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A Year in the Life of an Elementary School: One School's Experiences in Meeting New Mathematics Standards


by Karen Dorgan - 2004

This qualitative research project studied the efforts of a small public elementary school over the course of 1 academic year to meet higher standards imposed by the state. The state's department of education defined school success in terms of the percentage of students passing a set of multiple-choice, standardized tests in four core areas of the curriculum. The study looked particularly at strategies the school applied in an attempt to raise students' mathematics test scores. Interviews, classroom observations, and document analysis were used to analyze the effects of new standards and the accompanying testing program on teachers. The project showed the effects of the state testing program on classroom practices, both positive and negative, and it raised questions for further study.

In our state, it is difficult to discuss education these days without reference to the SOLs. Educators, parents, students, legislators, and citizens have all become aware of the state’s Standards of Learning, adopted in 1995 (Board of Education, Commonwealth of Virginia, 1995). This state curriculum framework, coupled with a rigorous plan for assessing student progress, is frequently the subject of newspaper articles, PTA panels, and conversation in supermarket aisles.


While the state has long provided a list of grade-by-grade goals by which school divisions are to develop their local curricula, the addition of standardized testing to the mix has raised the level of concern and seriousness about this latest reform movement. The linking of these test results to graduation requirements and state accreditation, placing the state testing program in the category referred to as high stakes (American Educational Research Association, 2001), has increased pressure on students to perform and on teachers to align their instruction with the state’s expectations.


Our state is not alone. Education Week reported in January 1999 the results of a 50-state survey of state policies on accountability. They found that ‘‘By 2000 every state but Iowa will have at least one form of a statewide test’’ (Olson, 1999a). At that time, 40 states had standards in all core subjects; nearly all states required tests in English and mathematics, and most also tested students in science, writing, and social studies. States varied in their approaches to accountability: Education Week cited Texas as an example of a state with a hard-line approach, while Connecticut was said to take a ‘‘more low-key approach’’ (Olson 1999b).


Virginia, the state in which this research was conducted, was placed in the hard-line category, both in constructing its state standards and in designing its assessment plan. The impact of the state’s approach to accountability on teaching and learning is the primary focus of this research.




IMPETUS FOR THE RESEARCH


When the state department of education released the Standards of Learning, school divisions received it without much fanfare. When the state’s newspapers published results of the first administration of the associated SOL tests in spring 1998, however, the reality of the situation hit home for many teachers, administrators, students, and parents. The state had significantly raised the bar for student academic achievement, and students would be held accountable for learning the new standards. While many school divisions began implementing curriculum changes during the 1998–1999 school year, the results of the first tests emphasized the distance most divisions needed to go if they were to meet the state’s expectations.


Virginia’s tests are criterion referenced and multiple choice (with the exception of the writing sample required as part of the English exams at Grades 5, 8, and high school end-of-course; Virginia Department of Education, 2001a). The tests are untimed but are considered standardized in that administrative procedures are uniform across the state. In 2007, schools at which fewer than 70% of the students pass the English, history, science, and mathematics tests risk losing their state accreditation. In addition, beginning with the high school graduating class of 2004, students are required to pass six SOL end-of-course tests to earn a diploma. Thus, for high school students, the SOL tests are appropriately referred to as high-stakes tests. At the elementary level, poor performance by an individual may result in retention or assignment to summer school, while poor performance at the building level may result in loss of accreditation (which would jeopardize the position of the building-level administrator).


The focus of publicity about the Standards of Learning─ both as a curriculum framework and as an accountability system─ is on results. And while this focus on results is understandable (see, e.g., Schmoker, 1999, 2001), it is also important to consider the means by which the ends are achieved. The questions emerged: What was the effect of a political decision─ to demand public school accountability─ on pedagogical decision making? How might the demands of a new testing program affect how teacher teach and how children are expected to learn?




METHOD


The study is descriptive, qualitative research on teachers as they attempted to meet new standards. Specifically it is a case study of an elementary school faculty, done in an attempt to understand how, and to what extent, their decisions about instruction were influenced by the Standards of Learning and the state tests. The study sought data concerning the manner in which teachers implemented daily lessons to help students meet higher standards as well as the means by which they prepared students to take part in the required testing program. Analysis of data revealed factors in the teaching environment that appeared to influence teachers’ decision making and strategies by which teachers, as a faculty, focused their efforts.


Data collection included three sources: interviews, observations, and document analysis. Participation in the study was on a voluntary basis. While in an ideal situation, all teachers in the grade levels of interest would choose to participate, in reality a smaller group of teachers was willing to take an active role in the study. The decision to make participation on a voluntary basis may have led to some skewing of data, a disadvantage in research design, but one which was offset by the advantage of working with teachers who had an interest in the research question. To collect data that is honest and rich necessitates a level of trust between teacher and researcher that requires time and patience, as well as self-selection for participation.


In keeping with basic tenets of naturalistic research, the researcher entered the setting to be studied with as few predisposed notions as possible, intending to listen to and observe teachers in their own environment. Interviews elicited teachers’ views on the curriculum they were to teach. Teachers discussed aspects of the curriculum that were comfortable for them and those that were less familiar. They talked about instructional materials they chose to use, allocation of instructional time, and teaching strategies. They commented on textbooks, professional development, and prior experiences in teaching.


The first interviews were conducted early in the 1999–2000 school year and follow-up interviews, discussions, and observations took place throughout the year, for a total of 25 visits to the school between July 1999 and June 2000. These were scheduled at various times of the day and included before-school and after-school meetings. Interviews were audiotaped, with full transcriptions done. In a few cases where audiotaping was not possible, the researcher made notes on the discussions during and immediately after the sessions.


In addition, the researcher attended a variety of meetings. These included curriculum meetings over the summer, opening faculty meetings, professional development sessions, a PTA meeting aimed at educating parents about the SOL tests, and grade-level planning meetings.


Documents examined included curriculum and pacing guides, textbooks, samples of instructional materials such as test-preparation sheets, and grade-level tests designed by the teachers.


All transcripts of interviews, notes from classroom visits and meetings, and documents were examined and analyzed. Coding of data revealed emerging themes, which served for categorization of data. Two participants reviewed an early draft of the report of results and provided feedback and suggested changes.


