Sharon K. Ninness

SUPERSTITIOUS MATH PERFORMANCE : INTERACTIONS BETWEEN RULES AND SCHEDULED CONTINGENCIES

Experimental conditions were designed to examine students’ sensitivity to scheduled contingencies and accurate or fallacious rules as these variables influence performance during computer-generated math problems. Experimental subjects were provided: scheduled contingencies followed by extinction, follow-up extinction, and a rules condition promulgating accurate or fallacious rules for accessing reinforcement. Control subjects did not have access to rules; however, sensitivity to direct-acting contingencies was measured during response independent reinforcement. Performing with accurate rules and scheduled contingencies, most experimental subjects correctly answered math problems at accelerated rates and extended durations. Also, providing fallacious rules during response independent reinforcement induced high rates and extended durations of superstitious responding. However, for most students response independent reinforcement, without rules, was insufficient to induce such behavior. Evidence from this study suggests that maintenance of high rate superstitious responding requires exposure to a fallacious rule in conjunction with making contact with response independent reinforcement. Implications from this study support the theory that superstitious behavior may become self-sustaining by precluding one’s opportunities to contact the null effects of not performing in accordance with fallacious rules. Ramifications regarding interactions between verbal fallacies and coincidental reinforcement are discussed.

CONTINGENCIES OF SUPERSTITION: SELF-GENERATED RULES AND RESPONDING DURING SECOND-ORDER RESPONSE-INDEPENDENT SCHEDULES

Experimental conditions explored the development of fallacious rules and assessed the rates and durations of superstitious responding by children under the influence of standard and second-order response-independent reinforcement. During the presentation of computer-generated math problems, subjects in Experiment 1 had access to a computer and keyboard. Group 1 received second-order, random-time (RT) reinforcement by way of a coin toss graphic procedure (mean reinforcement rate of 1/min). This procedure rendered an effect analogous to a “slot-machine” and matching icons produced monetary reinforcement displayed on the computer screen. A second group obtained response-independent reinforcement according to a standard random-time (RT) 30-s schedule (mean reinforcement rate of 2/min). A control group received no scheduled consequences but was exposed to the same demand conditions. After 10 min, students in all groups answered questions regarding “why” they had performed problems. Subsequently, experimental subjects were exposed to the same conditions for 10 min after which reinforcement was terminated; however, a series of problems remained available for solving. Over the course of the experiment, and particularly during extinction, Group 1 subjects performed at higher rates and longer durations. Experiment 2 replicated Experiment 1, but it examined the effects of second-order response-independent reinforcement on fixed-time (FT) schedules. Students who had been exposed to second-order response-independent reinforcement demonstrated higher rates and longer durations of problem solving. Outcomes suggest that, independent of FT or RT schedules, second-order response-independent contingencies appear to generate elaborate fallac ious rules and particularly long durations of superstitious responding.

A Relational Frame and Artificial Neural Network Approach to Computer-Interactive Mathematics.

Fifteen participants unfamiliar with mathematical operations relative to reflections and vertical and horizontal shifts were exposed to an introductory lecture regarding the fundamentals of the rectangular coordinate system and the relationship between formulas and their graphed analogues. The lecture was followed immediately by computer-assisted instructions and matching-tosample procedures in which participants were e)(posed to computerposted rules regarding the relationship between particular types of formulas and their respective graphs. After participants demonstrated mutual entailment on formula-to-graph and graph-toformula functions, they were assessed for 36 novel relations on complex variations of the original training formulas and graphs. In Experiment 1, 5 of 15 participants demonstrated perfect or near perfect performance on all novel relationships. Experiment 2 was directed at the remaining 10 participants who failed to correctly identify all mathematical relationships assessed in Experiment 1. The error patterns for these 10 participants were classified with the help of an artificial neural network self-organizing map (SOM). Training in Experiment 2 was directed exclusively at the types of errors identified by the SOM. Following remedial training, all participants demonstrated a substantial reduction in errors compared to their performance in Experiment 1. Derived transfer of stimulus control using mathematical relations is discussed.

Augmenting Computer-Interactive Self-Assessment with and without Feedback

Following a preexperimental assessment of computer-interactive math performance during VR 6 reinforcement and extinction, 4 regular education students and 2 students identified as behaviorally disordered participated in an A-BC-D-BC withdrawal of treatment design. Subsequent to baseline observations of math performance during self-assessment with and without accuracy feedback, students were trained in self-assessment procedures by way of a series of computer-interactive tutorials. During treatment, students were provided computer-displayed accuracy feedback plus reinforcement for correct self-assessments of their math performance. Reinforcement and feedback were gradually leaned, and in the final treatment condition, accuracy feedback was terminated; however, monetary reinforcement for correct self¬assessment was sustained. Following treatment, students were given opportunities to perform math problems in the absence of reinforcement while self-assessing their performances with and without accuracy feedback. This was succeeded by a withdrawal condition and a final session in which students, again, were given an opportunity to self-assess with and without feedback from the computer. Outcomes suggest that subsequent to training computer- interactive self-assessment with feedback may facilitate high rates and long durations of math performance even in the absence of compensation. Implications regarding the augmentai as a type of rule-governed behavior and the necessary and sufficient conditions for sustaining self-assessment as a learned reinforcer are discussed.

