Reforming mathematics instruction: The role of curriculum materials

The crisis in mathematics education is likely to grow. One of the targets for reform is the math textbook, which largely defines the math curriculum. Several aspects of math textbooks that strongly influence student learning are explained: the organization of lessons, the use of time, the rate of introducing new concepts, the quality of instructional activities, the nature of the examples, and the provision of guided and independent practice. Excerpts from math texts illustrate these factors. Research findings on an alternative to basais, represented by the Direct Instruction math curriculum, illustrate how conceptual understanding and proficiency can be developed for a full spectrum of students.     

Performance of humans in concurrent avoidance/positive-reinforcement schedules

Performance maintained under concurrent schedules consisting of a variable-interval avoidance component and a variable-interval positive-reinforcement component was studied in three human subjects using points exchangeable for money as the reinforcer. The rate of responding in the avoidance component increased, and the rate of responding in the positive-reinforcement component declined, as a function of the frequency of point-losses avoided in the avoidance component. The performance of all three subjects conformed to equations proposed by Herrnstein to describe behavior in concurrent schedules. The logarithms of the ratios of the response rates in the two components, and the logarithms of the ratios of the times spent in the two components, were linearly related to the logarithms of the ratios of the frequency of loss avoidance in the avoidance component to the frequency of reinforcement in the positive-reinforcement component. When a changeover delay of 5.0 sec was imposed, the slopes of the linear functions were close to 1.0 in the case of two subjects, whereas the third subject exhibited significant undermatching. For two subjects the changeover delay was then reduced to 2.0 sec; in both cases the slopes of the linear functions were lower than under the 5.0-sec condition. One subject participated in a third phase, in which no changeover delay was imposed; there was a further reduction in the slopes of the linear functions.     

PARENT REINFORCEMENT FOR CHILD ACHIEVEMENT: THE USE OF A LOTTERY TO MAXIMIZE PARENT TRAINING EFFECTS

This study describes and evaluates a reinforcement program in which parents earned lottery tickets and won prizes for the progress made by their handicapped children during home-based intervention. An ABAB reversal design replicated across three families was used to assess the effects of the lottery on the children's mastery of language skills. Results showed that the reinforcement of the parents for training accomplishments, as indexed by their children's achievements, produced clinically significant increases in the children's progress when compared with the children's progress under the routine supportive practices of the baseline condition. The implications of the findings for parent training programs in general are discussed.     

TRAINING FAMILY THERAPISTS: AN EXPERIMENTAL ANALYSIS

This study implemented and evaluated a training program (a written manual, videotaped models, rehearsal, role plays, and performance feedback) designed to teach five subjects the skills to become effective family therapists. The study examined the therapists' use of three target behaviors: instructing, informing, and praising. The therapists, each paired with a parent and a preschool-aged child (2 1/2–4 1/2 yr old), were trained in the clinic to use, and to teach to the parents, several behavioral skills (e.g., praising, planned ignoring, and time-out) relevant to teaching children compliance to parental instructions. A multiple-baseline design across triads (therapist/parent/child) demonstrated that after the training program was instituted, the therapists increased their rates of instructing, praising, and informing the parents; all parents increased attention to compliance, decreased attention to noncompliance, and increased rates of praise to their children; and all children increased their compliance and decreased their noncompliance.     

Issues in multivariate assessment of a large-scale behavioral program

Several social and research issues directly affected the development and implementation of multivariate assessment in a large community-based applied research program. Examples are drawn from experiences of the Preparation through Responsive Educational Programs Project for disruptive and skill deficient adolescents in suburban, rural, and urban junior high school settings, focusing on the assessment of academic and social skill development and long-term skill maintenance. The social context altered both project treatment and follow-up plans, requiring assessment of potentially unintended effects and decreasing consistency across sites. Future community acceptance of such programs may depend on the investigators' adaptation to diverse community pressures for program conduct and assessment and the measurement of phenomena that are not always directly observable.     

Community applications of instructional technology: teaching writers of instructional packages

A community education program, to develop a variety of performance competencies in large numbers of neighborhood residents, requires a technology for preparing learning units administerable by community members themselves. The effects of a writing manual, designed to teach nonprofessionals to prepare such instructional packages, were analyzed in two experiments. Experiment I employed a multiple-baseline design across three university student trainees. The results showed that appropriate program writing increased by 75% after completion of the manual. The results of Experiment II, with two low-income neighborhood residents serving as trainees, showed that packages produced by trained writers resulted in a greater increase in skill activities than sets of training stimuli produced by untrained writers.     

SOCIAL-SKILLS TRAINING FOR UNASSERTIVE CHILDREN: A MULTIPLE-BASELINE ANALYSIS1

The effects of social-skills training consisting of instructions, feedback, behavior rehearsal, and modelling were examined in a multiple-baseline analysis in four unassertive children. The treatment was effective in that the behaviors selected for modification changed markedly. The effects of treatment generalized from trained to untrained items (interpersonal situations requiring assertive responding) and gains were maintained at the two- and four-week followup probe sessions. In addition, overall assertiveness in all subjects increased from baseline assessment to the conclusion of treatment and into followup.     

TEACHING COIN EQUIVALENCE TO THE MENTALLY RETARDED1

A program was designed to teach coin equivalence to mentally retarded adolescents. Coin equivalence was defined as choosing several different combinations of coins to equal specified target values. A pretest-posttest matched-groups design was employed with an experimental group receiving the monetary training, and a no-training control group. A multiple baseline across coin-counting responses was also incorporated in the experimental group. Training was divided into six stages, each teaching one specific method of combining coins to equal 10 target values from 5¢ through 50¢. A three-component response chain was used, requiring (a) naming, (b) selecting and counting, and (c) depositing target monetary values into a coin machine. Experimental subjects improved significantly in coin equivalence performance and maintained their skill on follow up tests; control subjects did not.     

TWO-TO-ONE versus ONE-TO-ONE STUDENT-TEACHER RATIOS IN THE OPERANT VERBAL TRAINING OF RETARDED CHILDREN1

The operant training of two retarded children simultaneously on a picture-naming task was investigated as an alternative to the more commonly reported one-to-one student-teacher ratio. In Experiment I, two conditions were compared in which the children received primary reinforcement on a fixed-ratio schedule for responding correctly on prompt and probe trials in a standardized picture-naming procedure. During the “Group Condition”, the experimenter alternated from one child to the other after each primary reinforcement, after each incorrect response, after each response omission, and after each 10-sec period in which a child did not “attend” (by making a trial-initiating response) when it was his or her turn to be worked with. During the “Individual Condition”, the experimenter worked with only one child, and presented trials whenever the child made attending responses. Experiment I demonstrated that the Group Condition was more efficient than the Individual Condition in terms of total correct responses and total pictures learned per unit of training time. Incidental learning was also found in that the children learned some of each others' pictures as well as their own, thus indicating a further advantage of the larger student-teacher ratio. In Experiment II, an attempt was made to equate the two conditions, except for the presence of two children in the Group Condition, by ignoring the child in the Individual Condition for brief periods equal to those that occurred in the Group Condition when the experimenter presented training trials to the other child. The results demonstrated that the greater efficiency of the Group Condition was not due to the manner in which training time was allocated to the two members of a group. It also replicated the finding that the children learned some of each others' words in the Group Condition.