Over the course of the year, data related to language arts, mathematics, science, and social studies were gathered. The focus of this article is primarily on the description and analysis of data regarding the school’s mathematics program. This curriculum area was particularly interesting for a number of reasons. The content outlined in the Mathematics Standards of Learning is quite different from that taught in the past. (See Appendix A.) The reporting categories for the test include such traditional content as ‘‘Number and Number Sense’’ and ‘‘Computation and Estimation,’’ but they also include newer content such as ‘‘Measurement and Geometry,’’ ‘‘Probability and Statistics,’’ and ‘‘Patterns, Functions, and Algebra.’’ On the Grade 5 blueprint, for example, 30 out of 50 test items are in these last three categories. Instruction in these areas may require teachers to familiarize themselves not only with new terminology, algorithms, and concepts in these categories but also with instructional methods and materials not previously used. Thus the potential impact of higher standards on this subject might be greater than in the other three tested curriculum areas.


The categories in the Virginia Standards of Learning for Mathematics, as well as the language of those standards’ introductions, reflect the impact of the National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards (Commission on the Standards for School Mathematics of the National Council of Teachers of Mathematics, 1989). Indeed, the introduction to each grade level’s mathematics standards uses language closely related to that of the NCTM’s document. (See Appendix A for an example.) Of interest then was the question as to whether the recommendations of the NCTM were reflected, or indeed could be reflected, in an instructional program supported by a testing program such as the Virginia SOL tests. Such tests, being touted as the sole determinant of whether a child had mastered the curriculum, might seem to contradict the spirit of the evaluation standards described by the NCTM.


This study began with the premise that teaching is an enormously complex task. It looked at the changes that took place as a result of the Mathematics Standards of Learning and the SOL test program. It acknowledged the crucial role that teachers play in all educational reforms, and it began with an assumption that more rigorous curriculum demands and the accompanying accountability measures that were put into place would affect teachers’ work lives. While not involving a large sample of Virginia’s teachers, this case study might help us better understand how this enormous policy change played out in the day-to-day lives of teachers and students in our classrooms.




THE RESEARCH SITE


The selection of a school division in which to conduct research was a deliberate one. While school divisions serving wealthier, middle- to upper middle-class populations might find the challenges of the new tests small, it was assumed that more typically smaller school divisions with diverse student populations would find the challenge quite daunting. It was in such a setting that one would expect to hear teachers’ voices of frustration, determination, or triumph most clearly.


The school in the study is part of a small school division in a county with a population of approximately 13,000 (U.S. Census Bureau, 2000). Four schools serve the county’s population: a high school with approximately 700 students in Grades 9 through 12, a middle school with approximately 550 students in Grades 6 through 8, an elementary school with approximately 550 students in Grades 3 through 5, and a primary school with approximately 500 students in Grades K through 2. This research was conducted in the elementary school. About 15% of the students at the school received free or reduced lunch, and about 17% were non-White.


The staff of the school was a blend of experienced and new teachers, with a turnover rate slightly higher than neighboring school divisions, due perhaps to the county’s lower salary scale as well as the commuting distance for those teachers residing in the nearby city. During the year of the study, approximately 25% of the faculty was new to the school. Turnover during the summer following the study was somewhat higher, making follow-up interviews a challenge for the researcher. Some of the most active participants in the study left to teach in other public schools or in private schools, some left for maternity leave, and some left the teaching profession altogether.


Being a small school division, opportunities for professional development within the county were limited. However, funds were available for teachers who expressed an interest in attending conferences or workshops.


Because the school was the only elementary school in the division and because the central office staff was small, tasks related to curriculum revision, staff development, and long-range planning were done at the building level. Curriculum revision, as reported in this study, was done within parameters set by the state Department of Education.



RESULTS: HOW TEACHING AND LEARNING WERE AFFECTED BY STATE-REQUIRED STANDARDIZED TESTING



CURRICULUM CHANGES


An obvious first step in improving test scores is to determine that what is being taught matches what is being tested. Accordingly, the principal of this school formed a curriculum committee to align the school’s curriculum with the content of the Standards of Learning. As noted previously, the small size of the school division and that this school was the only one in the division serving Grades 3 through 5 resulted in this curriculum work being done by those who were closest to its implementation: the teachers. During the summer prior to the study, this group of teachers, one or two from each grade level, worked to write new curriculum guides for reading, language arts, and mathematics. Working from the previous curriculum guide, a large document in a thick three-ring binder, the teachers revised the scope and sequence charts to ensure that the content of the mathematics standards would be taught in its entirety prior to the tests in May. They removed content that was previously taught at those grade levels but was not to be tested. They worked closely with the textbook provided, cross-referencing SOL objectives with textbook pages and reviewing the publisher’s testing materials. They also updated lists of other instructional materials to support instruction.


Thus, when teachers returned to school in August, the principal provided each grade-level team with new curriculum guides and asked them to review them. At grade-level planning meetings, curriculum committee members who were part of each grade-level team explained the guide’s features and organization and noted changes from the previous guide. They asked others at their grade level to monitor use of the new guides in order to provide feedback for further revisions planned for the following summer.


Teachers who had worked on the curriculum writing team were quite knowledgeable about the content of the guides, having spent many hours developing them, but those who received the guides for the first time in August found it difficult to get a broad overview in the short time before students arrived. As the year progressed, there was a tendency for them to take a short view for instructional planning. Content to be tested was divided up across the six grading periods, and teachers seemed to focus on the content of each grading period exclusively, with little long-range planning. When questioned about how a weakness evidenced by students’ daily work might affect the next unit of study, a teacher commented that she hadn’t looked ahead at that unit yet.


The format of the pacing guide that was part of the curriculum guide supported such an approach, in that it specified exactly how much content was to be taught in each 6-week period. Having such a pacing guide proved helpful to some teachers, who appreciated the guidelines, stating, ‘‘The pacing guide was helpful in keeping me in line with other classes’’ and ‘‘It allowed a whole grade level to teach the same skills at the same time.’’ Others, however, commented on the stress induced by such a pacing guide. One said, ‘‘This school set up its own pacing guide and we (as new teachers) followed what the group did. However, because there was a need to keep up with the rest of the team, I was concerned at times we moved too quickly and the students were a little lost.’’ Another stated, ‘‘The pacing guide caused some stress to keep up. Those of us teaching slower kids need more time for certain concepts.’’ A third teacher seemed to sum it up with ‘‘I felt too rushed to get everything taught in five 6 weeks (periods).’’


