Academic Dishonesty: A Probabilistic Model Using Markov Chains

Academic dishonesty is modeled via Markov chains. The case of student behavior in class assignments, quizzes and exams is analyzed in modeling examples with various levels of surveillance. The choice of modeling based on surveillance and sanctions is motivated by the research literature on the deterrence theory analysis of cheating. In addition, surveillance and sanctions could be controlled to achieve the desired degree of intervention with the least intrusion. This could also be used to formulate optimal university policies regarding academic dishonesty. Section I: Introduction The body of research attempting to estimate the extent of academic dishonesty among college students has produced widely varying results. Karlins et. al. found that only 3% of college students engage in the act of academic dishonesty whereas Gardner et. al. reported a whopping 98%. According to McCabe and Trevino, this apparent disagreement in the literature on the prevalence of these incidents can be mainly attributed to the differences in the definitions of academic dishonesty, data collection methods and interpretations adopted by different authors investigating the phenomenon. Robinson et. al. defined cheating as: “[the] intentional use or attempted use of unauthorized materials, information or study aids in any work submitted for academic credit.” In light of this definition, it can be argued that there is a striking evidence of a large percentage of college students actually engaging in cheating. Regardless of the type or seriousness of the cheating behavior, there is a consensus that cheating appears to be inherent to the college experience. The motivation for writing this paper arose while one of the authors was teaching a junior level class on probability at The State University of New York at Buffalo. There seemed to be a growing evidence of duplication and cheating in both the homeworks and quizzes conducted as a part of the course. There was a strong need to bring this subject up in some form to alert the students to the negative consequences of such behavior on both the professional and personal levels as well as to remind them of the university policies in this regard. After considerable deliberation, it was decided to use the subject of the course itself to analyze the consequences of cheating and in the process, convey the moral and ethical messages to the students. As it turned out, the resulting analysis proved to be very enlightening and could be of value in evaluating school policies that deal with cheating and ethics. This analysis could also be used to help formulate such policies. By presenting this material as a part of the course in probability, it was very well received by the students and had a very good impact. P ge 11153.2 In section II of this paper, we present a theoretical background supporting our design of a probabilistic model to represent and analyze the cheating problem. In section III, we present a simple version of the probabilistic model. Even though the model is very simplistic, it offers useful insights. In section IV, we present a more complex model using Markov chains to represent the cheating behavior. It is shown how the results can be interpreted and used to formulate policies to deal with the problem of academic dishonesty. Proposals for further research conclude the paper. Section II: Theoretical support for a surveillance and sanctions-based model The research literature on the causes of academic dishonesty could be classified into two main types. One type of research is focused on individual/personal characteristics of offending students, while the other concentrates on the effect of contextual/situational factors. Individual/personal variables that were typically investigated include gender 6, , age 8, 9 , student GPA , race/social class 11, , field of study , and personality type . See the paper by Crown & Spiller for a detailed review of all of the above. Studies of such individual predictors of cheating have rendered mixed and conflicting findings. For example, while some studies have found males to engage in acts of academic dishonesty significantly more than females, many have found no significant effect of gender . Yet, one study found that females are significantly more likely to engage in cheating than males. Similarly, while many studies suggest that younger students are more likely to commit acts of academic cheating, some studies have shown that age is not a significant predictor of academic dishonesty . Research on demographic background has consistently found no differences in cheating practices based on race or social class 12, . Challenging the premise that cheating behavior is predisposed by individual student characteristics, the contextual/situational research suggests that certain social contexts inspire or reduce the occurrence of cheating. Crown and Spiller discuss surveillance, honor codes, sanctions, and value counseling as the main situational factors studied in the academic dishonesty literature. One focus that appears to be common to many of the different studies in the contextual/situational research relates to students perceptions of the effectiveness of the cheating countermeasures in place. The effectiveness of those measures obviously pertains to the student perceived chance of being caught cheating. Student perception about being caught was shown by previous research to be one of the most important determinants of the decision to cheat. In an early study, Tittle and Rowe went as far as concluding that cheating could only be reduced by a credible threat of being caught and punished. As the chance of being caught cheating is logically linked to the amount of surveillance present in a situation, surveillance as a variable was found to have a strong effect on cheating behavior. Surveillance was examined as a situational variable in many studies and was operationalized in different ways, including opportunity to cheat, student-proctor ratio, chance of success, and high risk versus low risk situations . All of these studies have found significant results supporting an inverse relationship between surveillance and cheating. P ge 11153.3 Students’ perceived chance of being caught and penalized for cheating was similarly inversely correlated with cheating in honor code settings. It is argued that the effectiveness of honor code schemes in reducing academic dishonesty is actually dependent upon the likelihood that another student would report the misconduct. The increased likelihood of reporting, in turn, creates a perceived stronger chance of being caught, and thus reduces cheating . McCabe and Trevino comment that because academic dishonesty may often be concealed from faculty members, peer reporting could play an important role in shaping students’ perception about the certainty of being caught in acts of academic dishonesty. In this sense, peer reporting, which is part of explicit honor codes in many universities, could be viewed as another form of surveillance. The contextual research in academic dishonesty showed little effect of value counseling on reducing collegiate cheating (see [14] for a review). This and the research results showing the significant role of students’ perception of the probability of being caught in shaping the decision to cheat, are supportive of the deterrence theory explanation of cheating as a deviant behavior . The theory suggests that cheating occurs within the boundaries of expected costs and benefits. As such, individuals would be less likely to cheat because of their expectation of negative consequences . Studies that used this theory suggested that the opportunities to cheat and the fear of external sanctions were the most significant factors in reducing cheating. Building upon the research literature presented above, and the deterrence theory explanation of cheating behavior, we argue that the factors of surveillance and threat of sanctions are the most reliable in analyzing college students’ cheating behavior. We therefore elected to build our probabilistic model based on the deterrence model taking into account the factors of surveillance and threat of sanctions. The choice to use this deterrence model was also driven by a perception that contextual factors such as surveillance and sanctions, unlike individual/personal predispositions for cheating, are open to administrative influence. Controlling these factors could offer the faculty and administrators a means to effectively respond to the problem of academic dishonesty. Despite the apparent theoretical support for the use of surveillance to deter deviant behavior, in an academic setting, deterrent benefits of surveillance must be weighted against the possible unfavorable effects on the academic atmosphere. Unnecessarily increased surveillance can create a sense of diminished trust and loss of privacy. The proposed model, as will be shown later in this paper, can be applied to accurately estimate the optimum amount of intervention to intercept acts of cheating. It may therefore provide to be a viable tool for achieving the desired control over cheating with minimal intrusion. Section III: A simple probabilistic model In this section, we develop a simple model to calculate the probability of getting caught after a given number of cheating incidents. A cheating incident here could mean cheating in a quiz in a particular class. The analysis then would reflect the probability of getting caught after cheating incidents in quizzes only in this particular class. On the other hand, the incidents could be counted based on cheating activities in all classes that a particular student is taking and in all Page 11153.4 types of activities such as homeworks, quizzes etc. The counting of the incidents could also be somewhere in between the above extremes. Let = probability of getting caught at least once in n cheating incidents. denotes the probability of being caught in any given inc