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This study looks at the implementation of the block schedule at one school, SHS, and tries to measure its success. It arrives at the conclusion that at most schools, and certainly in the case of SHS, educational leaders should carefully study the literature on both sides of the block schedule debate, present materials to the staff, wait for a clear consensus, and then attempt implementation.
The block schedule tries to improve student learning through a re-organizing of the seven or six period day into longer blocks of the time. The "Copernican" system, adopted in modified form by SHS, breaks the day into 4 blocks of time that meet on alternate days. All classes except 5th (which meets daily for 50 minutes) last a full 100 minutes.
The block schedule comes as yet another of the dramatic school reforms in the line of succession that includes middle schools, open schools, and modular scheduling. The literature seems to support the notion that, at best, the block results in some modest academic gains and more student interest in school; at worst, it results in some educational losses and wastes time and resources better spent elsewhere. Teacher commitment forms a necessary part of successful implementation.
SHS forms a unit of the DoDDs (Department of Defense Dependent Schools) system. SHS decided to go with the block schedule for the 1997-1998 school year. This followed upon the arrival, a year earlier, of a new principal, a strong block schedule advocate. Despite the principal's best efforts, the decisive vote on implementation resulted in a split that he decided in favor of implementation. The block schedule evaluation committee formed in May of 1997 for the purpose of measuring how the block changed the climate at SHS.
The block schedule evaluation committee, mainly the researcher working alone, gathered the data used in this study, which relies on four different sources of data and a mixed-methods approach. A climate survey, administered before and after to the entire faculty and student body, used Likert-type questions along with an open-ended final question. Coded responses on the open-ended question yielded a second source of data. A comparison of behavior incidents before and after implementation formed another set of data. Finally, the researcher interviewed seven students selected through purposeful sampling techniques. This study does not use standard test scores due to lack of availability and the high transiency rate (25%) at SHS.
The results do not indicate that the school became greatly better or worse as a result of the block. Students like the block better, but their favor stems largely from tangential aspects of the block such as longer passing periods and better flexibility in scheduling homework. A lot of their criticisms, also, seem to involve the same sort of peripheral considerations such as confusion about homework deadlines and desire for a longer lunch.
More importantly, however, the data seems to suggest that some teachers simply don't know or don't care about constructively filling the longer block of time. Without interesting activities, students become bored and do not receive the depth of instruction that justifies the block's adoption. A significant question pertains as to how the 50% who opposed the block teach their classes.
This study ends with a note of caution. Those who want to try to adopt the block should know their faculty. If a substantial proportion will probably remain uncommitted, no matter what the claims advanced for the block, the school should consider waiting until attitudes change and persevere with the Carnegie system. Should a large number of teachers "passively defy," the school will not benefit from the block because students will effectively lose learning time. Gaining the benefits from the block, then, largely relies on teacher commitment, and only sufficient commitment should inform adoption of the block.
i. Abstract Table of Contents List of Charts and Tables I. Introduction A. Problem Statement B. Research Question C. Conceptual Framework D. Researcher's Framework E. Related Literature II. Findings Conclusions A. Disciplinary Data B. Climate Surveys C. Comments on the Climate Surveys D. Interview Data E. The Teacher Factor F. Discussion Appendixes I. Methodology A. Setting B. Context C. Informants D. Research Tools E. Data Gathering 1. Sample of Field Notes 2. Sample of Informed Consent Form 3. Sample of Coding Systems II. Bibliography
Table 1: Supposed Gains from the Switch to Block Schedule Table 2: A Class to Itself Comparison on Disciplinary Data Table 3: Comparing 1996-1997 to 1997 on the Climate Survey Likert Items Table 4: Comparison of 1996-1997 to 1997, Overall Totals Only Chart 1: A Graphic Version of Table 4 Table 5: A General Analysis of the Comments on the Climate Survey Table 6: The Most-Cited Arguments For and Against the Block Table 7: Interview Results for Key Questions Table 8: Screening Spreadsheet to Select Students Interviewed Table 9: Individuals Selected for Interviews With Justifications for Selection
At Samurai High School, the discussion of the block had reached something of a climax by the May 1997 faculty meeting. In fact, a lot of the 1996-1997 school year seemed to revolve around the block. Samurai could boast a host of fans of the block and those seriously opposed.
Mr. Principal, new to Samurai, initially proposed the block as the cornerstone to a veritable laundry list of school "improvements" he introduced to Samurai. In a single year, Mr. Principal, freshly transferred from an assignment elsewhere within the system, implemented the following:
(1) a new tardy policy; (2) a revised discipline policy; (3) a changed and simplified teacher evaluation system; (4) a new and mandated version of cooperative learning; (5) a new program for student sports eligibility; (6) an in-school detention program; (7) a forced retirement of the Japanese support staff.
As works by Lortie (1975) and others suggests, teachers have a fundamental conservatism and resistance to change. Partly, this results from a realization that much so-called educational "reform" proves nothing more than either a new fad or a re-institution of an old program under a new name (Fullan: 1991). At SHS, an older faculty had remained in place many years, and most teachers had outlasted several administrations. In general, this constituted a group innately conservative to whom the changes mandated above seemed a veritable whirlwind.
Of the programs above, relatively few had a direct effect on the teachers, but, in those cases, the teachers did not hesitate to express their disapproval. The in-school suspension room, for example, resulted in the administration forcing teachers to give up a conference period to watch the worst students in the school, not a popular decision. The proposed evaluation policy also drew many less-than-enthusiastic responses. The last move, however, forcing retirement of the Japanese support staff, rankled the most staff members as it hit them emotionally. Several well-liked Japanese employees took their retirement.
The principal, however, made it clear that he considered the block the most important change of them all. Every faculty meeting seemingly offered the administration yet another chance to hand out a scholarly article or give another presentation in favor of the block schedule because, unlike the changes above, the administration wanted a faculty vote, a show of support, before proceeding.
The block schedule, then, came as the beloved program of a new and much-discussed new administrative regime. Despite numerous discussions, it became clear that the faculty vote on the block schedule represented not an abstract expression of belief in a proposed educational innovation but a vote of support for or rejection of the administration in general. When the dramatic vote came, however, neither side could claim victory. While several teachers abstained, the voting faculty split evenly. The administration considered this sufficient to decide in favor of the block.