In summary, one effect of the new tests was the standardization of the curriculum, including a standard amount of time spent on each topic and a standard sequence in which teachers introduced new content. In general, those new to teaching found such structure helpful, while some of the more experienced teachers expressed frustration at having to abandon previously constructed integrated units or to change the sequence of skills and concepts from that which had worked for them in the past.



SELECTION AND USE OF INSTRUCTIONAL RESOURCES


As suggested previously, one instructional resource seemed to have great potential for having an impact, either positive or negative, on student learning, and that resource was time. A major initiative at this school was to increase the hours per week devoted to mathematics instruction, an area on which previous test scores were relatively low. The principal asked that teachers spend 90 minutes per day on mathematics, a block comparable to time spent on reading/language arts. Not all teachers met this request with a solid block of time: One described her plan to incorporate 15 minutes of math problem solving into her early morning routine, while another described ‘‘30 minutes of review, 30 minutes on a new skill, and 30 minutes on problem solving.’’ Thus, one effect of the new demands was that teachers adjusted the way in which they allocated a limited number of minutes of class time per day to focus on those areas of the curriculum at which improved test results were especially emphasized.


Another major change came with the procurement and training in the use of new mathematics textbooks. In Virginia the state’s Board of Education has the authority to adopt textbooks for use in public schools (Virginia Administrative Code 8VAC-20-230-10). It provides the school divisions with an approved list of textbooks from which those at the division level can select. In recent years, such lists include a profile as to each textbook’s ‘‘degree of correlation with the SOL’s.’’ School divisions are given a period of 5 to 7 months to examine and choose materials, during which period teachers are involved in viewing, evaluating, and selecting textbooks.


One factor, then, taken into consideration in selecting these books was the degree to which they matched the state’s curriculum and the content to be tested at the end of the school year. On the second day of professional development in August, a representative from the publishing company whose textbooks had been adopted conducted a session to familiarize teachers with the materials. The arrival of fresh new textbooks is a time of excitement for most teachers, and these teachers appeared impressed with the many ancillary pieces that accompanied the student textbook, as evidenced by their lively chatter and exclamations when seeing particular items in their teacher kits. The representative highlighted that the kits included a student workbook designed to match the SOL tests in both content and test format, for regular practice prior to the ‘‘real test’’ in May.


Throughout the year, conversations with teachers revealed aspects of the new textbooks that they liked as well as parts that did not fulfill their hopes. Some of their concerns were related to the sequence in which particular skills were introduced or to the publisher’s decision to cluster some concepts and skills together in one lesson. Positive comments outweighed negative ones, however. One teacher described the new series as ‘‘well put together . . . you can teach from it even if you’re not a strong math person.’’ Another commented, ‘‘I think it’s better in many ways; I think that it’s higher level.’’ However, another added, ‘‘A lot of times in our old book, there were more manipulative-type activities to introduce (concepts), and with this book there aren’t as many. They don’t seem to give it the same amount of time and yet they expect a higher level of thought process.’’


This last comment suggested that another area affected was the choice of instructional materials. Like many elementary schools, this school had procured a supply of various manipulatives to represent mathematics concepts concretely. These were available to each grade level team, to be checked out by individual teachers as they needed them. One unanticipated problem created by the strict pacing guide was that all teachers at a given grade level needed the materials at approximately the same time. Some teachers, especially teachers new to the school, found this an obstacle to their use. Others, however, did not experience the problem; one (a ‘‘veteran’’ in this school) stated, ‘‘This school is real good about manipulatives anyway. I mean all you have to say is ‘‘I need pattern blocks’’ and the pattern blocks appear.’’


However, having materials available did not seem to be as great an obstacle to their use as that other resource, time. Repeatedly, teachers commented that while they would like to use more hands-on approaches to instruction, the pressure to keep moving forward, to cover the curriculum did not allow this. One teacher stated, ‘‘I haven’t used them (manipulatives) as much as I’d like . . . I don’t know that I’m going to have the time.’’ Another, after describing how beneficial manipulatives could be, stated with a shrug that she uses them less than in the past ‘‘because it takes time to get all the manipulatives out to give to 25 children and to put them in groups, to get them all focused back into the lesson.’’ A third teacher hesitated to admit that she took the time to use manipulatives, looking a bit sheepish and finally saying, ‘‘I use them anyway. And that’s slowing me down.’’ After a pause, she continued, ‘‘It takes longer, but I feel like they’re developing a better base.’’


As previously implied, the adoption of the new mathematics textbook appeared to be another reason for less use of manipulatives. For example, in identifying a section of the new textbook with which her students were having difficulty, a teacher described her students’ frustration in trying to understand place value. Having used the textbook’s recommended approach to this unit, she described the problem as follows:


I think (the problem is) the fact that they’re not having the opportunity to develop some strong concept of what a decimal is, with some hands-on manipulation of ‘‘how can I show decimals?’’


The same teacher, in discussing weak areas with which her students entered from a lower grade suggested that there was ‘‘possibly not enough hands-on at lower grades.’’


In general, teachers at the school seemed quite aware of the trend in mathematics education to use concrete representations for abstract mathematical concepts, though they had different levels of interest and experience in using them. A primary concern they expressed concerning the SOLs was a perceived need to change instruction to a more direct-instruction, textbook-centered approach. As suggested previously, their classroom practices appeared to be altered due to pressures to move quickly, pressure coming from a grade-level pacing guide to which teachers adhered. In addition, one result of the choice of textbooks seemed to be a shift toward practices that provided more teacher-directed instruction with a slant toward coverage of tested content. Some teachers who described the types of manipulatives they had used in past years seemed to be discouraged from previous practices that may have been more developmentally appropriate, citing the need to keep moving forward quickly to cover the curriculum. Despite language in the written standards, such as 3.7 (‘‘The student will read and write decimals expressed as tenths and hundredths, using concrete materials’’), teachers taught concepts in the form that they would be encountered on the SOL tests: as paper-and-pencil, forced-choice exercises.



