Contributions of dynamic systems theory to cognitive development

We examine the contributions of dynamic systems theory to the field of cognitive development, focusing on modeling using dynamic neural fields. After introducing central concepts of dynamic field theory (DFT), we probe empirical predictions and findings around two examples—the DFT of infant perseverative reaching that explains Piaget's A-not-B error and the DFT of spatial memory that explain changes in spatial cognition in early development. Review of the literature around these examples reveals that computational modeling is having an impact on empirical research in cognitive development; however, this impact does not extend to neural and clinical research. Moreover, there is a tendency for researchers to interpret models narrowly, anchoring them to specific tasks. We conclude on an optimistic note, encouraging both theoreticians and experimentalists to work toward a more theory-driven future.     

Teacher-child relationships as dynamic systems

The purpose of the present study was to examine factors associated with the quality of the teacher-child relationship from first through fifth grade using data from phases I, II and III of the National Institutes of Child Health and Human Development Study of Early Child Care and Youth Development, a prospective study of 1364 children from birth through sixth grade. On average, children evidenced moderately high quality relationships with teachers in fifth grade. However, there was extensive variation in fifth grade relationship quality across children. Children who received more support and stimulation at home and whose parents had higher quality interactions with the school had higher quality relationships. Additionally, children in classrooms with more positive environments and better management had higher quality relationships. Lastly, females, European-American children, children with lower levels of behavior problems and children who had higher quality relationships with their teachers in kindergarten also had higher quality relationships with teachers. On average, children evidenced decreases in the quality of their relationships with teachers from first through fifth grade. Interestingly, children whose parents had more contact with their schools, who were in schools where teachers received higher salaries and in classrooms that had more positive emotional climates and that were better managed evidenced slower rates of decline in relationship quality. Implications for theory and practice are discussed.     

Applying Skinner's analysis of verbal behavior to persons with dementia

Skinner's 1957 analysis of verbal behavior has demonstrated a fair amount of utility to teach language to children with autism and other various disorders. However, the learning of language can be forgotten, as is the case for many elderly suffering from dementia or other degenerative diseases. It appears possible that Skinner's operants may facilitate not only acquisition of language but also the ability to recall items or objects that may have appeared to be “forgotten.” The present study examined the utility of having a series of adults in long-term care emit tacts, echoics, or intraverbals upon presentation of various visual stimuli. Compared to a no-verbal response condition, it appears that the incorporation of Skinner's verbal operants can in fact improve recall for this population. Implications for the retraining of lost language are presented.     

The effects of advance notice of activity transitions on stereotypic behavior

Using an A-B-A-B design, two procedures for requesting a change of activity were compared for their effect on the stereotypic behavior of a man with autism. One procedure requested immediate change of activities, whereas the second procedure gave advance notice of a change. Less stereotypy occurred when advance notice of change was given.     

Applying behavior analysis to school violence and discipline problems: Schoolwide positive behavior support

School discipline is a growing concern in the United States. Educators frequently are faced with discipline problems ranging from infrequent but extreme problems (e.g., shootings) to less severe problems that occur at high frequency (e.g., bullying, insubordination, tardiness, and fighting). Unfortunately, teachers report feeling ill prepared to deal effectively with discipline problems in schools. Further, research suggests that many commonly used strategies, such as suspension, expulsion, and other reactive strategies, are not effective for ameliorating discipline problems and may, in fact, make the situation worse. The principles and technology of behavior analysis have been demonstrated to be extremely effective for decreasing problem behavior and increasing social skills exhibited by school children. Recently, these principles and techniques have been applied at the level of the entire school, in a movement termed schoolwide positive behavior support. In this paper we review the tenets of schoolwide positive behavior support, demonstrating the relation between this technology and applied behavior analysis.     

