Definition
In the field of mathematics education, the term heuristics has different meanings. Heuristics, for example, may refer to George Polya’s mental operations useful for understanding the process of solving problems (Mousoulides and Sriraman 2014). With a slightly more liberal use of the term, heuristics can refer to “intuitive rules theory” established by Tirosh and Stavy (e.g., Stavy and Tirosh 2000; Tirosh and Stavy 1999a, b). Differently, heuristics could refer to the research of Gerd Gigerenzer (e.g., Gigerenzer et al. 1999). However, there is less ambiguity surrounding the phrase heuristics and biases, which particularly refers to the judgment under uncertainty research program of psychologists Amos Tversky and Daniel Kahneman (e.g., Gilovich et al. 2002; Kahneman et al. 1982).
In a (1974) article in the journal Science, Tversky and Kahneman established “that people rely on a limited number of heuristic principles which reduce the complex tasks of assessing probabilities...
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References
Abrahamson D (2009) Orchestrating semiotic leaps from tacit to cultural quantitative reasoning – the case of anticipating experimental outcomes of a quasi-binomial random generator. Cogn Instr 27(3):175–224
Batanero C, Serrano L (1999) The meaning of randomness for secondary school students. J Res Math Educ 30(5):558–567
Batanero C, Green DR, Serrano LR (1998) Randomness, its meaning and educational implications. Int J Math Educ Sci Technol 29(1):113–123
Chernoff EJ (2009) Sample space partitions: an investigative lens. J Math Behav 28(1):19–29
Chernoff EJ (2012) Recognizing revisitation of the representativeness heuristic: an analysis of answer key attributes. ZDM – Int J Math Educ 44(7):941–952
Cox C, Mouw JT (1992) Disruption of the representativeness heuristic: can we be perturbed into using correct probabilistic reasoning? Educ Stud Math 23(2):163–178
Falk R (1981) The perception of randomness. In: Proceedings of the fifth conference of the international group for the psychology of mathematics education. University of Grenoble, Grenoble, pp 222–229
Falk R, Konold C (1997) Making sense of randomness: implicit encoding as a basis for judgement. Psychol Rev 104(2):310–318
Fischbein E (1975) The intuitive sources of probabilistic of probabilistic thinking in children. Reidel, Dordrecht
Fischbein E, Gazit A (1984) Does the teaching of probability improve probabilistic intuitions? Educ Stud Math 15:1–24
Gigerenzer G, Todd PM, ABC Research Group (1999) Simple heuristics that make us smart. Oxford University Press, New York
Gilovich T, Griffin D, Kahneman D (2002) Heuristics and biases: the psychology of intuitive judgment. Cambridge University Press, New York
Green DR (1983) A survey of probability concepts in 3000 pupils aged 11–16 years. In: Grey DR, Holmes P, Barnett V, Constable GM (eds) Proceedings of the first international conference on teaching statistics. Teaching Statistics Trust, Sheffield, pp 766–783
Green DR (1988) Children’s understanding of randomness: report of a survey of 1600 children aged 7–11 years. In: Davidson R, Swift J (eds) The proceedings of the second international conference on teaching statistics. University of Victoria, Victoria
Hirsch LS, O’Donnell AM (2001) Representativeness in statistical reasoning: identifying and assessing misconceptions. J Stat Educ 9(2). Retrieved from http://www.amstat.org/publications/jse/v9n2/hirsch.html
Jones GA, Thornton CA (2005) An overview of research into the learning and teaching of probability. In: Jones GA (ed) Exploring probability in school: challenges for teaching and learning. Springer, New York, pp 65–92
Kahneman D (2002) Maps of bounded rationality: a perspective on intuitive judgment and choice (Nobel Prize Lecture). In: Frangsmyr T (ed) Les Prix Nobel. Retrieved from http://www.nobel.se/economics/laureates/2002/kahnemann-lecture.pdf
Kahneman D (2011) Thinking, fast and slow. Farrar, Straus and Giroux, New York
Kahneman D, Frederick S (2002) Representativeness revisited: attribute substitution in intuitive judgment. In: Gilovich T, Griffin D, Kahneman D (eds) Heuristics and biases: the psychology of intuitive judgment. Cambridge University Press, New York, pp 49–81
Kahneman D, Tversky A (1972) Subjective probability: a judgment of representativeness. Cogn Psychol 3:430–454
Kahneman D, Slovic P, Tversky A (1982) Judgment under uncertainty: heuristics and biases. Cambridge University Press, Cambridge, MA
Konold C (1989) Informal conceptions of probability. Cogn Instr 6(1):59–98
Konold C, Pollatsek A, Well A, Lohmeier J, Lipson A (1993) Inconsistencies in students’ reasoning about probability. J Res Math Educ 24(5):392–414
Lecoutre M-P (1992) Cognitive models and problem spaces in “purely random” situations. Educ Stud Math 23(6):557–569
Leron U, Hazzan O (2006) The rationality debate: application of cognitive psychology to mathematics education. Educ Stud Math 62(2):105–126
Leron U, Hazzan O (2009) Intuitive vs. analytical thinking: four perspectives. Educ Stud Math 71:263–278
Mousoulides N, Sriraman B (2014) Heuristics in mathematics education. In: Lerman S (ed) Encyclopedia of mathematics education. Springer, Dordrecht
Piaget J, Inhelder B (1975) The origin of the idea of chance in students (trans: Leake Jr L, Burrell P, Fischbein, HD). Norton, New York. (Original work published 1951)
Rubel LH (2007) Middle school and high school students’ probabilistic reasoning on coin tasks. J Res Math Educ 38(5):531–556
Shaughnessy JM (1977) Misconceptions of probability: an experiment with a small-group, activity-based, model building approach to introductory probability at the college level. Educ Stud Math 8:285–316
Shaughnessy JM (1981) Misconceptions of probability: from systematic errors to systematic experiments and decisions. In: Schulte A (ed) Teaching statistics and probability: yearbook of the National Council of Teachers of Mathematics. NCTM, Reston, pp 90–100
Shaughnessy JM (1992) Research in probability and statistics. In: Grouws DA (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 465–494
Stavy R, Tirosh D (2000) How students (Mis-)understand science and mathematics. Intuitive rules. Teachers College Press, New York
Tirosh D, Stavy R (1999a) Intuitive rules: a way to explain and predict students reasoning. Educ Stud Math 38:51–66
Tirosh D, Stavy R (1999b) Intuitive rules and comparison task. Math Think Learn 1(3):179–194
Tversky A, Kahneman D (1971) Belief in the law of small numbers. Psychol Bull 76:105–770
Tversky A, Kahneman D (1974) Judgment under uncertainty: heuristics and biases. Science 185:1124–1131
Tzur R (2011) Can dual processing theories of thinking inform conceptual learning in mathematics? Math Enthus 8(3):597–636
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Chernoff, E.J., Sriraman, B. (2020). Heuristics and Biases. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_100010
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