RELATIONSHIPS WITH PARENTS


As citizens of the Commonwealth, teachers at the school were well aware of the origin of the Standards of Learning as well as the stated purposes. One commented that the SOLs ‘‘set a consistent standard for all students,’’ while another agreed that SOLs ‘‘bring focus to the school, the teacher, and the student.’’ Ultimately, as one teacher put it, ‘‘They provide parents with feedback’’ as to the success of the school and the student.


The administrators took on the task of educating parents about the Standards of Learning as well as about the school’s results and plans for improvement. They recruited several teachers to speak at a PTA meeting in the fall, and third-grade teachers planned to include relevant information in their spring orientation for new students and their parents. The school provided parents with copies of each grade level’s SOLs and notified them in writing about the dates of the testing period. The school counselor commented on appointments she had had with parents who were concerned about the likelihood of their children passing the SOL tests. However, others in the school were less convinced that parents really were demanding this type of accountability. When teachers tried to provide additional instruction after school in preparation for upcoming SOL tests, a teacher noted parents’ reluctance to send their children for such help: ‘‘He (the Governor of Virginia, in his State of the Commonwealth address) is saying that parents want these higher standards, but I’m not hearing that from my parents. They’re saying, ‘I want my kid in basketball (after school).’’’Another teacher, asked about parents’ response to a letter sent home about the upcoming SOL tests, responded with a blank look and a long pause: ‘‘ I don’t know how much they even care.’’


One experienced teacher who has lived through other state initiatives seemed skeptical about whether such tests should be used to measure quality of teaching and learning. ‘‘Kids in my class have parents who are on top of things. Not that others aren’t. But they have a strong desire for their children. They know how important education is, and therefore they hold them accountable. They’re pushing at that end.’’ Others have noted the correlations of test results with family background (see, e.g., Kohn, 2001; Sacks, 1999), and this teacher’s comments seemed to suggest that differences in test scores might as easily be attributed to home background as to specifics of curriculum, instruction, and assessment.


While parent-teacher relationships underwent no major changes during this study, the importance of communicating with parents about children’s progress remained high. Teachers clearly understood that they were to provide parents with information about their grade level’s instructional program and to provide data about how individual students were faring in mastering the content to be tested. They recognized, however, that the change in state curriculum and the addition of a new testing program were not enough to alter the differing levels of parent involvement that they had observed over their years in the classroom.



DEALING WITH INDIVIDUAL DIFFERENCES


In raising the bar for all students in Virginia, the state Board of Education seemed to suggest that equal outcomes should be expected of all students. How to enable a diverse population of students to achieve these equal outcomes was a challenge with which these teachers struggled.


All of the teachers interviewed seemed to accept that children differ. They differ in terms of background of experience, both academic and at home. They differ in terms of natural ability, interests, and talents. They differ in terms of learning styles and attitudes toward learning.


When combined into a class of twenty or twenty-five, these differences result in classes with different ‘‘personalities.’’ Teachers recognized this and commented on how, for instance, this year’s class compared with last year’s, or how their class compared with the class next door. A fine line may be drawn between having unfounded expectations and then having students live up (or down) to them and being realistic about human differences. Most teachers in this study seemed to accept and not resent the expectation that they adjust instruction to provide appropriate teaching from year to year, making adjustments based on the class they were assigned. For example, a fifth grade teacher commented, ‘‘This group doesn’t seem quite as well prepared to handle the terms the way they are being presented . . . I think as we get going, it will be better. I think teachers will adjust and pull those along who are struggling.’’


Nevertheless, it was in this area of life in the classroom that I observed the greatest degree of frustration on the part of teachers. Their task was to prepare all students to take the same test at the same time in May, and while the means by which teachers prepared their students were not specified by the state, teachers felt definite constraints as far as how they were to proceed. Having a one-size-fits-all curriculum left some teachers feeling that the gifted were unchallenged; a third grade teacher noted that ‘‘we don’t have a curriculum for gifted students. . . . Most of them, you know, if I pretested them they would already know the material.’’ Meanwhile accommodations for special education students were extensive. Adding to the pressure was the looming date for the tests: Teachers had to stay with the recommended pacing guide if they were to have time to introduce all the tested material before May.


The challenge sometimes became overwhelming to teachers, especially those whose students were lower level, students who had entered their present grade level without having mastered the previous year’s curriculum or who simply seemed to need more time to catch on to more complex concepts. (Note: While promotion from one grade level to the next was not automatic, there was variation in the degree to which students had mastered the content of the curriculum for the previous grade. In addition, students newly transferring into this school were placed in the grade level recommended by their previous school. Decisions concerning promotion or retention were made based on student’s performance, as reflected in grades, school history─ that is, prior retentions─ and the opinions of parents and the teacher. Although there was discussion during this academic year about the possibility of using SOL passing or failing as a major determinant in the decision to promote or retain, that policy was not enacted while I was there.)


Over lunch one day a teacher described a recent conversation with her colleague: ‘‘She called me last night. She’s feeling . . . ’’ (faded off and another teacher suggested, ‘‘agitated’’). She nodded and added, ‘‘Overwhelmed!’’ Explaining further, she said, ‘‘She had a pretty low group last year and has a weak one this year. She knows how they did last year. She’s feeling ‘How am I going to get them to the same point?’ She’s frustrated.’’ Even those teachers who were experiencing success with the majority of their students experienced frustration with those few who were struggling. A third-grade teacher described ‘‘a little boy who has difficulty with math. . . and it’s very difficult because we’re having to move on and he’s still back three skills, not having mastered that one. Trying to find time to help him with the skills that are still weak . . . ’’ Her voice faded off, and she shook her head. She then expressed concern about how this might affect students’ attitudes toward math:


Some of them might be (more confident if they slowed down). Some of them just take a longer time to get a particular skill. We’re expecting them all to get it done at the exact same time. They all can’t do it that way!


Both regular education teachers and special education teachers expressed concern for identified special education students. In a tone of great frustration, one teacher said:


Look around here! Look at all these special ed kids. What is their (State Department of Education’s) plan? What are they going to do with those people? And when all those kids fail─ what are they going to do? I mean those kids are already identified as not functioning on grade level. So how are they supposed to pass the SOLs?


A special education teacher, describing the modifications in test administration, was somewhat less concerned:


You can give it in a small group setting. You can give it untimed.

