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Over half of the high schools in Virginia utilized a block schedule in 1996-97. With an extended block of time, teachers have the opportunity to vary instruction to incorporate a range of strategies to enhance student engagement and increase student achievement. The purpose of this study is to provide a detailed description of algebra instruction in an extended alternate-day block schedule. Using case study methodology, data were gathered from six algebra teachers' classrooms. Data sources included multiple classroom observations, teacher interviews, surveys, and a review of students' final algebra grades. A case record was developed for each teacher and cross-case matrices were used to analyze the degree of teacher satisfaction with the block, teacher readiness to teach algebra in the block, the types of instructional strategies utilized in algebra lessons, the level of student engagement and achievement, and advice to others. Findings indicate that teachers viewed the planning process prior to implementation of the block schedule as inadequate. Teachers have utilized strategies including cooperative learning, student projects, and problem-solving with applications. They advise other algebra teachers confronting a block schedule for the first time to engage in activities prior to implementation, including researching alternative teaching strategies, designing and planning projects for students, finding applications, redesigning homework assignments, and purchasing hands-on materials and software. Teachers are concerned about student learning, especially for ninth graders, students who are math-anxious, or students who are frequently absent. It was concluded that, although the teachers had not actively participated in the decision to change to a block schedule, they have adjusted to the new schedule. Some now enjoy the block and others continue to be dissatisfied. Although the block offers time to incorporate a range of activities, the algebra teachers typically use a familiar three-part model of instruction (including a prompt focus, explanation with modeling, and time for practice and summarization.) Homework remains an essential feature of algebra lessons and teachers routinely allow students to use graphing calculators. Students' grades in algebra have not improved; the percentage of students failing algebra has increased slightly in the alternate-day block schedule / Ed. D.

Keeping students engaged in the learning process is a challenge faced by most teachers. Instituting a bell schedule that requires them to make changes in their traditional instructional delivery may increase that challenge exponentially. The benefit of an extended period, also known as the block schedule, is that it permits the opportunity for teachers to alter their instruction with learning experiences that require more than 55 minutes by using engaging student-centered instruction. One reality of teaching on a block schedule is that many teachers lack the knowledge of effective strategies and rely on instructional devices they employed on a shorter time period. The purpose behind this work is to create a manual that demonstrates engaging student centered strategies and becomes a resource for teachers who are searching for instructional models to utilize in the block schedule. It does this in part by featuring actual hands-on strategies from three instructional models that can be readily used by classroom teachers. With the generative information about the models and activities that is provided in the manual, teachers are encouraged to create their own activities. Finally, the work provides solicited teacher feedback on the utility of the manual. / Ed. D.

The primary purpose of this research was to investigate how science teachers engaged students under the 4 x 4 block schedule and how the teachers' understanding of how they used instructional strategies influenced their lessons. As an inquiry-based approach has been adopted by the National Science Standards, research has suggested that block scheduling provides more time for teachers to incorporate varied teaching strategies such as inquiry-based teaching. This research investigated the questions: What instructional strategies do science teachers use to engage students on the 4 x 4 block schedule? How do science teachers understand their use of instructional strategies? The methodology was qualitative in nature and involved a multiple case study of three high school science teachers at a large rural county high school. Data sources included pre-observation interviews, classroom observations, post-observation interviews, and the collection of documents and artifacts such as lesson plans, student hand-outs, worksheets, laboratory exercises, homework and other document(s) the teacher used to prepare for or implement a lesson. The evidence observed in this study, suggests that the strategies used by these three science teachers remain mostly didactic in nature. Although the teachers reported in the interview phase that they use a wide variety of strategies, what was observed within the 4 x 4 block structure was the use of didactic strategies, not different strategies. Although the teachers were aware of more holistic strategies, such as inquiry-based and cooperative learning, they were not adopted nor adapted within the lesson. The three teachers used strategies that were consistent with their scientific realist views concerning the nature of science. These scientific realist philosophies are antithetical to a social constructivist approach to teaching and learning, which is what the National Research Council suggests science teachers adopt. / Ed. D.