Both sides of the faculty, while disagreeing about many other issues, did seem to agree on one: the decision on continuing with the block schedule should ultimately depend upon its shown effects on students. The administration could point to a pile of literature that seemed to support the block schedule, yet this did not impress the opposition. After all, a lot of literature had supported many another educational "revolution." Most remembered DoDDs-Pacific's much-heralded move from a six to a seven period day, and almost all disliked it. Older faculty could point to the main school building designed to fit an "open school" concept long since discarded, a physical example of another failed revolution. If anything, the more journal articles in support of the block, the higher the mistrust.
No, for the administration to prove its case, the administration would have to provide something more concrete: It would have to prove that the block schedule had, in fact, improved SHS. The administration, acknowledging the challenge, created the Block Schedule Evaluation Committee. This author, sensing a graduate level paper in the works, volunteered to head that committee.
Both sides could sense that the work of the committee would result in something a bit more exciting than a peer review.
This paper intends to explore how the block schedule affected SHS. Schools occasionally undergo seemingly fundamental changes in organization and outlook, such as block schedules. In the 1970s, some critics proposed "open schools." In the 1980s, many districts experimented with different kinds of organizations to suit those in grades, six to eight, i.e. middle school programs. Block scheduling presents this kind of change, a dramatic change in the way the school functions.
As many writers have shown (Fullan: 1991), these kinds of changes tend to invite a certain cynicism among teachers. Typically, a journal article or two advocates a certain change. Quickly, a horde of "early adopters," administrators of other schools, testify to their success with the given change. Others hasten to join the new educational wave, often making little adjustment to differences in educational setting or cultural context.
Then, the negative reports start to arrive. Long-serving teachers, eventually (Lortie: 1975) come to view these educational revolutions as something one endures, not welcomes. Yet, if pressed, most teachers can point to some successes: the middle school movement, advisement periods, etc.
The block schedule arrived at SHS, as presented by the administration, with this kind of hype and promise.
A block schedule arrangement simply entails taking the traditional six or seven period day and re-arranging the times within. Some schools have each student take 3-4 classes per semester (Bateson: 1990), greatly expanding the times of each to ninety or one hundred. Others, including SHS, adopt the so-called Copernican Plan (the name implies its authors claims to substantiality: Carroll: 1993) that has students only attending four classes per day, but only attending each class on alternate days, much like college students. SHS slightly modified this approach so that students have three long classes that meet every other day and a half-block (5th) which meets daily and allows for two lunch periods. Each block period meets for a full 100 minutes.
The blockís promise lies in its claimed ability to transform teacher-creativity and student learning. Expanding the length of the class period opens up the possibility of extended instruction. Teachers can explores a subject in depth, using several activities in a single block period. Moreover, fewer classes means less hurrying around to go to classes and allows an extended passing period, reducing student and teacher stress. Advocates also claim that it allows teachers to get to know students better. On the other hand, as the literature review explores, detractors claim that little proof supports block advocates' claims and that, at best, one can say that learning remains about the same. So this study set out to determine, within the bounds of feasibility:
How did the block affect Samurai High School?
To a certain extent, this study could not rely on performance data. While a considerable body of evidence questions the validity of such measures as the SAT, ACT, etc., other schools on both sides use these as sources of evidence for or against the block. Unfortunately for SHS, students take these tests later in the year after this initial study ends. Questions also arise about the use of grades and GPAs as criteria: If, as both sides claim, teachers teach less material on the block, should one consider higher grades a sign of improvement? Moreover, DoDDs school endures about a 25% annual turnover rate due to 3-year military rotation patterns. A modified student body, alone, could probably explain any changes in grades or standardized test factors. So, to a certain extent, this study couldn't rely on the same performance criteria used by other schools.
Instead, this study focuses more on the issue of school climate. Partly, this stems from necessity, as previously indicated, but partly from choice. Using specially-written climate surveys allows focusing on exactly the issues SHS identified as important. Moreover, by including a question about whether students went to SHS the previous year, the surveys allow a simple before-and-after comparison.
Moreover, the climate remains a central part of the justification for the block and worthy of study per se. At the many meetings that led to the adoption of the block, the point came up again and again that the block schedule makes for a more relaxed, stressed-free, as well as more productive, environment. The students and teachers, our principal informed us, would like the change, and that would lead to gains in learning. In other words, climatic improvement seems a necessary underlying condition for improved learning under the block. This study, then, aims to find out:
How has adoption of the block schedule affected the school climate?
This study defines "school climate" as "what it's like to be at this school." A number of instruments exist to measure this, including the Kettering Climate Index. SHS, however, chose to create its own instruments for a couple of good reasons. First, this author couldn't find a copy of the Kettering, and the school didn't particularly wish to pay the copyright fees for using it. Second, the school had a fairly specific idea of the sorts of things the block should improve and designed its survey to measure these things.
The previous question contextualizes the work done at SHS. Still, the question needs even more narrowing. The school climate remains a difficult thing to measure. A number of studies, moreover, have shown that students and teachers often make a different evaluation of the same climate. Given the choice, this study focuses on the students. After all, the school exists for their benefit, not that of the teachers.
Second, this study focuses on perceptions. This question, after all, concerns feelings, not something tangible, like test scores. On the other hand, some measures used make attempts to convert these qualitative measures into quantitative data. For these reasons, this study attempts to determine:
How do SHS students think that the block schedule has effected school climate?
The block schedule presents a number of proposed advantages, some of them regarding climate and others regarding the educational process. The chart below summarizes these assumptions of how the block improves the climate and learning. Those items marked with an asterisk form part of the conclusions discussed in this study.
As explained in the sections above, this study doesn't claim to measure student learning directly. Follow-up studies may attempt to address this issue. On the other hand, one can make some logical connections between the educational issues and the climate ones. If classes stimulate a student more, this would presumable allows for more depth. Fewer discipline incidents, further, likely leads to student impressions of a better place and allow for the greater depth of instruction. This study assumes fewer tardies will result from simply having 4/7th as many classes and almost double the time to pass between them. My discussions with the assistant principal and around the campus indicate that, indeed, this has happened, so it doesn't merit further discussion.
The three issues indicated with an asterisk strike at the heart of the block schedule. The block schedule should allow the deeper level of instruction. The greater time allows teachers to try a variety of different instruction activities, games, plays, cooperative learning, etc., without the worrisome bell interrupting. Students, getting to know teachers and less pressured by day-to-day deadlines, come to enjoy school more. Everyone comes to enjoy school more and learn better.
