Transformations of mathematical and stimulus functions

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel formula-to-graph tests and 10 novel graph-to-formula tests. Seven of the 8 participants showed substantial improvement in identifying formula-to-graph relations; however, in the test of novel graph-to-formula relations, participants tended to select equations in their factored form. Next, we manipulated contextual cues in the form of rules regarding mathematical preferences. First, we informed participants that standard forms of equations were preferred over factored forms. In a subsequent test of 10 additional novel graph-to-formula relations, participants shifted their selections to favor equations in their standard form. This preference reversed during 10 more tests when financial reward was made contingent on correct identification of formulas in factored form. Formula preferences and transformation of novel mathematical and stimulus functions are discussed.     

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

The Psychological Record - Fifteen participants unfamiliar with mathematical operations relative to reflections and vertical and horizontal shifts were exposed to an introductory lecture regarding...     

USE OF CHAINING TO INCREASE COMPLEXITY OF ECHOICS IN CHILDREN WITH AUTISM

Echoics are a critical target of language intervention for children with autism, because a well‐established echoic repertoire on the part of the child allows the clinician to use vocal modeling as a flexible, low‐effort prompting procedure during teaching. In this study, we implemented a chaining procedure to increase the complexity of echoics in 2 children with autism and 1 child with developmental delay. The procedure was effective for all 3 participants, and gains were maintained after treatment was withdrawn in most cases.     

CONSTRUCTING AND DERIVING RECIPROCAL TRIGONOMETRIC RELATIONS: A FUNCTIONAL ANALYTIC APPROACH

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula‐to‐graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula‐to‐graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires.     

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.     

OBSERVATIONAL LEARNING AND THE EMERGENCE OF SYMMETRY RELATIONS IN TEACHING SPANISH VOCABULARY WORDS TO TYPICALLY DEVELOPING CHILDREN

One 9‐year‐old child was taught conditional discriminations between dictated names in Spanish and their corresponding pictures across three stimulus sets while her 10‐year‐old brother observed. Posttests revealed the emergence of symmetry relations in the form of oral naming skills by both children.     

ON THE REINFORCING EFFECTS OF THE CONTENT OF VERBAL ATTENTION

During a functional analysis, a boy with autism and oppositional defiant disorder displayed destructive behavior that was maintained by attention in the form of verbal reprimands (e.g., “Don't hit me”). In a second analysis, contingent verbal reprimands produced higher rates of the behavior than contingent statements that were unrelated to the target response (e.g., “It is sunny today”), suggesting that some forms of attention were more reinforcing than others. A treatment based on these analyses reduced the behavior to near-zero levels.     

Using the stimulus equivalence paradigm to teach course material in an undergraduate rehabilitation course

In 2 experiments, we examined whether the stimulus equivalence instructional paradigm could be used to teach relations among names, definitions, causes, and common treatments for disabilities using a selection-based intraverbal training format. Participants were pre- and posttested on vocal intraverbal relations and were trained using multiple-choice worksheets in which selection-based intraverbal relations were taught and feedback was delivered until mastery. Most participants in Experiment 1 showed the emergence of vocal intraverbal relations, but responding did not generalize to final written intraverbal tests. Participants in Experiment 2 showed the emergence of not only vocal intraverbal relations but also written intraverbal relations on final tests. Results suggest that the stimulus equivalence paradigm can be effectively implemented using a selection-based intraverbal training format, the protocol may be an effective means of emphasizing important concepts in a college course, and emergent skills may generalize to novel response topographies.     

ACQUISITION OF MANDS AND TACTS WITH CONCURRENT ECHOIC TRAINING

Previous studies have identified a number of effective teaching procedures to increase verbal behavior in individuals with developmental disabilities. However, few studies have evaluated modifications of treatment procedures when children fail to acquire communication skills. In the present investigation, a 4‐year‐old boy with autism failed to acquire unprompted mands and tacts during mand‐only and tact‐only training. Results indicated that combining echoic training with mand or tact training increased unprompted manding and tacting.     

EFFECTS OF SELF-MANAGEMENT TRAINING AND REINFORCEMENT ON THE TRANSFER OF IMPROVED CONDUCT IN THE ABSENCE OF SUPERVISION

The instruction, maintenance, and transfer of training of social skills of 3 seriously emotionally disturbed adolescents were accomplished by a self-management training and reinforcement package. During baseline sessions these students, who were covertly filmed in their classroom, averaged over 90% off-task or socially inappropriate behavior while their teacher was out of the room. They showed similar behaviors when walking between classes, unattended by their teacher. Treatment was introduced in the classroom and consisted of social skills and self-management training and reinforcement. Treatment procedures included instruction, modeling, and role playing of social skills, as well as self-assessment, self-recording, and self-reinforcement for correct approximations of these skills. After 5 weeks of training, all subjects demonstrated substantial improvements in the classroom during the teacher's absence and when distracted by other students; however, transfer of social skills did not occur to the between-class setting until students were given explicit instruction to initiate self-managing procedures in this setting.