(Note: SOL tests are untimed for all students.) I can read the math directions. I can read the items to them (so the reading doesn’t hinder their ability to figure out the math). So that will be good.


But no one class was composed of all gifted or all special education students, and balancing the instructional program to challenge the quicker while accommodating slower students was a challenge:


I have a faster-paced class with lower students too. So if I move too fast I’ve lost them, which is already happening. And yet I have another group that you know are pretty much working independently . . . because I’m having to take so much time with the lower ones.


Another teacher recognized that covering the curriculum with his class was quite different from that task as tackled by his colleagues:


I have the gifted kids. And we push, we push and push. I feel my strategy is expose them to it once and then come back to everything again. Now the upstairs (other) classes─ there’s no way that they’ll . . . I think that their strategy is get through as much material as possible and if there’s any time for review, just hit the really really weak spots.


Finally, a few teachers simply cited natural differences in people and their abilities. One commented, ‘‘As adults you know yourself that we have people who function at high levels, people who function at middle levels, people who function low, and we need all those levels in society.’’ Another teacher simply said, ‘‘You have your weak ones. You always have your weak ones.’’


Given these differences, whatever their source, teachers still had to find ways to teach all students the contents of the SOLs and to prepare them for the grade-level tests. Several mentioned intraclass adjustments they had made. However, for many, others outside their classrooms were called on to meet the challenge of ‘‘keeping the lower level kids up.’’ Some students were provided with special education services through a pull-out program, and for regular education teachers of these children, there was an assumption that they were not really responsible for SOL coverage for these students.


The school’s plan for providing remedial help to those not under the special education umbrella was ambitious and two-pronged. The primary means of providing extra help was the school’s after-school program. The program had been started the previous year, at which time one teacher from each grade level instructed struggling students several afternoons a week for additional pay. The burden on these people was heavy, however, and this school year the administrators opted to change organization of the after-school program.


The principal took on the task of organizing the after-school program for students who failed to demonstrate mastery on the 6-weeks review tests (testing those SOL skills for the grading period, as specified in the new curriculum guide). This after-school program included sessions both for reading/language arts and for mathematics. For each 6-week period, two teachers at each grade level provided this after-school help. Grade-level teams were permitted to determine which teacher took on this additional responsibility; however, when no volunteers arose, the administration exerted some pressure to ensure that each section was staffed. Teachers all had the responsibility for identifying students in need of this service, and the principal provided support in notifying parents and setting up the schedules and transportation.


The after-school program began after parents received the first 6-weeks evaluations. The first after-school sessions included approximately 80 students in the three grades, with larger numbers from the two tested grades (third and fifth). That number rose to over 100 in the second block, held after the mailing of the second 6-weeks evaluations. Again the numbers for Grades 3 and 5 were larger than those for fourth grade; in fact, more than twice as many children were referred for after-school help from Grade 3 than from Grade 4. While numbers of children referred to the after-school program remained high throughout the year, it was noted that during the winter months (when many after-school activities, including sports practices, were at their peak) the number of students actually attending the after-school sessions dropped. On one afternoon of observation, for example, the researcher found approximately one fourth of the referred students attending after-school help sessions.


The second prong of the remediation effort was uncertain at the beginning of the school year but was implemented as money became available about halfway through the school year. At that time the school division hired a full-time remedial teacher. A fourth-grade teacher at the school filled this position, and a newly graduated teacher took on the responsibilities of her regular classroom position. The remedial teacher’s job description included the provision of small-group help to students struggling in either reading/language arts or mathematics. Teachers identified students for these groups, based on both classroom performance (reflected in their report card grades) and on mastery of the SOLs for the previous quarter (as demonstrated through practice tests). Regular classroom teachers and the remedial teacher jointly made decisions as to what content was to be taught in these small groups. Because students were referred on an as-needed basis each week, the roster of students involved changed constantly. The tracking of effects of this remedial help was thus difficult, and the remedial teacher herself recognized this weakness in design.


However, teachers welcomed the opportunity to get extra help for their students during the school day. Some referred to the remediation program those students whose parents had refused permission for them to attend the after-school program. Others commented on their belief that the program during the school day was more beneficial for students, in that the children were more alert and their attendance could be controlled.


In summary, providing instruction intended to maximize the number of students passing the SOL tests was a challenge that was faced in a variety of ways by these teachers. They made adjustments in daily lessons to provide regular review and practice in hopes of increasing the number of students mastering the basic curriculum. In addition, students who needed extra help were assisted through special education classes, the after-school program, and the services of a remedial teacher.



ASSESSMENT AND ACCOUNTABILITY


If one aspect of accountability is record keeping, the faculty of this school worked hard to be accountable. The administrators asked teachers to track their instructional planning for each grading period, to ensure that the designated quantity of the curriculum was covered in that 6-week period. In addition, teachers were expected to keep records on each student, to indicate that child’s success or failure in mastering specified Standards of Learning objectives, as demonstrated by performance on the mathematics textbook publishers’ tests. The principal collected data each 6 weeks in which teachers recommended students for remedial services, and he informed parents about schedules for these after-school sessions and the pull-out program during the school day (in the second half of the year). Efforts were made for all written assessment to mirror the form of the Standards of Learning assessments, in an attempt to prepare students for the process of test taking as well as the subject matter itself.


Teachers in this building chose to assess students in mathematics using the textbook publisher’s tests as a primary tool. Included in the curriculum guide were pretests, practice tests, chapter tests, review tests, and so forth. These tests used the same format as the SOL tests─ that is, multiple-choice items.


But the real assessment, in the teachers’ minds, was the state test, due to be given in May. Support for the idea of a clearly stated state curriculum, in the form of Standards of Learning, seemed considerably stronger than support for the accompanying testing program. Several teachers commented on the need to ‘‘teach them how to take the test.’’ The seemingly simple act of bubbling responses on an answer sheet was an obstacle for some children, and teachers of lower grades spent instructional time teaching students how to record answers in this form. One teacher said, ‘‘On Fridays we have SOL day, skill practice day, where I give them skill sheets that have bubbles.’’ Even with older children, there was concern about ‘‘that one child who can’t bubble,’’ concern that a child might know the content being tested but be unable to show this on the SOL test itself.