Motivational systems of agonistic behavior in muroid rodents: A comparative review and neural model

The data on agonistic behavior of muroid rodents that have been obtained from field observations and laboratory experiments are reviewed and compared in terms of a hypothetical model of the neural organization of these behaviors. The neural model has been presented elsewhere and is used here only as a way to organize the data. The data are organized in terms of four hypothetical motivational systems: Offense, defense, submission, and patrol/marking. The various behaviors are considered as motor patterns and are compared and analyzed in terms of the proposed motivating, releasing, and directing stimuli of the motivational systems. Interactions and overlaps between the motivational systems are also considered. It is concluded that the organization of agonistic behavior may be similar across all species of muroid rodents. Generalizations are complicated by the profound effects of ontogenetic factors. Four categories of behaviors differ from species to species: Scent-marking, submissive behaviors, threat behaviors, and alarm signals. The possible phylogenetic and ontogenetic factors in these differences are considered.     

Sensitivity of children's behavior to probabilistic reward: effects of a decreasing-ratio lottery system on math performance

Probabilistic reward has been shown to affect children's choice behavior in game-like activities. We examined the effects of a lottery system containing progressively lower exchange ratios on children's completion of math problems. Two of the 3 children completed problems above baseline levels until the chance of exchange dropped to 25%. This study describes a potentially useful method for examining reinforcement schedules in applied settings and extends previous research on probabilities of reinforcement.     

Tests for stability in linear structural equation systems

Interpretations regarding the effects of exogenous and endogenous variables on endogenous variables in linear structural equation systems depend upon the convergence of a matrix power series. Convergence depends upon the eigenvalues of the structural coefficient matrix. The test for convergence developed by Jöreskog and Sörbom is shown to be only sufficient, not necessary and sufficient.     

Effects of self-generated rules on the development of schedule-controlled behavior.

College students responded under a multiple differential-reinforcement-of-low-rate 5-s fixed-ratio 8 schedule, with components alternating every 2 min. After 40 programmed minutes of acquisition and 12 min of maintenance, without notice, both schedules changed to extinction for 28 min. During acquisition, between alternations of the multiple schedule, some subjects were asked to develop rules describing the schedule contingencies. Other subjects were given these same rules between alternations, and a third group neither received nor were asked to develop rules. By the end of the acquisition phase, self-generated-rule subjects were more likely to show schedule-typical behavior than were subjects not asked to generate rules. The behavior of those given rules was similar to those asked to generate rules at the end of acquisition, but yoked-rule subjects acquired schedule-typical behavior at a quicker rate. By the end of extinction, during the period corresponding to the previous fixed-ratio interval, all no-rule subjects who had earned points during acquisition and maintenance were responding at a rate of less than 30 responses per minute. Only 3 of the 9 self-generated-rule subjects and 2 of the 5 yoked-rule subjects were similarly responding at this low rate. Results suggest that asking subjects to develop self-rules facilitates acquisition, but can retard extinction. Results also suggest that self-generated rules function similarly to external rules.     

Order and chaos in fixed-interval schedules of reinforcement

Fixed-interval schedule performance is characterized by high levels of variability. Responding is absent at the onset of the interval and gradually increases in frequency until reinforcer delivery. Measures of behavior also vary drastically and unpredictably between successive intervals. Recent advances in the study of nonlinear dynamics have allowed researchers to study irregular and unpredictable behavior in a number of fields. This paper reviews several concepts and techniques from nonlinear dynamics and examines their utility in predicting the behavior of pigeons responding to a fixed-interval schedule of reinforcement. The analysis provided fairly accurate a priori accounts of response rates, accounting for 92.8% of the variance when predicting response rate 1 second in the future and 64% of the variance when predicting response rates for each second over the entire next interreinforcer interval. The nonlinear dynamics account suggests that even the “noisiest” behavior might be the product of purely deterministic mechanisms.     