Behavioral and Physiological Neural Network Analyses: A Common Pathway toward Pattern Recognition and Prediction.

Using 3 diversified datasets, we explored the pattern-recognition ability of the Self-Organizing Map (SOM) artificial neural network as applied to diversified nonlinear data distributions in the areas of behavioral and physiological research. Experiment 1 employed a dataset obtained from the UCI Machine Learning Repository. Data for this study were composed of votes for each U.S. Representative on 16 key items during a particular legislative session. Experiment 2 employed a dataset developed in our human neuroscience laboratory and focused on the effects of sympathetic nervous system arousal on cardiac and inner-ear physiology. Experiment 3 employed the well-known Wisconsin Breast Cancer dataset, which was used to develop a sensitive, automated diagnostic method of distinguishing between malignant and benign cells. We suggest that the SOM is capable of identifying cohesive patterns of nonlinear measurements that would be difficult to identify using traditional linear data reduction procedures and that neural networks will be increasingly valuable in the analysis of a wide range of complex behaviors.

Shaping and Instructing Performance Descriptions During Computer-Interactive Problem Solving

Twelve graduate and undergraduate students participated in one of two experimental preparations. During baseline, subjects in both groups performed computer-interactive math problems during 2-min cycles of multiple random-time (RT) random-ratio (RR) schedules of monetary reinforcement. During the RT component, response-independent reinforcement was delivered in the context of a blue screen, and during the RR component, contingent reinforcement was delivered on a white screen. However, during every 1-min blue-screen component, response rates in excess of 15/min terminated all random-time reinforcement for the duration of that min. Between cycles of the multiple RT RR schedule, students responded to computer- posted descriptions of the most efficient method of accessing monetary reinforcement. For Group 1, selections of performance descriptions were differentially reinforced (shaped) in opposition to scheduled contingencies, and subsequently shaped in conjunction with contingencies. Group 2 subjects were instructed in opposition to contingencies and later instructed in conjunction with scheduled contingencies. Thus, subjects in both groups could earn money in two ways: (1) Points/money was delivered throughout each 2-min cycle of the multiple RT RR schedule and (2) between cycles, subjects could obtain additional money by responding to computer-posted performance descriptions. In this way, performance descriptions between cycles of problem solving could be placed in opposition to or in conjunction with scheduled reinforcement. Results suggest that during computer-interactive responding, shaping performance descriptions was a more powerful procedure for influencing rates of problem solving. Implications regarding the differential effects of response-independent and scheduled reinforcement, shaping and instructing verbal performance descriptions are discussed.

Self-Assessment as a Learned Reinforcer during Computer Interactive Math Performance: An Experimental Analysis

Following a preexperimental assessment of computer interactive math performance, four 6thgrade students from a regular education classroom participated in an ABAB reversal of treatment design. Prior to training, students were given an opportunity to self-assess their speed and accuracy of math performance at the computer. Treatment entailed computer-displayed monetary reinforcement for correct self-assessments. During treatment, monetary reinforcement for correct self-assessmentswas faded, whereas feedback for accuracy of self-assessmentswas sustained. Following treatment, students were given an opportunity to perform math problems while self-assessing their speed and accuracy independent of any form of monetary reinforcement. Thiswas followed by a session in which all opportunities to self-assess were removed and a final session during which students were again given opportunities to self-assess their performance at the computer. Data indicate that three of four students demonstrated high rates of correct problems/minute during the self-assessment only conditions. Implications from this study support the theory that, with practice, self-assessment may become a source of secondary reinforcement and may sustain high rates of academic behavior in the absence of external reward systems. Ramifications regarding self-assessment as a learned reinforcer are discussed.

Fixed-Interval Responding During Human Computer-Interactive Problem Solving

Experiment 1 was designed to investigate student patterns of responding during fixed-interval (FI) 30-s reinforcement. During the experiment, students were able to respond to multiplication problems by typing answers on the keyboard. Correct answers/min were calculated by the computer program and automatically recorded on disk. Following the experiment, students were questioned regarding what they believed to be the best way to earn the money while working problems. Outcomes from the first experiment showed that only one of the five students was dominated by a pause-respond pattern of temporal disparity. This student provided a verbal rule that accurately described the contingenCies associated with FI reinforcement. The other four students in this experiment responded at relatively constant rates in the majority of their intervals and provided verbal descriptions of contingencies suggesting that reinforcement became available only after the completion of a number or a changing number of problems. Experiment 2 replicated the preparations of Experiment 1; however, prior to initiated computerinteractive problem solving, the two subjects were shown the accurate rule generated by the subject in Experiment 1 who had exhibited pause-respond performance. Response patterns produced by these subjects showed conspicuous and consistent patterns of pauserespond throughout all intervals of FI 30-s reinforcement. Experiment 3 was conducted to further assess the possibility that scalloping (or some other pattern) might emerge over an extended series of sessions. Outcomes confirmed that performance patterns did not change significantly over sessions. Moreover, the subjects’ verbal description of programmed contingencies conformed to the pattern of responding they produced. Outcomes are discussed in terms of selfgenerated and socially mediated rule-following.