Superstitious Math Performance: Interactions between Rules and Scheduled Contingencies

Bridging the gap between laboratory and applied research on response-independent schedules

In 1948, Skinner described the behavior of pigeons under response-independent schedules as "superstitious," and proposed that the responses were reinforced by contiguous, adventitious food deliveries. Subsequently, response-independent schedules have been of interest to both basic and applied researchers, first to understand the mechanisms involved, and later, as "noncontingent reinforcement" (NCR) to reduce undesirable behavior. However, the potential superstitious effects produced by these schedules have been challenged, with some researchers arguing that antecedent variables play a significant role. This paper examines the evidence for adventitious reinforcement from both laboratory and applied research, the results of which suggest that antecedent, nonoperant functions may be important in fully understanding the effects of NCR. We propose an applied-basic research synthesis, in which attention to potential nonoperant functions could provide a more complete understanding of response-independent schedules. We conclude with a summary of the applied implications of the nonoperant functions of NCR schedules.

Optimizing large-scale gambling prevention with adolescents through the development and evaluation of a training course for health professionals: The case of PRIZE

In the field of adolescent gambling prevention, there is a lack of intervention studies reporting and assessing training courses for the intervention providers. The present work fills this gap by realizing a dissemination study inside the PRIZE program aimed at modifying a set of cognitive protective factors and affective risk factors. The purpose of this work was twofold: To develop and evaluate a training course with the intervention providers (Study 1), and to assess the short- and long-term effects of the intervention itself (Study 2). The training course was delivered to 44 health professionals (32 females, Mage = 39.34 years). Results showed a significant increase of correct knowledge about gambling and a significant reduction of their susceptibility to probabilistic reasoning biases. Participants also actually learnt the main competencies to conduct the educational activities, they were satisfied for the training course received, and they felt high levels of self-efficacy. The intervention was implemented with 1894 high school students (61% males; Mage = 15.68 years). In the short term, we found a significant increase of adolescents' correct gambling knowledge, random events knowledge, and probabilistic reasoning ability, and a significant decrease of superstitious thinking, monetary positive outcome expectation, and gambling-related erroneous thoughts and fallacious behavioral choices. In the long-term, a significant decrease of gambling frequency, gambling versatility, and gambling problem severity was obtained. Overall, this work highlights the importance to train prevention program providers in order to optimize the effectiveness of large-scale gambling intervention programs towards adolescents.

Effects of reinforcement and response-cost history on instructional control

The present study compared the effects of reinforcement or punishment versus no additional consequences for instruction following on instructional control and subsequent rule-governed insensitivity. In two experiments, adult participants were presented with repeated choices between a short progressive-time schedule and either a fixed time-schedule or a longer progressive-time schedule. In Experiment 1, three groups were given an initially accurate instruction relative to the direct contingency. A control group experienced no additional consequences for compliance with instructions, whereas compliance resulted in additional points for a second group, and noncompliance led to the subtraction of points for a third group. In a subsequent phase, instructions became inaccurate and there were no additional consequences for compliance or noncompliance for any group. Consistent with previous results, rule-governed insensitivity was observed in all participants. Experiment 2 employed the same procedure, except instructions were inaccurate throughout all sessions, and compliance in the subsequent phase resulted in diminishing points per session. Reinforcement for following instructions increased instructional control and subsequent rule-governed insensitivity. This increase was maintained even after the termination of additional consequences, a result that supports theoretical suggestions that a history of reinforcement for complying with instructions and rules is an important factor in rule-governed insensitivity.

The rule-based insensitivity effect: a systematic review

Background

Adherence to inaccurate rules has been viewed as a characteristic of human rule-following (i.e., the rule-based insensitivity effect; RBIE) and has been thought to be exacerbated in individuals suffering from clinical conditions. This review intended to systematically examine these claims in adult populations.

Methodology

We screened 1464 records which resulted in 21 studies that were deemed eligible for inclusion. Each of these studies was examined to determine: (1) if there is evidence for the RBIE in adults and (2) if this effect is larger in those suffering from psychological problems compared to their non-suffering counterparts. In addition, we investigated how (3) different operationalizations of the RBIE, and (4) the external validity and risks of bias of the experimental work investigating this effect, might influence the conclusions that can be drawn from the current systematic review.

Results

(1) Out of the 20 studies that were relevant for examining if evidence exists for the RBIE in adults, only 11 were eligible for vote counting. Results showed that after the contingency change, the rule groups were more inclined to demonstrate behavior that was reinforced before the change, compared to their non-instructed counterparts. Critically, however, none of these studies examined if their no-instructions group was an adequate comparison group. As a result, this made it difficult to determine whether the effects that were observed in the rule groups could be attributed to the rules or instructions that were manipulated in those experiments. (2) The single study that was relevant for examining if adults suffering from psychological problems demonstrated larger levels of the RBIE, compared to their non-clinical counterparts, was not eligible for vote counting. As a result, no conclusions could be drawn about the extent to which psychological problems moderated the RBIE in that study. (3) Similar procedures and tasks have been used to examine the RBIE, but their precise parameters differ across studies; and (4) most studies report insufficient information to evaluate all relevant aspects affecting their external validity and risks of bias.

Conclusions

Despite the widespread appeal that the RBIE has enjoyed, this systematic review indicates that, at present, only preliminary evidence exists for the idea that adults demonstrate the RBIE and no evidence is available to assume that psychological problems exacerbate the RBIE in adults.