Instructed versus shaped human verbal behavior: Interactions with nonverbal responding

Undergraduate students' presses on left and right buttons occasionally made available points exchangeable for money. Blue lights over the buttons were correlated with multiple random-ratio random-interval components; usually, the random-ratio schedule was assigned to the left button and the random-interval to the right. During interruptions on the multiple schedule, students filled out sentence-completion guess sheets (e.g., The way to earn points with the left button is to...). For different groups, guesses were shaped with differential points also worth money (e.g., successive approximations to “press fast” for the left button), or were instructed (e.g., Write “press slowly” for the left button), or were simply collected. Control of rate of pressing by guesses was examined in individual cases by reversing shaped or instructed guesses, by instructing pressing rates, and/or by reversing multiple-schedule contingencies. Shaped guesses produced guess-consistent pressing even when guessed rates opposed those characteristic of the contingencies (e.g., slow random-ratio and fast random-interval rates), whereas guesses and rates of pressing rarely corresponded after unsuccessful shaping of guesses or when guessing had no differential consequences. Instructed guesses and pressing were inconsistently related. In other words, when verbal responses were shaped (contingency-governed), they controlled nonverbal responding. When they were instructed (rule-governed), their control of nonverbal responding was inconsistent: the verbal behavior sometimes controlled, sometimes was controlled by, and sometimes was independent of the nonverbal behavior.     

Limited matching on concurrent-schedule reinforcement of academic behavior

Three adolescent students with special educational needs were given a choice between completing one of two available sets of math problems. Reinforcers (nickels) across these alternatives were arranged systematically in separate experimental phases according to three different concurrent variable-interval schedules (reinforcement ratios of 2:1, 6:1, and 12:1). Time allocated to the two stacks of math problems stood in linear relationship to the reinforcement rate obtained from each stack, although substantial undermatching and bias were observed for all subjects. However, changes in the schedules were not followed by changes in allocation patterns until adjunct procedures (e.g., changeover delays, limited holds, timers, and demonstrations) were introduced. The necessity of adjunct procedures in establishing matching in applied situations is discussed as a limitation to quantitative applications of the matching law in applied behavior analysis.     

The temporal organization of behavior on periodic food schedules.

Various theories of temporal control and schedule induction imply that periodic schedules temporally modulate an organism's motivational states within interreinforcement intervals. This speculation has been fueled by frequently observed multimodal activity distributions created by averaging across interreinforcement intervals. We tested this hypothesis by manipulating the cost associated with schedule-induced activities and the availability of other activities to determine the degree to which (a) the temporal distributions of activities within the interreinforcement interval are fixed or can be temporally displaced, (b) rats can reallocate activities across different interreinforcement intervals, and (c) noninduced activities can substitute for schedule-induced activities. Obtained multimodal activity distributions created by averaging across interreinforcement intervals were not representative of the transitions occurring within individual intervals, so the averaged multimodal distributions should not be assumed to represent changes in the subject's motivational states within the interval. Rather, the multimodal distributions often result from averaging across interreinforcement intervals in which only a single activity occurs. A direct influence of the periodic schedule on the motivational states implies that drinking and running should occur at different periods within the interval, but in three experiments the starting times of drinking and running within interreinforcement intervals were equal. Thus, the sequential pattern of drinking and running on periodic schedules does not result from temporal modulation of motivational states within interreinforcement intervals.     

Precurrent contingencies: Behavior reinforced by altering reinforcement probability for other behavior

The present study explored the effects of a precurrent contingency in which one (precurrent) activity increased the reinforcement probability for another (current) activity. Four human subjects responded on a two-key computer mouse. Each right-key press was reinforced (points exchangeable for money) with .02 probability. In one condition (no precurrent contingency), pressing the left key had no scheduled consequence; in another condition (precurrent contingency), pressing the left key increased the reinforcement probability for right-key responding to .08 for 15 s. Initial exposure to the precurrent contingency resulted in acquisition of precurrent left-key responding for 3 subjects, but for the 4th subject a special contingency was required. Right-key responding occurred at a high stable rate across the conditions. Changeovers to left-key responding dropped to near zero when the precurrent contingency was absent and were maintained at enhanced levels when the precurrent contingency was present. Contacts with the left key consisted of short response runs. Right-key responses were more frequently emitted within 15 s of a left-key response when the precurrent contingency was present, an efficient adaptation to the contingency. Continued research on precurrent behavior may produce insights into complex phenomena such as autoclitics and self-control.     

