eds.), Proceedings of the 33rd Annual Boston University Conference on Language Development (pp. 24–48). Medford: Cascadilla Press.Google Scholar
  39. Schaeken, W. S., Girotto, V., & Johnson-Laird, P. N. (1998). The effect of an irrelevant premise on temporal and spatial reasoning. Kognitionswisschenschaft, 7, 27–32.CrossRefGoogle Scholar
  40. Schaeken, W. S., Johnson-Laird, P. N., & d’Ydewalle, G. (1996). Mental models and temporal reasoning. Cognition, 60, 205–234.CrossRefPubMedGoogle Scholar
  41. Shanahan, M. (2016). The frame problem. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. https://plato.stanford.edu/entries/frame-problem/
  42. Skoura, X., Vinter, A., & Papaxanthis, C. (2009). Mentally simulated motor actions in children. Developmental Neuropsychology, 34, 356–367.CrossRefPubMedGoogle Scholar
  43. Sleeman, D. (1986). The challenges of teaching computer programming. Communications of the ACM, 29, 840–841.CrossRefGoogle Scholar
  44. Zimmerer, V., & Varley, R. A. (2010). Recursion in severe agrammatism. In H. van der Hulst (Ed.), Recursion and human language (pp. 393–405). Berlin: De Gruyter.Google Scholar

Copyright information

© Psychonomic Society, Inc. 2018

Authors and Affiliations

  • M. Bucciarelli
    • 1
  • R. Mackiewicz
    • 2
  • S. S. Khemlani
    • 3
  • P. N. Johnson-Laird
    • 4
    • 5
  1. 1.Dipartimento di Psicologia and Centro di Logica, Linguaggio e CognizioneUniversità di TorinoTorinoItaly
  2. 2.Department of PsychologyUniversity of Social Sciences and HumanitiesWarsawPoland
  3. 3.Navy Center for Applied Research in Artificial IntelligenceNaval Research LabWashingtonUSA
  4. 4.Stuart Professor of Psychology, EmeritusPrinceton UniversityPrincetonUSA
  5. 5.Department of PsychologyNew York UniversityNew YorkUSA

Personalised recommendations