Readability of the tests (including the mathematics test) was also an issue brought up by teachers. (See Appendix B.) A teacher mentioned a student in her class who ‘‘is good in math but weak in reading comprehension,’’ saying that the child would likely fail the SOL (math) test because of the reading required. Another commented, ‘‘Yes, yes, reading is going to be our difficulty. That’s, you know, understanding. Mine will come to me and say ‘I don’t know what they’re asking me to do.’ And some of that is terminology and some of that is their ability to break down what a problem is saying. They just need to develop better skills to do that.’’


The issue of readability level of the mathematics test arose because successful performance on the SOL test demanded that students apply mathematics skills in a real-world context, not just do isolated computation. A third-grade teacher cited as a strength of the mathematics Standards of Learning ‘‘the fact that they are teaching the children applications of skills rather than just computation.’’ While potentially more useful in their adult lives, this also presented a challenge; a fifth-grade teacher said ‘‘the thing that makes them hard is that they’re all applications-type questions.’’ A third-grade teacher agreed, saying, ‘‘The approach of the SOL tests is total application. They don’t have to do as much plain computation anymore. They have to read it and decide what they’ve got to do.’’ Her colleague followed with ‘‘I think it’s overwhelming too, when that’s all they have. I mean, they look at it and see sixty applications problems. It’s a lot of reading.’’ Chimed in a third teacher, ‘‘It is. It’s a bit too tough.’’ Another opined, ‘‘It should have some basic computation, not all applications and problem solving.’’


Length of the test was also considered a problem. One stated plainly, ‘‘The math test for third graders was much too long. Once many got tired, I am afraid they did not put much thought into their work.’’ Two others made similar comments. A fourth-grade teacher said, ‘‘Depending on the grade level, the test is too long for the students.’’ Another simply responded, ‘‘Too long!’’


Absent from all discussions was any mention of other, alternative means of assessing students in mathematics. I heard no mention of group projects, journals, performance assessment, or portfolios. It was not clear whether teachers had used other options for assessing student progress in the past, but clearly during this year assessment equaled the number correct on a multiple-choice test.




RESULTS OF TEACHERS’ EFFORTS: HOW STUDENTS PERFORMED ON STATE TESTS


Tension mounted in the spring as the Standards of Learning tests neared. Teachers reviewed and provided practice tests. They drilled students on skills. Parents received letters notifying them about the upcoming tests, and teachers lectured students about the importance of doing their best.


The school was uncommonly quiet during the testing period, which stretched over most of a week. As a visitor to the building, I was asked not to venture into hallways where students were testing. Custodians adjusted their daily routines so as not to have the sounds of their work interfere with students’ concentration. Resource teachers cancelled or rescheduled their art and physical education classes. All were attuned to the task at hand.


The school’s assistant principal had the responsibility for accounting for all testing materials. She had to count each class’s test booklets and pack them for return to the state department of education (including one test booklet on which a student had gotten sick, that one being packaged separately in a sealed plastic bag). She commented that a few defective test booklets had been found on which several pages were omitted; she wondered how this would affect the scoring. She also wondered whether there had been other defective test materials that had not been called to the teacher’s attention by the 8-year-olds taking the test.


Then the waiting began. Results, received in early summer, allowed both teachers and principal to let out a sigh of relief: The passing rate had risen in all but one area: Grade 5 English, which showed a 3% drop from the previous year (though a 7% rise from the baseline 1998 percent passing). The Grade 3 English, on the other hand, showed a 10-percentage point increase over the previous year (when the school had a 1 point drop from the 1998 baseline).


Similar increases were recorded in science, social studies, and technology (areas not affected by revised curriculum guides, professional development, new textbooks, or remedial services). In science, the percentage of third graders passing rose from 66% in 1998 to 71% in 1999 to 76% in 2000. Fifth graders showed increases from just under 60% to 73% to almost 74% passing over the 3-year span. In social studies, where passing rates were set lower, the third-grade percentage rose over 10 percentage points between 1999 and 2000, while fifth graders’ percentage rose more than 12% in the year. Fifth-grade technology scores, which had been high to begin with, exceeded the previous year’s results, with over 89% of students passing.


In mathematics, where much time, money, and effort had been expended, students also performed at higher levels. Third-grade passing rates, which had been at 60% in 1998, continued their increase and registered at 76% passing. Fifth-grade passing rates showed even more dramatic results, doubling from the 1998 pass rate of 36% to a 2000 passing rate of 72%.


Given improved test scores both in areas in which much effort was exerted to influence those scores and in areas in which no specific measures were taken, one is left with the question of cause. Why did test scores rise? Did any of the faculty’s strategies have a direct impact on scores, or were other factors at work? Did a curriculum aligned with the tests, new textbooks (said to be correlated with the SOLs), or remedial teaching make a difference at all?


This study did not attempt to identify specific causal factors in rising test scores, but only to observe the efforts made by teachers when they were directed to make higher test scores their goal. The study also did not attempt to determine whether higher test scores actually reflected more or better learning of mathematics. Certainly the format of the test items did not allow for a thorough examination of students’ problem solving and reasoning ability, their ability to justify solutions, or their ability to communicate effectively about mathematical concepts, all goals advocated by the Commission on Standards for School Mathematics (1989).


But the tired, happy teachers at this school obtained the results they desired. So what’s the problem?



COSTS OF IMPROVEMENT


Teachers in this school applied time-honored methods of improving students’ performance on a standardized test. Specifically their efforts included the following:


A curriculum aligned with the content to be tested


Instructional materials appropriate for that newly aligned curriculum


Professional development for teachers


Systematic collection of data on student progress


Rapid provision of remedial services for students falling behind


Education of parents about the standards, the SOL tests, and the school’s plans


These efforts may have contributed to significantly higher test scores on the end-of-year tests for students in this school. However as might be anticipated, there was a price to be paid.



Effect on the Curriculum


Improvement on test scores depended on teachers’ maximizing instructional time spent on tested content. For better or worse, this focus caused teachers to eliminate the teaching of some content that they had included in the past. A teacher who had previously introduced his fifth-grade students to the concept of ratio stated, ‘‘There’s really nothing in the SOLs about ratios, so although ratios do a really good job of reinforcing fractions, I’m skipping that.’’ Some commented on having to give up special activities that they had planned for students in the past, these being special projects or field trips that did not align with that grade’s SOLs. Another stated, ‘‘I only taught what was specifically mentioned.’’


