Didactical-Cognitive Contributions of Mathematics to Problem Gambling

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Types of didactical interventions and their characteristics
It is necessary before proceeding toward an optimal mathematical didactical intervention in problem gambling to state its goals, namely that of limiting the risk factors and result in a significant desirable change in gamblers' behavior. These goals define the optimality of such an intervention and distinguish it from a regular mathematical intervention, where knowledge about and understanding gambling mathematics are aimed. Regarding the setting in which such an intervention could take place, there are three non-exclusive options: in secondary to post-secondary public schools as optional course or module attached to the probability/statistics courses, within private companies or institutions dealing with gambling and problem gambling, and as experimental interventions within the problem-gambling research.
Although over the last two decades, probability and statistics were present in the curricula of most of the secondary schools as well as some 7th and 8th grades worldwide, studies have indicated a decrease in the role of probability and a greater focus on data processing at these educational levels (Borovcnik, 2006). Among the reasons given for this decrease there is the puritanistic view that probability is too closely connected to games of chance, which are seen as plagues of contemporaneous society even in the jurisdictions where they are legal (Borovcnik, 2006). With this trend, probability theory came to be taught in schools only because it is necessary to justify the methods of inferential statistics. However, this principle is not applied in all countries. The best example is Australia, where not only do syllabi outline the role of probability in everyday life and decision making, but teaching modules on the mathematics of gambling have been implemented with success in the secondary schools (see Peard, 2008). Some US states also implemented mathematics of gambling within courses in public schools.
Past studies on the impact of a mathematical didactic intervention with gamblers, testing whether learning about mathematics of gambling does change gambling behavior, were mainly empirical (see Abbott & Volberg, 2000; Gerstein et al., 1999; Hertwig et al., 2004; Lambros & Delfabbro, 2007; Pelletier & Ladouceur, 2007; Peard, 2008; Steenbergh et al., 2004; Williams & Connolly, 2006). The experimental setup of those studies was of two types with respect to the teaching module, which was either assimilated with standard Probability Theory & Mathematical Statistics courses taught in secondary and post-secondary schools but including more applications from the games of chance, or was designed and taught outside the curricula. The content of most of the teaching modules fell within Introduction to and Basics of Probability and Statistics, covering definition and properties of probability, basics of descriptive and inferential statistics, discrete random variables, expected value, classical probability distributions, and central limit theorem. The modules were packed with examples and applications from games of chance and had lessons dedicated to demystifying mathematically the common gambling fallacies.
Results and conclusions from the past and current interventions
In the literature on this matter, contradictory results have been published and a clear conclusion has not yet been drawn. Some of these results were declared by their authors as "paradoxical" or "unexpected," as they did not confirm the expectation of a significant change in the gambling behavior of the subjects. Thus, Hertwig et al. (2004) found that students who received education on probability gambled on low-odds events more than the students who did not know the actual odds; Steenbergh et al. (2004) found that students who were taught about and given warning about gambling fallacies and mathematical expectation gained superior knowledge on these matters, but were just as likely to play roulette as students who did not receive this intervention; Williams & Connolly (2006) found that students who received instruction on probability theory applied in gambling demonstrated superior ability to calculate gambling odds, as well as resistance to gambling fallacies, but this enhanced knowledge was not associated with any decreases in actual gambling behavior. On the other side, additional theoretical studies proved that post-secondary statistics education developed critical thinking, which also applied to gambling, and gamblers who get such education tend to have significantly lower rates of problem gambling (Gray & Mill, 1991; Gerstein et al., 1999; Abbot & Volberg, 2000). 
Conclusions of the conclusions
These studies are problematic from the standpoint of the experimental setup in three important areas: sampling, evaluation, and testing of hypotheses. Regarding the sampling, all studies were undertaken with groups of college students, who are not representative of the gambling population with respect to age as well as an assumed psychological profile whose features could affect interpretation of the results. For example, the fun/entertainment goal of gambling specific to this age group might take precedence over other goals specific to different age groups. With regard to evaluation, the studies were laboratory-based and thus cannot reproduce real-world gambling activity. Filling out a questionnaire on future intentions can neither substitute for nor predict real actions. And finally, concerning the testing of the hypotheses, two issues arise: first, the monitoring period should not be the same for the entire sample group, but different for each gambler according to his/her profile; second, there are constraints induced by participation itself in the study, as gamblers are apprised of the expectations of the study and thereby, their gambling behavior might be influenced. Either of these issues may provide an explanation for the contradictory results (Barboianu, 2013). Aside from these issues, two main questions arise:
1. What mathematical knowledge would an optimal teaching module contain, with respect to the intended effect of limiting excessive gambling? In other words, what is missing in the current didactic interventions?
2. How important is the previous mathematical background of the student for reaching the intended effect? In other words, even if content and structure of the teaching module are optimal, is it enough for the student to understand and assimilate the mathematical facts presented, or is mathematical thinking necessaryŚnot only computational but also conceptual inquiring, and highly critical, attainable only through long-term previous mathematical education and experience?
One thing is clear: If we teach the mathematics of gambling with the goal of changing gambling behavior, we must do it in a different manner, with respect to both content and approach, from the customary methodology.
Further research
Basing on a structural analysis of the mathematical knowledge available for gamblers, as being attached to the mathematical models of games of chance , we identified the epistemic knowledge related to gambling mathematics and the act of modeling as one component missing in the regular didactical interventions, and argued for its potential within an optimized intervention (Barboianu, 2015). Considering the functional models and not only the probabilistic & statistical ones is another principle that we identified as having potential in a didactical intervention, as creating for the student a representation of the games as pure mathematical structures free of risk factors (Barboianu, 2015, and forthcoming).
Further research, both theoretical and empirical, is necessary in various directions for establishing the following:
- whether the learning principles identified are practicably applicable to gamblers;
- what would be the optimal content and structure of the teaching enhanced with such principles;
- whether the potential of this non-standard knowledge will actually manifest, given the various levels of education of the gamblers.