I volunteered to head this committee because of my relative indifference to its conclusions. Hearing both sides of the argument, I didn't really find either conclusive. I actually abstained on the ballot in May. It did seem to me, however, extremely logical to simply measure the results and to work from there. Therefore, I volunteered, keeping an eye on using the research materials to support my own educational goals at Boston University, to study the changes the block brought about.
Personally, I find myself in something of an awkward political position. Mr. Principal's support base relies heavily on the younger members of the faculty who support the block. On the other hand, most older members of the faculty oppose it. At age thirty-seven, I find myself something of anomaly, not really part of either group and a target for recruitment by both. If asked, probably each side would count me as a member of the other. On the other hand, I have a reputation for integrity that makes me a person that neither side tries that hard to recruit. In my public statements to students and other teachers, I have carefully guarded my remarks so that no one regards me as advocate. In other words, both sides on this study perceive me as a fairly honest broker.
In terms of school reform, I come to this study as an informed skeptic. I believe a lot of so-called reforms turn out to be fads. On the other hand, because a school does something one way, doesnít necessarily make it the right way. This study offers a rare chance to really look at what occurs during a so-called "educational revolution."
I also think that a change that well fits one school may poorly fit another, making a focused, qualitative or mixed method the most appropriate. I think each individual school needs a method for judging school reforms, just the sort envisioned by our evaluation committee. I find it somewhat tragic that typically schools do not rely on much in-depth research of the kind performed for this study. Having invested probably $2000 worth of unpaid research into this study, however, I can easily suggest some reasons why they don't.
I should add that upon reading this paper over, I find that my own experiences as a classroom teacher often acted as an un-credited source of input into the process. I heard things said at departmental and grade level meetings and in student remarks that impacted, for example, my choice of questions for the interviews and, even more, my follow-up questions. In other words, while I define myself as a fairly neutral observer, I often knew exactly where to observe and how. I had some fear, then, that the study might result in a series of foregone conclusions, and I found myself gratified to find myself writing conclusions that surprised me and did not conform to my expectations. If I can claim to have "guided the camera," it still often caught some ill-rehearsed scenes.
The two most difficult parts of performing this study proved working with the interviewed students and the administration. I teach most of the interviewed students in my classes and, in interviewing them, I found they often needed my follow-up questions to insure a satisfactory response. I tried hard to avoid the "Clever Hans" effect, especially with the younger students. I think the older students knew me well enough to know that, even if they disagreed with me, I welcomed them to speak their minds.
Another difficult part required my burying my guarded sympathy for the administration. My own experiences with DoDDs administration included many negative experiences. I consider that the system creates a lot of administrators who constitute a danger to teachers in general and me in particular. This administration, on the other hand, strongly supports me. I find it hard to express negative conclusions about an administration apparently "on my side." On the other hand, I understand that, should this change go well, Mr. Principal may well receive a promotion, leaving me with someone worse. Not only that, ironically, a new administration may well revert to a seven-period day. So concluding one way or the other probably doesn't benefit my career.
In general, then, I find myself, though an insider, on neither side of the debate, a good position for an evaluator. While some might question my ability to evaluate a process in which I must participate, few question my impartiality regarding this study.
Block scheduling represents yet another of the educational revolutions praised and condemned over the years. It follows a familiar pattern. A few scholarly articles tout the concept. Early adopting schools then give the change a try. Their anecdotal positive reports serve as "evidence" of success. Other schools, citing the earlier ones, come on board the band-wagon.
Gradually, however, detractors begin to surface pointing out the lack of concrete evidence in favor of the proposed change. Both sides, then, try to gather more evidence. Eventually, the change either becomes a permanent part of most schools (such as the middle schools) or rates final condemnation (such as the "New Math," "Modular Scheduling," and the "Open School"). A typical cycle takes seven or eight years to progress from articles to advocacy to reflection to choice.
Authors who have surveyed the cycle of reform advocate a more cautious, thoughtful approach to genuine school reform. Fullan (1991) and Newman and Wehlage (1995) for example, note that many of the educational "revolutions" of the 19960s and 1970s accounted for little in terms of concrete achievement, particularly in contrast to the more subtle and successful changes proposed in the 1980s. Further, the failure of much-hailed educational innovations feeds into the inherent conservatism of teachers (Lortie: 1975) who tend to view most educational change as bothersome hype fostered upon them by unknowing outsiders. A failed revolution, then, can hurt not just students but inhibit the adoption of future, more worthy, changes.
To a certain extent, the block schedule movement seems to fit the same pattern. It comes supported by its body of scholarly articles, advocacy groups, and "pioneers." It boasts its early adopters and its success stories. New technology, however, meaning the Internet, has, however, changed both the speed and dimensions of the kind of debate that even 3 years ago would've excited only a few educators and a couple of dozen academics. This use of the Internet causes two important changes in the cycle outlined above, and an exploration of this phenomena would certainly merit a doctoral thesis by itself.
First, the pace of the cycle quickens. Schools, downloading materials and suggestions, can adopt the block schedule within a year. They can contact other schools already using it and explore its plusses and minuses. Detractors of the block, in contrast, can just as easily assemble materials powerful enough to weigh a school vote against the block. A single visit, for example, to the Lindsay website (1997) can well-arm any block foe with arguments and evidence.
Second, the internet "democratizes" the process of educational change. Whereas before university professors and educators, i.e. the "professionals," dominated the debate on both sides, now parents, journalists, and even students have a much bigger say. In reality, in the districts that have gone to block scheduling, one can characterize the battle as one between a school administration-and its website and links-and parents and students-and their websites and links with teachers often in both camps. Significantly, parents maintain the two biggest "anti-block scheduling" websites. Having set the stage, then, one can explore the anti-block and pro-block arguments.
An important argument that ought to inform both sides refers back to the work of Lortie (1975). Lortie shows that teachers, by and large, make any revolution in schooling either sink or swim. Accordingly, the most meaningful school changes tend to result from local teacher-derived initiatives supported by sympathetic administrations. Cunningham and Nogle (1996), whose school implemented the block, considered teacher ownership the most important point and set a 70% teacher "yes" vote as a condition before adoption. This point becomes extremely important in a debate such as that concerning block scheduling in which the real changes must occur in what teachers do within their classrooms. Further, research indicates (Hoy and Woolfolk: 1996) that teachers sense of efficacy directly impacts learning. For this reason, much respected educators as Roland Barth (1997) advocate a cautious, pragmatic approach to educational "revolution" with constant re-evaluation and tailoring of program to context.