On the other hand, what was left in the curriculum was extensive. Teachers repeatedly commented on ‘‘not enough time.’’ What was specified in the curriculum was also viewed by some as inappropriate for the grade level at which it was required. A fifth-grade teacher said, ‘‘I will admit, I think some of the things we’re asking them to learn in math are above what they should be doing.’’ Developing deeper understanding of concepts was also challenging because of quantity. Another teacher admitted, ‘‘I’m pushed between finishing the SOLs and teaching them well. And I can tell you now: I’m not teaching them well─ I’m finishing them.’’ A teacher at a different grade level stated, ‘‘That’s one thing that the SOLs have done that’s detrimental: they’re having to rush through stuff so much faster that you’re able to spend less time with it. ‘‘ Other teachers mentioned ‘‘the fast pace─ [I]always feeling rushed!’’ A fourth-grade teacher commented, ‘‘Due to the number of areas that must be covered, time is difficult to manage while also trying for mastery.’’


Other writers, including researchers from the TIMMS study (U.S. Department of Education, 1997, p. 169), have cited the tendency for American schools’ curricula to be ‘‘a mile wide and an inch deep.’’ In firmly adhering to the requirements of the state curriculum, teachers recognized that they were giving up some depth of learning to cover what was required.



Effect on Teacher Autonomy


Phrases such as ‘‘I would have liked to . . . ’’ and ‘‘In the past I have . . . ’’ peppered teachers’ comments in interviews. It was clear that one effect of tightening the schedule and the curriculum was to remove teachers’ opportunities for applying their own professional judgment. As noted previously, this was particularly evident in teachers’ decision making about pacing. Some commented that they knew they were moving on to new content when students had not yet mastered the previous content. Others commented on the sequence with which they were required to introduce math content, indicating that their previous experiences with children had suggested to them that a different sequence was more helpful to students’ learning.


One area on which many teachers expressed skepticism was the format of the after-school remedial program. Some questioned whether having students spend several more hours in school, after a full day of studies, was very productive. Others questioned whether another teacher at the grade level would successfully remediate their students, whom they knew best and understood. In fact as the year went on, some teachers referred fewer students to the after-school program, preferring to simply provide extra help to their own students, outside the structure of the organized after-school program.


Some teachers seemed to feel that their voices were unheard when it came to decision making. A fourth-grade teacher stated, ‘‘There are policies made that I can’t change. When I get the opportunity to express my concern or whatever, I think that it falls on deaf ears.’’ Most seemed to feel that they knew their students well and were capable of leading students to whatever goals were set, including achievement of passing scores on the state tests. One stated, ‘‘I don’t have any brighter children than I did last year, but I feel that I was better prepared from the get-go, and I’ve done a better job of teaching the test. That’s what we have to do.’’



Fatigue and Stress


Teachers who had begun the year with energy and enthusiasm began to look increasingly tired as the year went on. This was especially evident in those who taught in the after-school program. For these teachers, their workday might begin at 7:30 a.m. or 8:00 a.m. Following a full day of instructing their own students, they moved into a second shift, teaching students at their grade level during the 1.5-hour after-school program. When they left the school late in the afternoon, it was with papers to grade and lessons to plan for the next day. What would normally have been their work time for these tasks was taken up by the after-school teaching.


My observations of the after-school remedial lessons noted the fatigue shown by both students and teachers. I observed one teacher who normally incorporated hands-on activities and problem solving into her regular math teaching, leading a group of students, step-by-step, through a photocopied worksheet. She commented afterwards, ‘‘I don’t like doing worksheets in the afternoon. But they’ve got to have something to do.’’ In another classroom, much overheated on a cold winter afternoon, students were seen struggling to keep their eyes open and on the screen as the teacher led them through a drill.


More generally, a third-grade teacher stated, ‘‘This is the way I’m feeling at the moment: that there’s not enough time and there’s not enough individual help.’’



Effect on School Climate


As noted previously, as the testing dates approached, tension was apparent in the building. Teachers reminded students of the need to pay attention and to work their hardest, stressing how important the tests were. One teacher did a complete ‘‘practice SOL test’’ with her students, deliberately including more difficult content than they might encounter on the ‘‘real’’ test in order to get their attention focused on studying for the SOL test. She pointed out to her students, ‘‘You can study for the SOL (test). There are people who say that you can’t study for a standardized test, but they are wrong. You can.’’


During the 2-week period before the state tests, teachers led their students through extensive review of the content expected to be tested. One chuckled, saying, ‘‘We’ve done so much review that kids are ready to go screaming into the streets!’’ Another commented on ‘‘going through the SOL review materials’’ but feeling much more confident about her students’ preparedness than last year: ‘‘I feel that I’ve taught every one of them (the SOLs), and that’s all I can do.’’ Teachers mentioned taking time to review test-taking strategies such as eliminating unreasonable answers. One teacher, looking exhausted, simply stated, ‘‘These tests have taken all the fun out of teaching.’’




CONCLUSION


Do demands for meeting higher standards result in increased learning? Does the requirement to assess student learning objectively through standardized tests result in better-educated young people? The political powers seem to work from the assumption that these questions can be answered in the affirmative. However, as is often the case, the present study was unable to address questions such as these directly; instead, this study documented the lengths to which teachers will go in attempting to meet the demands put on them by those who ‘‘make the rules.’’ In this study, one school made multifaceted plans to raise test scores and to show that its students were learning more as a result of the new state standards. The school’s staff invested an enormous amount of time and energy into the pursuit of higher test scores, demonstrating clearly that they and their students were doing what was expected of them.


Other writers have noted strategies by which teachers help their students toward higher test scores (see, e.g., McColskey & McMunn, 2000; McNeil, 2000). As was the case in the present study, these include becoming familiar with expectations, aligning curricula and teaching test-taking strategies, and other ways by which schools tool up to meet the challenge.


The staff members of this elementary school did all that they could to meet the standards. In this case, test scores were higher at the end of the school year. But again, it cannot be shown with our data that test score improvements resulted from the efforts observed. And, as is always the case, trade-offs occurred. Time spent on content to be tested and on teaching test-taking skills is time not spent on other potential areas of learning and growth. Increasing time devoted to mathematics came at the cost of decreasing time devoted to other areas of the curriculum.