Combining dynamic systems and multivariate analyses to compare the mother-child interactions of externalizing subtypes

A dynamic systems analysis was conducted to distinguish the parent–child interactions of pure externalizing children from children comorbid for externalizing and internalizing problems. Thirty-three parents and clinically referred children (8–12 years old) discussed a problem for 4 min and then tried to wrap up in response to a signal (a perturbation). The perturbation was intended to increase the pressure on the dyad, triggering a reorganization of their behavioral system. We hypothesized that the comorbid group would be distinguished from the externalizing-only group as a result of this reorganization, but not before. The sequential data were analyzed using a combination of case-sensitive (state space grids and chi-square analyses) and group-based, multivariate techniques (log-linear modeling). Results revealed that externalizing dyads engaged in a permissive pattern throughout the problem-solving session, whereas comorbid dyads shifted from a permissive pattern to a mutually hostile pattern after the perturbation. These findings punctuate the need for a dynamic systems approach to the study of relationship processes associated with the development of childhood psychopathology. Theoretical and clinical implications are discussed.     

The linear system theory's account of behavior maintained by variable-ratio schedules.

The mathematical theory of linear systems, which has been used successfully to describe behavior maintained by variable-interval schedules, is extended to describe behavior maintained by variable-ratio schedules. The result of the analysis is a pair of equations, one of which expresses response rate on a variable-ratio schedule as a function of the mean ratio requirement (n) that the schedule arranges. The other equation expresses response rate on a variable-ratio schedule as a function of reinforcement rate. Both equations accurately describe existing data from variable-ratio schedules. The theory accounts for two additional characteristics of behavior maintained by variable-ratio schedules; namely, the appearance of strained, two-valued (i.e., zero or very rapid) responding at large ns, and the abrupt cessation of responding at a boundary n. The theory also accounts for differences between behavior on variable-interval and variable-ratio schedules, including (a) the occurrence of strained responding on variable-ratio but not on variable-interval schedules, (b) the abrupt cessation of responding on occurrence of higher response rates on variable-ratio than on variable-interval schedules. Furthermore, given data from a series of variable-interval schedules and from a series of concurrent variable-ratio variable-interval schedules, the theory permits quantitative prediction of many properties of behavior on single-alternative variable-ratio schedules. The linear system theory's combined account of behavior on variable-interval and variable-ratio schedules is superior to existing versions of six other mathematical theories of variable-interval and variable-ratio responding.     

Emergent complexity: What uphill analysis or downhill invention cannot do

In these notes we review emergent phenomena in complex systems, emphasizing ways to identify potential underlying universal mechanisms that generate complexity. The discussion focuses on the emergence of collective behavior in dynamical systems when they are poised near a critical point of a phase transition, either by tuning or by self-organization. We then present the rationale for our proposal that the brain is naturally poised near criticality and review recent results as well as the implications of this view of the functioning brain.     

"Replacing" problem behavior: an analysis of tactical alternatives

A number of textbooks and professional volumes in applied behavior analysis suggest that interventions designed primarily to decrease a problem behavior should routinely be accompanied by efforts to increase the frequency of at least one appropriate behavior. Some sources describe the objective of this tactic as "replacing" the problem behavior. This paper considers rationales that might underlie this advice, as well as reasons why a general rule to this effect is inappropriate. This review reveals that although there may well be good reasons for considering this tactic, their rationales are often not well articulated and may even be unsound. It is also the case that there are good reasons why this tactic may not always be necessary, thus conflicting with an argument for a general rule.