The work of Fruit (1993) and Oshirto (1973) suggests that DoDDs teachers, in general, tend towards conservatism, a strong argument against any major school change. In other words, any DoDDs school makes a fairly poor choice for experimentation, particularly one like SHS in which 50% of the faculty vote against the proposed change. The question, then, becomes not only what literature supports the block but also to what extent that literature has specifically convinced a given faculty. Keeping this in mind, one can examine the literature-and websites-informing the spread of the block and the spread of opposition.
Both sides agree that block scheduling hardly constitutes a "new" concept. They attempted it, for a while, in Massachusetts (Smith: 1997).To some, this indicates its essential faultiness. If it's such a great schedule, they suggest, why didn't it sweep the nation already? Unfortunately, these earliest adopters didn't document their gains or their losses, and they lacked the Internet to quickly spread their ideas.
The necessary scholarly articles, however, appear in the educational journals. Canady (1993 and 1995), Carroll (1994), Edwards (1993), Buckman (1995), and Willis (1993) all found desirable outcomes expected in this kind of restructuring efforts. Canaday's school went with the block and recorded the better school climate typically lauded by block schedule advocates. O'Neil (1989), while praising the work of Canaday, warns that many pitfalls remain. Caroll's work explains the Copernican plan, the idea of having fewer, longer classes and alternating them on alternate days. Anti-block writers note that several of these authors now make a fair amount of money peddling workshops in implementing the block (Canaday: 1997).
Pro-block scheduling advocates can generally point to concrete results of fewer drop-outs, fewer discipline problems, and a less hectic school atmosphere (National Council of Teachers of Mathematics: 1996). The presentation to the Indiana school boards (Boley and Corn, 1997) fairly accurately summarizes the typically advantages found in block schools:
*Has shown to decrease stress among students *Discipline referrals and absenteeism decreases *Teachers more readily available for consultation and tutoring *Total GPS rises and failure rate decreases *Decreases passing time *Most students like it
If a general body of evidence "proving" the block schedule's benefits does not exist,, individual schools readily support their own "case studies." Garfield-Central High (Boley and Corn 1997), for example, claims that various high schools in its area report better attendance, test scores, college admission, and more credits; fully 74% of the students reported like the schedule better. A more systematic study, conducted by CAREI (1997) of four schools in Minnesota found that, indeed, student attitudes towards school rose and school climate improved. For this study, the researchers interviewed students and found most very supportive of the 4-period schedule. The CAREI closely matched comparable schools in something close to a true experimental design. Wasson and Putnam county schools (Canaday: 1995), in addition, found not only did 70% of students like the new schedule, but more graduated and joined the honor role. Caroll, (1994) studying 7 Copernican plan schools found better behavior, improved attendance, and an improvement in dropout rates. Friendswood High School in Texas (1996) also reported academic gains. The North Carolina education department (1997) also claims that, at worst, block schools do about as well academically.
Anti-block schedule advocates, however, can make a strong case against the block. In general, their argument often follows this form. The block entails an enormous shift in mindset and resources for a school. To justify such a change, the school should produce significant achievement gains, not merely equal or slightly better performance. Otherwise, shifting to the block simply wastes time and energy. They can, likewise, offer a list of usual disadvantages that seems to about equal that of the advantages above (Lindsay: 1997):
1. Problems with short attention spans; 2. Problems in transferring; 3. Specific course problems; 4. Difficulty with absences; 5. Questionable or no academic gains.
Academically, block schedule opponents can point to the fact that most schools made little or no measurable improvement (National Council of Teachers of Mathematics: 1996) on standardized tests. An oft-cited study by the Canadian Ministry of Education (Bateson: 1990), showed students actually performing worse though the Canadians used a non-Copernican block. A number of other schools (Intensive Block Scheduling: 1997) support a similar lack of results.
Anti-block schedule forces also point to the fact that block scheduling comes with exactly the amount of fanfare that surrounded new math (Bentham: 1997). One anti-block advocate in Brevard (Bentham: 1997) asks: "Do you like New Math? Word Recognition? or perhaps Whole Language Instruction?" In other words, they argue that a whole host of educational "experts" favor the block actually argues against, not for, the block. The fundamental flaw of all these educational "innovations" they find in the lack of serious, controlled experimentation with the proposed change.
Anti-block also match their experts against those of the pro-block forces. They cite psychologist Tony Buzan (1997) whose work seems to indicate that more repetition results in more learning. The works of Lofland (1997) suggests, also, that greater memory results from more frequent class periods.
Then, also, block schedule opponents can point to their own "case studies." Spencer (1996a) cites the case of a teacher who admitted to not covering as much material and the teacher who placed one of the answers to a mid-term question, preprinted, in exam books to give students a "fair chance." Spencer (1996b) relies on his observation of a single block period to discredit the ideas behind it. One of the "Articles" against block scheduling (Articles: 1997) points out the fact that many times the pro block schedulers use testimonials as evidence instead of concrete, measurable results.
Anti-block forces also boast a host of experts of a less credential-bearing variety. Alan Kors (quoted in Spencer: 1996b), a University of Pennsylvania history professor, for example, calls block scheduling "one of the most extraordinary frauds I've ever seen," before adding, "and I've seen a lot of them." Significantly, Kors does not oppose the block as a professor of education (he holds a Ph.D. in history), but rather as a local taxpayer. These intelligentsia perceive in block scheduling yet another example of educational "experts" proclaiming the benefits of a system as proven without application of the same rigorous standards employed in other scientific fields. A doctor wouldn't, for example, prescribe a pill to patient that merely results in the patient feeling "happier" without any real improvement in his condition.
In conclusion, then, the block schedule debate has not reached its final round. Schools interested in trying the schedule can find information about and for it, but can probably only expect student attitudes to improve and some modest educational gains. At worst, adopters could experience some drops in academic performance as measured on traditional measures of achievement. In either case, conversion entails a major effort on the part of a faculty, a "paradigm" shift, from thinking in 45 minute to thinking in 90 or 100 minute blocks. Without a significant emotional investment on the part of the faculty in the proposed "block schedule revolution," one can hardly expect any gains whatsoever.
Having determined some of the parameters of the block schedule debate, one can turn to the actual case of Samurai High School.
In order to consider the conclusions, one must first look at several different sources of data. In general the data indicates, at best, a qualified success with some real points of concern. To see this in its full dimensions requires looking, in turn, at each of the four main data sources.