Abbott, M.W. & Volberg, R.A. (2000). Taking the Pulse on Gambling and Problem Gambling in New Zealand: A Report on Phase One of the 1999 National Prevalence Survey. Department of Internal Affairs, Government of New Zealand.

Barboianu, C. (2013). The mathematical facts of games of chance between exposure, teaching, and contribution to cognitive therapies: Principles of an optimal mathematical intervention for responsible gambling. Romanian Journal of Experimental Applied Psychology, 4(3), pp. 25-40.

Barboianu C. (2015).  Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research. UNLV Gaming Research & Review, 19(1).

Borovcnik, M. (2006). Probabilistic and statistical thinking. In M. Perpinan, & M. A. Portabella (Eds.), Proc. of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 484-506). Sant Feliu de Guixols, Spain : ERME

Gerstein, D., Volberg, R.A., Murphy, S., Toce, M., et al. (1999). Gambling impact and behavior study. Report to the National Gambling Impact Study Commission. Chicago: National Opinion Research Center at the University of Chicago.

Gray, T. & Mill, D. (1991). Critical abilities, graduate education, and belief in unsubstantiated phenomena. Canadian Journal of Behavioral Science, 22, pp. 162-172.

Hertwig, R., Barron, G., Weber, E.U., Erev, I. (2004). Decisions from experience and the effect of rare events in risky choice. Psychological Science, 15 (8), pp. 534-539.

Lambros, C. & Delfabbro, P. (2007). Numerical Reasoning Ability and Irrational Beliefs in Problem Gambling. International Gambling Studies, 7(2), pp. 157-171.

Peard, R. (2008). Teaching the Mathematics of Gambling to Reinforce Responsible Attitudes towards Gambling. Retrieved from http://www.stat.auckland.ac.nz/~iase/publications/icme11/ICME11_TSG13_15P_peard.pdf

Pelletier, M., Ladouceur, R. (2007). The effect of knowledge of mathematics on gambling behaviours and erroneous perceptions. International Journal of Psychology, 42(2).

Steenbergh, T.A., Whelan, J.P, Meyers, A.W., May, R.K., & Floyd, K. (2004). Impact of warning and brief intervention messages on knowledge of gambling risk, irrational beliefs and behavior. International Gambling Studies, 4 (1), pp. 3-16.

Williams, R.J., Connolly, D. (2006). Does learning about the mathematics of gambling change gambling behavior? Psychology of Addictive Behaviors, 20 (1), pp. 62-68.


This entry should be cited as:
Barboianu, C. (2014). Didactical-Cognitive Contributions of Mathematics to Problem Gambling. Retrieved from http://probability.infarom.ro/didactical.html.


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