American high schools have been criticized for failing to meet the demands of a rapidly changing society. These demands have resulted in the implementation of various educational reform measures and innovations. One innovative effort in Virginia secondary schools has been the implementation of the 4 X 4 block schedule. In this scheduling arrangement, a student would complete four courses in a semester by attending four ninety-minute classes each day. Change made in any organization is usually accompanied by problems. The purpose of this study was to determine the kinds and numbers of problems which were experienced related to implementing the 4 X 4 block schedule in Virginia secondary schools. This study also described some of the problem management strategies. In addition, the types of resources available and the relationship between the resources and the problem solutions were investigated. The study involved surveying 28 schools which implemented the 4 X 4 block schedule during the 1994-95 school year. The survey instrument was used as an initial screening device to identify two schools for case studies which demonstrated unique or revelatory cases in the implementation of the 4 X 4 block schedule. The case studies were conducted using interviews to gather in-depth information from key members of each school. The interview protocols were developed to correlate with the survey instrument. Data obtained through the interviews were analyzed. The findings indicated schools that implement the 4 X 4 block schedule will encounter varied kinds and numbers of problems unique to each school. The problems may be related to administrative, instructional, or school climate issues. The administrators at each school used their available resources and creativity to manage problems. Those problems not satisfactorily resolved remained under study. In a school where the perception existed that the school system was willing to do anything it could to help, educators were more contented and creative in solving problems. The perception of limited and withheld resources in a school contributed to squelching the persistence in solving problems. This study presented clear implications for practice. / Ed. D.

The realm of manufacturing is replete with instances of uncertainties in job processing times, machine statuses (up or down), demand fluctuations, due dates of jobs and job priorities. These uncertainties stem from the inability to gather accurate information about the various parameters (e.g., processing times, product demand) or to gain complete control over the different manufacturing processes that are involved. Hence, it becomes imperative on the part of a production manager to take into account the impact of uncertainty on the performance of the system on hand. This uncertainty, or variability, is of considerable importance in the scheduling of production tasks. A scheduling problem is primarily to allocate the jobs and determine their start times for processing on a single or multiple machines (resources) for the objective of optimizing a performance measure of interest. If the problem parameters of interest e.g., processing times, due dates, release dates are deterministic, the scheduling problem is relatively easier to solve than for the case when the information is uncertain about these parameters. From a practical point of view, the knowledge of these parameters is, most often than not, uncertain and it becomes necessary to develop a stochastic model of the scheduling system in order to analyze its performance. Investigation of the stochastic scheduling literature reveals that the preponderance of the work reported has dealt with optimizing the expected value of the performance measure. By focusing only on the expected value and ignoring the variance of the measure used, the scheduling problem becomes purely deterministic and the significant ramifications of schedule variability are essentially neglected. In many a practical cases, a scheduler would prefer to have a stable schedule with minimum variance than a schedule that has lower expected value and unknown (and possibly high) variance. Hence, it becomes apparent to define schedule efficiencies in terms of both the expectation and variance of the performance measure used. It could be easily perceived that the primary reasons for neglecting variance are the complications arising out of variance considerations and the difficulty of solving the underlying optimization problem. Moreover, research work to develop closed-form expressions or methodologies to determine the variance of the performance measures is very limited in the literature. However, conceivably, such an evaluation or analysis can only help a scheduler in making appropriate decisions in the face of uncertain environment. Additionally, these expressions and methodologies can be incorporated in various scheduling algorithms to determine efficient schedules in terms of both the expectation and variance. In our research work, we develop such analytic expressions and methodologies to determine the expectation and variance of different performance measures of a schedule. The performance measures considered are both completion time and tardiness based measures. The scheduling environments considered in our analysis involve a single machine, parallel machines, flow shops and job shops. The processing times of the jobs are modeled as independent random variables with known probability density functions. With the schedule given a priori, we develop closed-form expressions or devise methodologies to determine the expectation and variance of the performance measures of interest. We also describe in detail the approaches that we used for the various scheduling environments mentioned earlier. The developed expressions and methodologies were programmed in MATLAB R12 and illustrated with a few sample problems. It is our understanding that knowing the variance of the performance measure in addition to its expected value would aid in determining the appropriate schedule to use in practice. A scheduler would be in a better position to base his/her decisions having known the variability of the schedules and, consequently, can strike a balance between the expected value and variance. / Master of Science