First, consider the disciplinary data. When SHS adopted the block, the schools supposed that the lessened stress, higher student, interest, etc. would yield better behavior. The table below seems to indicate success. The areas highlighted on the second line show improvement.
Some words of caution, however seem in order. No one gathered comparable disciplinary data for November of last year. As a result, the comparison uses figures for the entire year and compares them to that representing only a portion of this year. To make the numbers comparable required multiplying this year's figures by a "fudge" factor of 3.16. This leads to several points for consideration:
(1) A small group of students may cause all infractions. The fudge factor then would result in over-estimating the percentage of total students involved (2 below). In general, the percentage figures probably deserve less trust than that for total incidents.
(2) Incidents may not occur uniformly over the course of the year.
(3) A new administration last year may have led to more student "tests" of will than this year, and this may account for some reduction in the number of incidents.
(4) These figures do not exclude new or departed students. Hence the departure or arrival of one or two students may distort the figures, especially for the smaller upper level classes.
The climate surveys could provide the strongest data supporting or undermining the suppositions of the block schedule advocates and detractors. Unlike the case with the disciplinary data, this author planned in advance for two iterations of the survey. Further, a question asking students if they attended SHS the previous year allowed a straight comparison between the same students before and after the block. The survey appears below showing all classes but only including returning students. As with the disciplinary survey, the bold lettering marks areas of improvement.
The bottom of the table indicates a relatively low response rate. A couple of factors contribute. First, this table necessarily filters out students new to SHS. Second, a number of students simply forgot to check their student status and required omission. As for the 1996-1997 survey, some teachers never administered the surveys or forgot to return them. This leads to some questions of validity about classes such as the 11th grade that under both surveys only reach about a 30% response rate.
As the chart shows, students don't see much of an improvement in the school. Looking at all measures, less than half appear in bold. If some areas show improvement, others seem to get worse.
To look at this in another way, the following simply compares the overall totals:
At most, it presents an inconclusive set of data. While a lot of measures show improvement, the overall improvement seems slight. At most, one can point out that students find themselves less teased (# 3), treated more kindly (#4), enjoying slightly better relations with the faculty (#6), and less stressed (#9). They also seem to have to complete less homework (#14). These factors may explain their rising love for the block schedule (#15).
One, however must contrast this with their feelings of less safety (#1) and their enduring an atmosphere of greater disruption (#10). Also, the school seems to have suffered a decline in school spirit (#8). More significantly, perhaps due to the first two factors mentioned, students consider SHS significantly worse as a learning environment (#11). Strangely, though student measures of several affective measures above rose, SHS students consider SHS a less pleasant place to be (#12).
Overall, then, one can conclude that the surveys show a student body generally more pleased with the atmosphere of the campus, but less pleased with factors relating to their education, such as the behavior of other students and the learning process. In other words SHS seems an easier place to live, but a harder place to learn.
Interestingly, the data about discipline seems to contradict that found in both the disciplinary data above and in interviews below. This leads to a couple of possibilities. Discipline may have improved, but students may not feel it has. Also, the disciplinary problems they cite may start in the classroom and not reach the administration as often. In other words, students may notice off-task behavior.
The surveys above yielded another set of data in the form of comments. Using a coding system (explained below), this produced the data in the table above that indicates, again, students feel better disposed towards the block than its seven period predecessors.
This leads to several interesting areas of thought. First, the general affective comments seem to favor the block schedule. Compared to the 45% who like it, only 23% dislike it. A large percent, however, felt indifferent to the schedule. The favorable comments, however, appeared on a respectable 30% of the surveys. That's a lot, and, while time doesn't permit a comparable analysis of the earlier survey, a lot fewer students had an opinion on the schedule either way. This suggests that students do like the block.
Looking at the particular comments, however, one gets a somewhat more balanced appraisal. A breakdown by areas addressed allows looking at some particular aspects of the block. Of those comments, the negative 55% outnumbers the 45% positive. This, however, takes the shortened lunch complaints as negative.
Unlike the longer class periods, the lunch period doesn't form an integral part of the block. Middle school students, who eat on campus, often feel pressed to eat during the allotted time. High school students, on the other hand, feel pressed to drive somewhere, eat, and return. Subtracting those, the figures for and against about equal.
At first glance, the results from the comments sections seem a bit odd. It seems unreasonable that students would like the block two to one and yet offer slightly more negative than positive comments. In reality, however, many students took the comments section to offer their approval of the block with a comment such as "good" and then to offer a constructive criticism such as "but classes are too long."
Relatively few comments addressed actual academic or even climatic concerns. For example, only 4 surveys talked about stress. This comes from reading a total of over 600 surveys. Such comments do not have statistical significance. For that reason, a second chart shows the most cited complaints and the blocks most lauded features:
This shows several important factors. Consider, first, the negative issues: The issue of most importance to students involves the length of the classes. This comes as no real surprise and constitutes a valid criticism, returned to in the next section, because the longer periods of time form an integral part of the block. One might suppose, also, that bored students learn less. This also ties into the other comments and interviews that suggest that teachers don't know how to fill that long block successfully.
Below this 10% figure, one comes down to two fairly tangential issues, the length of lunch and the issue of confusion. "Confusion" in this case refers to students forgetting for which class they have to do homework, going to wrong place, etc. This comment most often appears on middle school surveys. None of the other issues has much statistical significance: the numbers simply do not justify paying much attention.
The positive issues balance the negative ones. The longer time for homework does constitutes an integral part of the block, but not as important as, say, depth of instruction. The longer passing period, again, constitutes a luxury afforded by fewer classes, but the school could just as easily have a shorter passing period and a shorter day. To consider it a stronger argument for the block seems as weak as arguing the shorter lunch argues against the block. The other numbers, again, don't supply too much advocacy for keeping the block. They do, however, show some proof that students get deeper instruction, better grades, etc. all factors often cited by block advocates.
Finally, one must note that the faculty also filled out surveys. They constitute, altogether about 10% of those surveyed. Even assuming half remained violently opposed to the block, one could suppose this would leave 5% left to express comments lauding the deeper instruction, less stress, etc., particularly considering how often these phrases appeared in SHS's discussions leading to the block. On the other hand, the 50% who voted against the block did not supply a vast number of comments on the other side lamenting the lack of retention, delays between classes, etc..
