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.     

Child performance on discrimination tasks: Effects of amount of stimulus variation

Two independently conducted studies investigated stimulus variation effects on children's discrimination learning. The stimuli in the first study were generated by a conjunctive rule and were presented in pairs. Mean trials to criterion was significantly lower for the single-feature change treatment (17.4) than for the multiple-feature change treatment (29.9). Single-feature change-treatment transfer scores were significantly higher only for stimuli that differed in terms of one of the features. The second study not only replicated the initial finding concerning the single-feature change treatment but also found that students made more errors in reaching criterion when stimuli were generated by an exclusive disjunctive rule and were presented singly. For all tasks, the single-feature change treatment with stimuli presented in pairs was accompanied by fewer errors to criterion than the other treatments.     

Effects of two teacher-presentation rates on off-task behavior, answering correctly, and participation

Off-task behavior, correct answering, and participation during beginning reading instruction were recorded for two low-achieving first-grade children during two different rates of teacher presentation. A slow-rate presentation (A) was compared with a fast-rate presentation (B) in an ABABAB design. In slow-rate presentation, there was a delay between the children's response and introduction of the next task. In fast-rate presentation, there was no delay. A new teacher taught during the final AB phases, which allowed for a brief replication. Both teachers were reminded on a fixed-interval 90-sec schedule throughout all phases of the experiment to praise the subjects, thus preventing a confounding of social praise and rate of teacher presentation. Fast-rate presentation was accompanied by a lower per cent occurrence of off-task behavior for both Subjects 1 and 2. For Subject 1, correct answering and participation were more frequent during all three fast-rate phases. For Subject 2, correct answering and participation were more frequent during the fast-rate phases after the first reversal.     

CONTROL OF ARITHMETIC ERRORS USING INFORMATIONAL FEEDBACK AND GRAPHING1

The effect of informational feedback and graphing on reducing the number of arithmetic worksheet errors was investigated. The present study replicated and extended earlier findings with other populations (Journal of Applied Behavior Analysis, 1974, 7 , 547–555; 1970, 3 , 1–4; 1970, 3 , 235–240) to a first-grade classroom. Ten first-grade pupils (four males and six females) served in an ABAB design. During the feedback-only phase, subjects were provided informational feedback, in the form of a written number, on the number of errors made on individual arithmetic worksheets. The feedback-only phase lasted seven days and was followed by the feedback-plus-graphing phase, during which subjects graphed the number (of errors written at the top of the individual worksheet) daily on individual graphs on their desks. The feedback-plus-graphing phase lasted 10 days and was followed by a reversal to feedback only for 10 days. The final phase was a replication of the feedback-plus-graphing phase. All subjects showed a change in number of worksheet errors, in the predicted direction, during the feedback-plus-graphing phases. An overall mean difference of ?2.66 was found to be statistically significant (P < 0.01), using a Wilcoxson Matched-Pairs Sign Test. The results were interpreted as being empirical support for earlier findings in other populations. In addition, the present findings represented a successful extension of feedback and graphing interventions to the management of academic behaviors in a first-grade classroom.     

Direct instruction: What it is and what it is becoming

This essay describes the principles of Direct Instruction design and delivery used to establish clear, unambiguous communication and maximize student responding. Direct Instruction research findings are summarized: achievement of low-income students in Follow Through, longitudinal results, and the effectiveness of Direct Instruction for students with handicaps. Finally, new directions for Direct Instruction, technological applications and instruction of higher-order skills, are discussed.     

Trustworthiness,useability, and accessibility of educational research

Conclusion My contention is that research is under-utilized because of the shortcomings described in this article and because practitioners do not routinely look to research when they make decisions (Carnine, 1995). Researchers must take responsibility not only for systematically remedying these shortcomings but also for trying to influence practitioners to make research findings an integral part of their decision-making process (Carnine, in press, a, b, c, d, e).     

The integration of research and practice in the prevention of youth problem behaviors

The prevention of youth problem behaviors is increasingly guided by science. Sound epidemiological research is coming to guide preventive efforts. Valid methods of monitoring the incidence and prevalence of youth problems increasingly shape preventive practice. The identification of empirically supported prevention interventions is becoming more sophisticated, and numerous scientific organizations have begun to engage in dissemination activities. These trends will be accelerated by increased media advocacy for the use of scientific methods and findings, the development of a registry of preventive trials, achievement of consensus about the standards for identifying disseminable interventions, and increased research on the factors that influence the effective implementation of science-based practices.