The systematic review was registered in PROSPERO (CRD42018088210).

Gambling-Related Distortions and Problem Gambling in Adolescents: A Model to Explain Mechanisms and Develop Interventions

Although a number of gambling preventive initiatives have been realized with adolescents, many of them have been developed in absence of a clear and explicitly described theoretical model. The present work was aimed to analyze the adequacy of a model to explain gambling behavior referring to gambling-related cognitive distortions (Study 1), and to verify the effectiveness of a preventive intervention developed on the basis of this model (Study 2). Following dual-process theories on cognitive functioning, in Study 1 we tested a model in which mindware gap, i.e., susceptibility to the gambler's fallacy, and contaminated mindware, i.e., superstitious thinking, were the antecedents of gambling-related cognitive distortions that, in turn, affect gambling frequency and problem gambling. Participants were 306 male adolescents (Mage = 17.2 years). A path analysis indicated that cognitive distortions have a mediating role in the relationship that links probabilistic reasoning fallacy and superstitious thinking with problem gambling. Following these findings, in Study 2 we developed a school-based intervention aimed to reduce gambling-related cognitive distortions acting on the above cited mindware problems. A pre- and post-test design - with a 6 months follow-up - was performed with 34 male adolescents (Mage = 16.8), randomly assigned to two groups (Training and No Training), and their baseline equivalence was verified. A Mixed 2 × 2 ANOVA attested a significant Time X Group interaction, indicating a significant reduction of the cognitive distortions from pre-test to post-test only in the Training group. The follow-up attested to the stability of the training effects and the reduction of gambling frequency over time. These findings suggest that prevention strategies should address mindware problems, which can be considered as predictors of gambling-related cognitive distortions.

Prevention of problematic gambling behavior among adolescents: testing the efficacy of an integrative intervention

This study aimed at testing the efficacy of an integrative intervention to prevent adolescent problem gambling acting on a multidimensional set of factors including gambling related knowledge and misconceptions, economic perception of gambling, and superstitious thinking. A pre- and post-test design was performed with 181 Italian adolescents (64% boys; Mean age = 15.95) randomly assigned to two groups (Training and No Training). Results revealed that the intervention was effective in improving correct knowledge about gambling and reducing misconceptions, perception of gambling's profitability, and superstitious thinking. Except for misconceptions, these effects were obtained both in participants who were classified as Non-problem and At-Risk/Problem gamblers at the beginning of the intervention. Findings attested also that the training effects were stable over time, and that some changes in gambling behavior were produced. Findings were discussed referring to indications for future research aiming at confirming and extending the present results.

A functional analytic approach to computer-interactive mathematics

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on particular formula-to-formula and formula-to-graph relations as these formulas pertain to reflections and vertical and horizontal shifts. In training A-B, standard formulas served as samples and factored formulas served as comparisons. In training B-C, factored formulas served as samples and graphs served as comparisons. Subsequently, the program assessed for mutually entailed B-A and C-B relations as well as combinatorially entailed C-A and A-C relations. After all participants demonstrated mutual entailment and combinatorial entailment, we employed a test of novel relations to assess 40 different and complex variations of the original training formulas and their respective graphs. Six of 10 participants who completed training demonstrated perfect or near-perfect performance in identifying novel formula-to-graph relations. Three of the 4 participants who made more than three incorrect responses during the assessment of novel relations showed some commonality among their error patterns. Derived transfer of stimulus control using mathematical relations is discussed.

Effects of random outcomes on choice behavior

Decision-making researchers have shown that making optimal decisions is aided by the detection of information salient to the task. When the task involves random events, humans tend to perceive these events as contingent. In this study, outcomes were grouped together with choices to identify some of the conditions under which random events are correctly perceived. Of the two groups (ns=40) only one was provided information regarding the relationship between choice and outcome. This provision did not improve the detection of the relationship between random events any more than direct contact with the underlying contingencies. Findings are discussed in terms of experiential contact with and sensitivity to underlying contingency.

Rule-governed versus contingency-governed behavior in a self-control task: effects of changes in contingencies

Rule-governed behavior is typically acquired faster than contingency-governed behavior but is less sensitive than contingency-governed behavior to unverbalized contingency changes. The present study investigated these relationships in a computer task frequently used to study human self-control. Instructions for one group of participants contained a hint about how to maximize long-term reinforcement; the other group performed the task without the hint. Participants given the hint came closer to maximizing reinforcement in the long term, but their behavior was less sensitive to an unsignaled contingency change than that of those not given the hint. The study shows that, like other complex behaviors, self-control may be contingency-governed or rule-governed.

Effect of delay of reinforcement on superstitious inferences

Temporal contiguity is positively associated with ease of detecting contingencies. When actions and outcomes are not contiguous, intervening responses might be strengthened by adventitious reinforcement. In the current study, participants engaged in a task where pressing 1 of 10 keys was reinforced either immediately or after various delays. Outcomes were scheduled either according to an FR 1 or FR 2 schedule. Participants also answered a question designed to assess their illusion of control. As the latency between the instrumental response and the reinforcer increased, participants attributed less importance to the instrumental response, attributed more importance to other nonessential responses, and began to show stereotyped patterns of responding. The illusion of control was positively related to the intricacy of such patterns. Results are discussed in terms of a contiguity which implies causality heuristic and the relationship of superstition with adventitious reinforcement and illusion of control.