In sum, then, the comments from the surveys show that SHS students, in general, like the block schedule. They tend to like it, though, for reasons having to do with simplifying their lives not necessarily with better education.
Fourth, this study relied on in-depth interviews of a number of students and faculty. This researcher felt that having a longer time to actually talk to a single person would increase the power of the study and provide a measure of individuality to match the overall picture provided by the more impersonal data above. Whereas the other sources of data dealt with all and a relatively random sampling, the interviews dealt with a few. In order to screen and obtain people who fit the necessary category, this author used a slightly modified version of the initial survey to screen candidates. The author then interviewed those selected using the questions listed in the appendix.
The interviews yielded the following comments summarized in the table below:
These areas require some exploration. First, according to these students, the block seems to have negligible effects on behavior and parent involvement. This seems to reinforce the contradictory data yielded from the survey and discipline data.
Second, in terms of stress and extra-curricular, the effects tend to vary. Some students claim more stress; others claim less due to the block. Some students claim that the ability to decide when to schedule homework makes them more able to participate in outside activities. In contrast, others claim that simply receiving more homework inhibits their participation. The fact that the older, upper classmen report having more time may imply their greater maturity enables them to better schedule their time so as to continue their participation.
Third, the lower classmen seem to report more learning. On the contrary, the upper classmen seem to report the same amount. Yet the older students report to obtaining more depth. This suggests possible problem with the question: How does one distinguish more learning from the same learning in greater depth. It may also imply that, indeed, students do get the promised depth.
Fourth, students seem to appreciate the greater depth of instruction and time to learn, yet they dislike the longer classes. A good follow-up might ask if they would willingly trade the one for the other. Here, in the interview, they seem to support the idea of getting more teacher attention as a plus, a fact not noted on any surveys.
Fifth, students seem to like a number of the more peripheral aspects of the block. They enjoy, for example, the longer passing period and needing to worry about fewer classes. Further, most like the fact that they can more effectively schedule their homework.
Sixth, the strongest criticisms of the block may stem from the more focused comments of the upper classmen. Both F and U thought that some teachers generally didn't adapt to the schedule: they seemed to merely recycle two lessons into one. This also re-occurs in the comments of S that he thought teachers merely filled half a block period with homework time. This could relate to P's comment that teachers didn't seem very caring. U thought that teachers misunderstood the block. All of this, again, returns to a fundamental weakness of block scheduling: If teachers don't buy into the schedule, it fails. The interviews suggest that at least a portion of teachers, particularly those of upper classmen, have not made that commitment.
It's necessary to examine, for a moment, the effect that teacher lack of commitment could have on the effectiveness of the block. The longer passing periods, three ten minutes versus six five minutes, means that, with the block schedule, total instruction time remains about the same as before. As the following analysis shows, teacher lack of commitment can effectively result in a loss of instructional time.
Assume for a moment, as the initial vote and some interviews suggests, that about half the teachers remain unconvinced of the block. They passively resist the schedule, and the analysis above suggests two presumed methods: (a) simply cramming two 50 minute lessons into one period (b) teaching for 50 minutes and leaving the remainder for homework time. Each student day consists of three block periods along with a 50 minute period. A student, then, in a two day rotation would encounter 3 highly committed block proponents and 3 opponents along with two 5th periods not taught as a block. Further, dividing the opponents' classes by the two strategies above yields 1.5 classes of 2 classes crammed into 1 block and another 1.5 of a block lesson following by homework time.
The former strategy would likely have a negligible overall effect on student learning or homework load. By putting two fifty minute periods into one block, the "crammer" simply teaches about as much material as the previous year. Students might register exhaustion, but they would also see the greater variety of instruction noted in the interviews above.
The latter strategy, however, devoting more time in class to homework, however, would result in some different effects. Consider that the average student received 2.49 hours of homework per night during the 1996-1997 school year. That means, in a 2 day cycle, students received about 5 hours of homework. Elective classes and physical education, moreover, typically give little homework. This means that, on average, students report about an hour of homework per academic class. Students would have a fair opportunity to finish that much homework during the second half of a block period. Students finishing early, obviously, might resort to misbehavior and register the boredom indicated above. Significantly, students would receive half as much instruction in each class using this strategy, in other words, a loss of .75 of a block period. This results in a net LOSS per student of 75 minutes of learning time per cycle or 37 minutes per day.
Further, students in classes using that strategy would end up with less homework. To put it another way, the student's loss in learning time equals his gain in free time. The exact same figures apply. The student, then, receives 37 fewer minutes per day of homework.
The figures for homework in the Climate Likert item, do not fully support the assumptions above. The homework per night dropped from 2.49 to 2.17, about a 20 minute drop. Still, this analysis suggests that even a 20 minute drop in homework time probably equals a 20 minute loss of learning time. Naturally, students, except the most perceptive, which includes some of the upper classmen interviewed above, would not consider this as a loss. In fact, less homework would lead to a more positive outlook on the block, but the school should take note.
Presuming, further, that each loss in homework represents an equal loss in homework hours, one can conjure up a rough estimate of teacher resistance to the block. Simply divide the 20 minute loss per day by the total number of hours in academic classes, typically about 220 minutes (i.e., 55 times 4). To do some simple arithmetic 20/220 = 9%. This seems, actually, quite an improvement over the initial vote that indicated as much as 50% might resist the schedule, but this also doesn't include those teachers who merely go along by "cramming."
To make any decision about the block, then, requires weighing whether the gains in terms of student enthusiasm and depth in some classes outweighs the losses in instructional time. Again, obviously, the work here calls out for further research among the faculty.
From the data, then, one cannot conclude any lofty gains from block scheduling nor can one conclude any dramatic failures. Overall, the overall picture emerges as follows.
One, students seem to like the block, but one can somewhat question if their liking stems from educationally sound reasons. They like the longer passing time. They like the greater flexibility of not attending every class every day. On the other hand, the measures only provide the weakest evidence that students get the main benefits proposed for block scheduling: depth of instruction, less stress, and more interesting and varied learning activities. The climate survey, further, doesn't show the kinds of dramatic gains in school climate that one expects from such a revolutionary change in the school day.
Second, student criticisms of the block, however, don't justify necessarily rejecting it per se. The school, for example, could easily extend the lunch period. Moreover, as students, especially middle school students, become more acquainted with the block, their level of confusion should about equal what they would experience should the school revert to the seven period day. Several of the most-cited criticisms in the data above, then, shouldn't merit too much attention or the block's immediate demise.
