Abstract
Probabilities are a pervasive aspect of human life and probabilistic thinking is part of (sociological, psychological) models of rational (social) actors. Yet research documents poor understanding of probability in the general public and suggest that people do not update their estimates about future events when given additional information. This may point to the difficult nature of Bayesian thinking, the framework that would allow rational decision makers to update their estimates about future probabilistic events. Drawing on first-person methods for the study of cognition, I articulate invariants of learning an advanced statistical topic: Bayesian statistics. The first case study focuses on the learning of some fundamentals (such as those that one may find as content of a Wikipedia page); the second case study presents and analyzes a learning episode in the case of quantitative social science research that takes into account prior studies for establishing prior probabilities required for calculating posterior probabilities given the information collected in the study. The analyses show—consistent with pragmatic theories of language—that the essential dimension of learning is what equations, terms, and formulae require to be done rather than their (elusive) “meaning.”
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Bakker, A., & Hoffmann, M. H. G. (2005). Diagrammatic reasoning as the basis for developing concepts: a semiotic analysis of students’ learning about statistical distribution. Educational Studies in Mathematics, 60, 333–358.
Bakker, A., Kent, P., Derry, J., Noss, R., & Hoyles, C. (2008). Statistical inference at work: statistical process control as an example. Statistics Education Research Journal, 7(2), 130–145.
Berry, D. A. (1997). Teaching elementary Bayesian statistics with real applications in science. American Statistician, 51, 241–246.
Bourdieu, P. (1992). The practice of reflexive sociology (the Paris workshop). In P. Bourdieu & L. J. D. Wacquant (Eds.), An invitation to reflexive sociology (pp. 216–260). Chicago: University of Chicago Press.
Bourdieu, P. (1997). Méditations pascaliennes [Pascalian meditations]. Paris: Éditions du Seuil.
Castro Sotos, A. E., Vanhoof, S., van den Noortgate, W., & Onghena, P. (2009). The transitivity misconception of Pearson’s correlation coefficient. Statistics Education Research Journal, 8(2), 33–52.
D’Agostini, G. (2003). Bayesian reasoning in data analysis: a critical introduction. Singapore: World Scientific.
Davidson, D. (1986). A nice derangement of epitaphs. In E. Lepore (Ed.), Truth and interpretation (pp. 433–446). Oxford: Blackwell Sci.
Depraz, N., Varela, F., & Vermersch, P. (2002). On becoming aware: steps to a phenomenological pragmatics. Amsterdam: Benjamins.
Hahn, C. (2011). Linking academic knowledge and professional experience in using statistics: a design experiment for business school students. Educational Studies in Mathematics. doi:10.1007/s10649-011-9363-9.
Handa, Y. (2003). A phenomenological exploration of mathematical engagement: approaching an old metaphor anew. For the Learning of Mathematics, 23(1), 22–28.
Handa, Y. (2011). What does understanding mathematics mean for teachers? New York: Routledge.
Hoffmann, M. H. G. (2004). How to get it. Diagrammatic reasoning as a tool of knowledge development and its pragmatic dimension. Foundations of Science, 9, 285–305.
Holzkamp, K. (1993). Lernen: Subjektwissenschaftliche Grundlegung [Learning: subject-scientific foundations]. Frankfurt/M: Campus.
Husserl, E. (1939). Die Frage nach dem Ursprung der Geometrie als intentional-historisches Problem. Revue Internationale de Philosophie, 1, 203–225.
Konold, C. (1995). Issues in assessing conceptual understanding in probability and statistics. Journal of Statistics Education, 3(1). Accessed December 22, 2011 at http://www.amstat.org/publications/jse/v3n1/konold.html.
Langemeyer, I. (2006). Contradictions in expansive learning: towards a critical analysis of self-dependent forms of learning in relation to contemporary socio-technical change. Forum Qualitative Sozialforschung (Forum Qualitative Social Research), 7(1). http://nbn-resolving.de/urn:nbn:de:0114-fqs0601127.
Lecoutre, M.-P., Rovira, K., Lecoutre, B., & Poitevineau, J. (2006). People’s intuitions about randomness and probability: an empirical study. Statistics Education Research Journal, 5(1), 20–35.
Liu, Y., & Thompson, P. (2007). Teachers’ understandings of probability. Cognition and Instruction, 25, 113–160.
McGinn, M. K. (2010). Learning to use statistics in research: a case study of learning in a university-based statistical consulting centre. Statistics Education Research Journal, 9(2), 35–49.
Merleau-Ponty, M. (1945). Phénoménologie de la perception. Paris: Gallimard.
Moore, D. S. (1997). Bayes for beginners? Some reasons to hesitate. American Statistician, 51, 254–261.
Nickerson, R. S. (1998). Confirmation bias: a ubiquitous phenomenon in many guises. Review of General Psychology, 2, 175–220.
Noss, R., Pozzi, S., & Hoyles, C. (1999). Touching epistemologies: meanings of average and variation in nursing practice. Educational Studies in Mathematics, 40, 25–51.
Rorty, R. (1989). Contingency, irony, and solidarity. Cambridge: Cambridge University Press.
Roth, W.-M. (2001). Phenomenology and mathematical experience. Linguistics & Education, 12, 239–252.
Roth, W.-M. (Ed.) (2005a). Auto/biography and auto/ethnography: praxis of research method. Rotterdam: Sense Publishers.
Roth, W.-M. (2005b). Doing qualitative research: praxis of methods. Rotterdam: Sense Publishers.
Roth, W.-M. (2007). Emotion at work: a contribution to third-generation cultural historical activity theory. Mind, Culture and Activity, 14, 40–63.
Roth, W.-M. (2010). An anthropology of reading science texts in online media. Semiotica, 182, 409–442.
Roth, W.-M. (2012). First-person method: for a rigorous approach to the study of living/lived experience. Rotterdam: Sense Publishers.
Varela, F. J. (2001). Intimate distances: fragments for a phenomenology of organ transplantation. Journal of Consciousness Studies, 8, 259–271.
Vidal-Madjar, A. (1978). Teaching mathematics and statistics to adults who are keen on psychology. Educational Studies in Mathematics, 8, 381–390.
Vygotsky, L. S. (1927/1997). The historical meaning of the crisis in psychology: a methodological investigation. In W. R. Rieber & J. Wollock (Eds.), The collected work of L. S. Vygotsky (Vol. 6, pp. 233–343). New York: Kluwer Academic.
Wittgenstein, L. (1976). Wittgenstein’s lectures on the foundations of mathematics, Cambridge, 1939. Hassocks: The Harvester Press.
Wittgenstein, L. (1997). Philosophische Untersuchungen [Philosophical investigations] (2nd ed.). Oxford: Blackwell Sci. (First published in 1953).
Wagner, D. (2011). Opening mathematics texts: resisting the seduction. Educational Studies in Mathematics. doi:10.1007/s10649-011-9372-8.
Wagner, D., & Davis, B. (2010). Felling number: grounding number sense in a sense of quantity. Educational Studies in Mathematics, 74, 39–51.
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Roth, WM. (2014). Learning Bayesian Statistics in Adulthood. In: Chernoff, E., Sriraman, B. (eds) Probabilistic Thinking. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7155-0_24
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DOI: https://doi.org/10.1007/978-94-007-7155-0_24
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