Only time will tell whether, in the long run, elementary students in the Commonwealth of Virginia will truly learn the contents of a more rigorous curriculum. Meanwhile, teachers will continue to spend their days doing what they are told to do, reaching for goals they did not themselves establish, and worrying about whether or not they are doing enough.




APPENDIX A


Samples from Mathematics Standards of Learning, Board of Education, Commonwealth of Virginia (1995)


Grade 3:


The third grade standards place emphasis on using a variety of methods to solve problems involving addition and subtraction of whole numbers. Students also will learn the multiplication and division facts through the nines table. Concrete materials will be used to introduce addition and subtraction with fractions and decimals and the concept of probability as chance. While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies such as calculators and computers. However, facility in the use of technology shall not be regarded as a substitute for a student’s understanding of quantitative concepts and relationships or for proficiency in basic computations. Students also will identify real-life applications of the mathematical principles they are learning that can be applied to science and other disciplines they are studying.


Mathematics has its own language, and the acquisition of specialized vocabulary and language patterns is crucial to a student’s understanding and appreciation of the subject. Students should be encouraged to use correctly the concepts, skills, symbols, and vocabulary identified in the following list of standards.


Problem solving has been integrated throughout the six content strands. The development of problem solving skills should be a major goal of the mathematics program at every grade level. Instruction in the process of problem solving will need to be integrated early and continuously into each student’s mathematics education. Students must be helped to develop a wide range of skills and strategies for solving a variety of problem types.


Number and Number Sense


3.1 The student will read and write six-digit numerals and identify the place value for each digit.


3.2 The student will round a whole number, 999 or less, to the nearest ten and hundred.


3.3 The student will compare two whole numbers between 0 and 9999, using symbols (>, <, or = ) and words (‘‘greater than’’, ‘‘less than’’, or ‘‘equal to’’).


Computation and Estimation


3.8 The student will solve problems involving the sum or difference of two whole numbers, each 9999 or less, with or without regrouping, using various computational methods, including calculators, paper and pencil, mental computation, and estimation.


3.9 The student will recall the multiplication and division facts through the nines table.


3.10 The student will create and solve problems that involve multiplication or two whole numbers, one factor 99 or less and the second factor 5 or less.


Measurement


3.14 The student will estimate and then use actual measuring devices with metric and U.S. Customary units to measure:


Length─ inches, feet, yards, centimeters, and meters;


Liquid volume─ cups, pints, quarts, gallons, and liters; and


Weight/mass─ ounces, pounds, grams, and kilograms.


3.15 The student will tell time to the nearest five-minute interval and to the nearest minute, using analog and digital clocks.


3.16 The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.


Geometry


3.18 The student will analyze plane and solid geometric figures (square, rectangle, triangle, cube, rectangular solid, and cylinder) and identify relevant properties, including the number of corners, square corners, the shape of faces, and edges.


3.19 The student will identify and draw representations of line segments and angles, using a ruler or straightedge.


Probability and Statistics


3.21 The student, given grid paper, will collect data on a given topic of his/her choice and construct a bar graph showing the results. A title and key will be included.


3.22 The student will read and interpret data represented in bar and picture graphs.


Patterns, Functions, and Algebra


3.24 The student will recognize and describe patterns formed using concrete objects, tables, and pictures and extend the pattern.




APPENDIX B


Samples from Released Test Items 2000 Mathematics Test, Grade 3 (Virginia Department of Education, 2001b)


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References


American Educational Research Association. (2001). Position statement concerning high-stakes testing in PreK–12 education. (Retrieved March 26, 2003, from ww.aera.net/about/policy/ statkes.htm


Board of Education, Commonwealth of Virginia. (1995). Standards of learning for Virginia public schools. Richmond, VA: Author.


Commission on Standards for School Mathematics of the National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.


Kohn, A. (2001). Fighting the tests: A practical guide to rescuing our schools. Phi Delta Kappan, 82, 349–357.


McColskey, W., & McMunn, N. (2000). Strategies for dealing with high-stakes state tests. Phi Delta Kappan, 82, 115–120.


McNeil, L. (2000). Creating new inequalities: Contradictions of reform. Phi Delta Kappan, 81, 729–734.


Olson, L. (1999a, Jan. 17). Making every test count. Education Week, 17, 11–20.


Olson, L. (1999b, Jan. 17). Shining a spotlight on results. Education Week, 17, 8–10.


Sacks, P. (1999). Standardized minds. Cambridge, MA: Perseus Books.


Schmoker, M. (1999). Results: The key to continuous school improvement (2nd ed.). Alexandria, VA: ASCD.


Schmoker, M. (2001). The results fieldbook: Practical strategies from dramatically improved schools. Alexandria, VA: ASCD.


U.S. Census Bureau. (2000). Census 2000. Retrieved September 12, 2002, from http://www.census.gov/census2000/states/Va.html


U.S. Department of Education, Office of Educational Research and Improvement. (1997). Attaining excellence: TIMSS as a starting point to examine curriculum: Guidebook to examine school curricula. Washington, DC: Author.


Virginia Department of Education. (2001a). Every child can succeed: A parent’s guide to Virginia’s Standards of Learning Program. Richmond, VA: author.


Virginia Department of Education. (2001b). Virginia Standards of Learning assessments: Spring 2000 released items, Grade 3 mathematics test. Retrieved September 12, 2002, from http://www.pen.k12,va.us/VDOE/Assessments/release2000/grade3.pdf






Cite This Article as: Teachers College Record Volume 106 Number 6, 2004, p. 1203-1228
https://www.tcrecord.org ID Number: 11571, Date Accessed: 10/27/2021 7:34:00 PM

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About the Author
  • Karen Dorgan
    Mary Baldwin College
    E-mail Author
    KAREN DORGAN is an associate professor of education at Mary Baldwin College. Her research interests include the curriculum change process, elementary teachers’ and students’ understanding of fractions, and how textbooks approach instruction about fractions. Her publications include ‘‘Addressing Prospective Elementary Teachers’ Beliefs About the Nature of Mathematics,’’ in Journal of Mathematics and Science, and ‘‘What Textbooks Offer for Instruction in Fraction Concepts,’’in Teaching Children Mathematics.
 
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