Third, the most serious criticism of the block refers to the long, boring classes. While the longer classes form an integral part of the block, the boredom does not. Those who advocate for the block, as the literature points out, assume that teachers can provide a variety of lessons, if given the chance, and that 55 minute class periods provide the only impediment. The fact that few students or teachers mention depth of instruction and only some of those interviewed found more classroom activities, suggests that some teachers do not provide this variety or depth.
Fourth, this last conclusion relates to the third. Adopting something as revolutionary as adopting the block schedule makes a presumption that teachers want to make the necessary, admittedly great, effort. SHS proceeded to the block schedule with at least half the faculty not in favor. The administration presumed that the others would eventually "come on board" the bandwagon. The data here suggests that many have not. The numbers involved could range as low as 10% or as high as the original 50%. Further, many may never come on board. While the administration may try to force these teachers to become block schedule converts, the administration can by no means visit every classroom, every period. To this effect, then, the unconverted can effectively "veto" the administration's vote in favor of the block through simply not teaching to it. The comments and reduced homework time argues that a sufficient number of opponents remain to effectively subtract instructional time from the school day.
Fifth, the administration should look at the negligible and questionable gains outlined above and faculty resistance and make a decision about the block if only one to continue further study. The literature suggests that many schools continue with the block simply because students and faculty like it. The data above suggests some at SHS do, indeed, like it, but perhaps not a percentage sufficient enough to continue the experiment. Moreover, initial study indicates SHS will see a measurable, if not astronomical, drop in performance on standardized tests and possibly other traditional academic measures such as GPAs, honor rolls, etc. Certainly, SHS should commit to a continued, broad-based study of the block and its implications before deciding whether to continue with the block or discard it.
Sixth, other schools should take a close look at this study before making their decision. By and large, it may not make much sense to proceed with the block schedule unless a high percentage of the school's faculty want to go along. At SHS, the evidence strongly suggests another year of gestation, discussion, and gathering of converts should've proceeded the decision to adopt. As it is, the evidence suggests at least another year of study before deciding whether, again, the school should persevere or take the great leap backward.
This takes place at SHS, a Department of Defense Dependent School in Japan. SHS functions as a fairly typical Department of Defense School. Students from the local Samurai Air Force Base have no real other option than attending Samurai as the nearest American high school sits several hourís drive away. The area houses several private schools, but, on a military salary, the costs put this out of the reach of the average school parent.
Samurai includes grades 7-12. It does not feature a separate middle school program as plans exist for building a middle school several years into the future, so that the administration doesnít consider investing in a separate program worth the cost.
Samurai reflects the varied nationalities of the air base. About 60% of the students come from minority background and another 60% have European ancestry. If this seems like an example of poor math on the part of this author, it serves to show the percentage of students of mixed racial ancestry.
While the majority of the students come from military backgrounds, about thirty percent come from officer families, i.e. families with, by definition, a college education. Probably another 20% come from enlisted families in which a parent, eventually, obtains a college education. Thus, one might characterize SAB as a middle class neighborhood with one caveat: every student, by definition, has at least one working parent.
Samurai High School sits at a campus considered, by some experts, the most beautiful in the Pacific. It sits about halfway across the base, far from either of the main housing areas. The other nearby buildings, mostly military facilities, offer little attraction to students. In effect, then, the school exists in relative isolation, away from other schools and away from distractions.
This study took place at Samurai High School mentioned above. It took place during the 1996-1997 school year. In order to understand the reasons for this study, one must examine the context of DoDDs schools and the administrator promotion system.
Administrators, especially principals, typically function as politicians, playing one bureaucracy off against another, and seldom advocate the kind of serious structural changes suggested above. Rather, they attempt to minimize parent complaints and keep those above them in the hierarchy as happy as possible. Moreover, they realize that even if their efforts improve instruction, with the 30% transfer rate per school year, they would likely not receive credit anyway.
This results in a dearth of productive experimentation. Students come and go from one DoDDs school to the next, and yet, to students, the schools all seem pretty much the same. While this eases the pain of frequent transitions, it denies the students the opportunity to experience some of the more interesting innovations in school climate and effectively eliminates what school choice advocate Charles Glenn terms the schoolís "distinctive character." For that reason, SHSís attempt to create a major change in environment represents a unique experiment, a conscious attempt to create a school somewhat different from the others.
From the point of view of the school administration, the block schedule represents something of a gamble. On the one hand, Mr. Principal's fellows in Germany already use the block schedule, so SHS's adoption doesn't constitute that much of a leap. Further, his superior and good friend recently received another promotion to a new job. Should he claim success, she can reasonably move and promote him. The block schedule, obviously, represents a means of showing such success. On the other hand, should the schedule fail, he will remain at SHS with a highly disgruntled group of teachers and a highly vocal opposition.
Accordingly, this study took place in a highly charged political atmosphere. Advocates of Mr. Principal and his change to SHS took more than a passing interest in the results of the studies summarized. Those opposed to the block schedule specifically or to Mr. Principal, in general, took an active interest in the results also.
This study, purposely, draws students with different viewpoints. I gave students an initial screening form, which they signed, so that I could identify their general attitudes towards the school.
I solicited volunteers from among my own students and those who happened by. The following chart shows all those interviewed and their answers on Likert-style items of the screening form.
From that grouping, the following individuals earned selection. I tried to draw students that represented the "average" with a small number of extreme answers and the "extremists" with a high number. I also tried to find a mix of upper and lower class students. I made no provisions for gender by ended up, accidentally, interviewing four girls and three boys.
This study uses a mixed methodology. Partly, this results from simple time constraints on the author/researcher. Also, though, it results from a genuine desire to triangulate the data. This relied on three different sources of data and other materials derived from those.
First, it used the SHS school climate survey. One form of that appears below. An opposite form appeared in which each of the negatively worded questions received positive wording and the reverse. Students completed the survey in May of 1997 and again in November, after the block began.
This survey yielded two types of data. First, it created the general one to one comparison cited in the conclusions. The responses from the "free response section" yielded the analysis of comments stated above.
Second, this study used student interviews. A spreadsheet (shown n the informants) section looked at the responses of students to another iteration of the survey above. After this, the researcher purposefully sampled so that he could extract students that represented (a) both extreme case and "average" students (b) junior high and high school. As it happened, the students selected happened to represent both genders about equally, but this occurred as an accident. The students were interviewed using the following set of questions (below). A sample interview appears in the following section.
Finally, this study used two sets of referral notices, one gathered in May and the second in November. The school computer sorted these by student. This researcher further sorted referrals by student and gender to yield the one to one comparison data listed above.
1. Sample of Field Notes
I had to make one last substitution regarding the interviews. I had really wanted to interview subject N. A mere glance at the numbers below shows why: a proliferation of extreme views. Further, I know N, and she's an outspoken student (though seldom outspoken by many) certain to have lots of forceful opinions. Unfortunately, I couldn't get her free from her class on the 14th. Today, when I intended to wrap up the interviews, she was absent.
N 5 8 0 8 2 5 10 10 0 5 0 10 2 4 10 5
This left me with student U: Grade Ext
U 10 4 3 3 4 5 5 5 4 7 5 5 5 2 10 1
When I entered Mr. O's room to try to claim N, a number of students urged me to interview U instead. At first, this seemed a poor substitution. A glance above shows little in common in terms of their views. Moreover, U struck a lot closer to the average views. On the other hand, U was available and, as students said, had a lot of interesting things to say:
Annotated INTERVIEW WITH STUDENT U
Unlike most of the students interviewed, I don't know U. A big student, I suspect he players either j.v. or, more likely, varsity football. He seems a popular student.
Fruit: What is your grade level; are you new to Samurai High School?
U: My grade level is 10, and I've been here for 3 years.
This helps. He's been here about as long as N.
Fruit: Question number one: Is your stress level more, less, or the same as last year?
Fruit: Do you think that stress is related to the block schedule, or do you think it's just being a 10th grader.
U: I think it's related to the block schedule and being an 10th grader. Because of the block schedule, teachers think that since we have 2 days to finish the assignment, they give us a lot more work.
Interestingly, this directly contradicts what the previous interview said, but it does correspond to a lot of comments heard around the school.
Fruit: So you think the work is causing you stress?
This is, of course, exactly the opposite of the supposed effect of the block.
Fruit: Question number two: What do you like the least about block scheduling?
U: The teachers think that since we have 100 minutes to do this, and we don't see each other every day, we see each other every other day, that they need to cram two class lessons into the 100 minutes, instead of taking the 100 minutes to make sure everybody understands what they're trying to teach.
Fruit: So, in your opinion, you think the teachers are misinterpreting the way the block should be done?
Fruit: And you see it as one lesson in depth, instead of two lessons crammed together.
This directly contradicts the idea behind the block. Teachers were supposed to teach each lesson deeper, not cram two lessons together.
Fruit: Okay, question number three: What do you like the most about the block schedule?
U: There are some good points. When they do give us an assignment, they do have the 100 minutes to turn it in, completed. Therefore, we can search over it and go through it completely.
This, again, contradicts the past statement. This doesn't mean, though, that some teachers aren't doing one and some the other.
Fruit: Okay, number four, and this is regarding you: Are you are behaving better, worse, or about the same as last year? Now, this isn't other students; this is yourself.
U: About the same.
He doesn't strike me as a student likely to misbehave though as one likely to speak up forcefully, again, a good match for N.
Fruit: Question number five: Are you learning as much as, less than, or more than last year?
U: About as much.
Fruit: So the block has not really had an effect in that respect.
Fruit: Well, let me define the next question. Learning activities is when you switch from doing one kind of thing during class to doing another. Say lecture for awhile, then people do a small group assignment, and then maybe people work on the computers. Do you think teachers use more, fewer, or the same number of learning activities within a class period than last year?
U: I think they use more.
Again, this might contradict earlier answers. Are teachers cramming two lessons into one period, teaching one over 100 minutes, or both?
Fruit: Question number seven: Are your parents more or less involved with schooling than last year?
U: About the same.
Fruit: That's been kind of a wash too. Question number eight: Has the block schedule effected your extra-curricular activities?
U: Yes, since I've had more homework each night, I've had less time to play sports.
This, again, does not agree with what other students said, but does agree with his earlier comments. Note that in the screening form he claimed to have 2 hours of homework per night; N claimed to have four hours.
Fruit: So it has actually taken away from extra-curricular time. Actually, some of the other students have remarked just the opposite, but not everyone has the same experiences, of course. All right, any other comments you want to add about the block schedule or about the school climate in general. And I don't mean weather here: I mean kind of the atmosphere here.
U: I think the atmosphere is a lot more tense than it was the two years I've been here, but I think the block schedule would just take some getting used to.
Again, this is surprising. Most informal comments have been the opposite.
Fruit: So you think the block schedule has added some tension?
U: Yes, it has... I think it would be a very good program if the teachers learn how to use it.
Fruit: So you see the problem as being the teachers' interpretation-
Fruit: Not necessarily the block per se.
This is interesting. I kind of expected him to condemn the block outright. Instead, he's saying some teachers are simply not doing it right.
Fruit: Okay. Anything else?
Fruit: Thank you very much.
2. Sample of Informed Consent Form
I give my permission for my child to participate in a study conducted in association with Boston University by Daniel Richard Fruit. The study looks at how student perceptions change in response to a major change in the school environment.
The procedures used in this study have been purposely designed so as not to inflict any mental, physical, or emotional harm on my child.
I understand that the results of this survey may appear in print or some other form of publication. I realize that my childís name and all identifying characteristics will be disguised so that his/her anonymity may be preserved.
I waive the right to sue either (a) Boston University (b) the research, Daniel R. Fruit, as a result of my childís participation in this study.
childís signature date parentís signature date
departmental chairmanís signature researcher (Mr. Fruitís) signature date
3. Sample of Coding Systems
This study used two different coding systems both with the survey forms. First, it used the free comment section to come up with a score between one and five on the measure of student preference for the current schedule (i.e., the seven period day in May 1997 and the block in November). The study excluded those who wrote nothing. The following were considered "modal," organizing responses.
MODAL RESPONSES 5= Love the block. 4= The block is better. 3= The block is slightly better. 2= The 7 period schedule is better. 1= The 7 period schedule is lots better. 0= The 7 period schedule is wonderful.
On a more informal basis, this study groups together responses on the extend comment section into more general categories. For example "great" and "good" seem synonymous whereas "all right" seems about the same as "okay" resulting in the groupings in the earlier sections above.
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"Building Block or Stumbling Block? A Look at Block Scheduling in Mathematics Education." (1997) News Bulletin: National Council of Teachers of Mathematics. September 1996.
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