By: Douglas Trelfa
If I aim the expectation at the better students, the other ones are so left behind that they don't have the vaguest idea of what's going on. If I make it too easy, it bores the brighter ones, so the idea is to try to hit a middle. At least that is my idea. And sometimes it's pretty good and sometimes the middle bores the ones at the top and it's too hard for the ones at the bottom. (Physics teacher, Springdale High School)
Although all educators acknowledge the existence of large individual differences in ability among students, in this study we found a diversity of beliefs regarding the question of how to deal effectively and fairly with these differences. For instance, while some parents and teachers reported believing that children learn best in classrooms with other children of similar ability, there were others who felt that students learn best when taught in classrooms with peers who have a wide range of ability. Some teachers and administrators stated that even early tracking of low-ability students into vocational programs would be beneficial, while several argued for eliminating tracking and vocational courses at the high school level.
We found that the variety of beliefs about how to deal with individual differences in ability was mirrored in the variety of actual practices at the schools. Some schools had two or three levels of courses in math and science; others had four or five levels in these subjects. Some schools were working to eliminate or reduce ability grouping; others were increasing the levels of courses offered. Some schools emphasized portfolio grading; others emphasized standardized test scores in computing students' grades.
The variety of practices regarding individual differences is in part a consequence of a system of local control of schools. Local school districts in the localities we visited had a great deal of autonomy. They used this autonomy to create a diverse mix of educational programs designed to meet the needs of diverse student populations. Even principals and teachers were given a great deal of autonomy in managing individual differences at the school and classroom levels.
In this chapter, we use the phrase "individual differences" with some reservation. When we speak of individual differences, we refer to individual differences in academic performance among students that are based on variations in aptitude, interest, life history, personality, and the characteristics of the evaluator. This inclusive conception recognizes that individual differences have multiple sources and occur within a social context. It takes into account the many domains in which children vary. Our focus is on individual differences as they are related to achievement in math and science.
We had conversations with teachers, administrators, students, and parents in three cities in the United States and conducted related classroom observations of the 16 schools that we visited in these 3 cities. Our discussions focused on the views of respondents about the sources of individual differences in ability, the practices related to these differences, and their efficacy and fairness. Most of the respondents voiced strong opinions about these topics and were generally frank and forthcoming in offering their opinions about the problems they see in this area.
At the primary site, Metro City, the author conducted most of the interviews and observations pertaining to individual differences. In addition, a number of interviews dealing with this topic were conducted in Spanish by Carmen Maldonado de Johnson. Also, Mavis Sanders conducted a portion of the interviews with African-American respondents. Carmen Maldonado de Johnson and William Foraker conducted the interviews and observations on this topic in West City, while Gerald LeTendre and Sally Lubeck collected the interview and observation data in East City. Foraker, Maldonado de Johnson, LeTendre, Lubeck, and Sanders shared their data with the author, and these data are reflected in this chapter.
In pursuit of information on individual differences, the author and his research colleagues conducted 33 interviews at high schools, 8 at vocational high schools, 27 at middle schools, and 27 at elementary schools. Of all the interviews pertaining to this topic, approximately 17 were held in West City and 10 in East City. In addition, approximately 34 classroom and general observations were included in the data analysis. Printed information obtained from schools, school boards, and other secondary sources was also integrated into research findings.
This chapter presents findings in four areas related to the topic of individual differences. One area concerns the perception people have about the important sources of individual differences in student learning. To what extent are effort and differences in ability seen as important to students' academic achievement? A second area deals with the ways schools and school districts respond to individual differences by creating tracks and programs and how teachers manage individual differences in the classroom. A third area is concerned with the attitudes people have about these practices. We wanted to know if people thought that these programs or practices were effective and fair. The fourth area of investigation was the attitude of people toward the education of students with either severe handicaps or special talents.
American children begin formal schooling in the first grade at the age of five or six. The early years of schooling are characterized by classrooms where students with a wide range of abilities are taught together by a single teacher. Since elementary school teachers typically spend the entire day with the same children, they gain great familiarity with the individual abilities and personalities of their students.
In addition to the classroom teacher, federal law provides for resource teachers and special education teachers when students with handicaps or students from disadvantaged backgrounds are present. Many schools try to retain these students in regular classrooms during the elementary school years. As a result, it was not unusual for us to observe two or three adults in a single elementary school classroom.
In general, the American system of education supports a process of tracking students by ability, and most parents with whom we talked were supportive of providing instruction that parallels the academic level of students. However, a number of respondents expressed reservations about schools denying certain students the opportunity to learn on the basis of what are perceived as narrow measures of ability, such as test scores. These reservations were primarily explained in terms of concerns about the over-representation of certain ethnic and racial minorities in lower tracks.
In accordance with the desire to teach to the level of each student's ability, many elementary school teachers we talked with focused on individualized instruction rather than attempting to teach to a whole group. Pullouts and cooperative learning groups were also reflective of a preference for individualized instruction, as were the common practices of offering time for peer tutors and computerized instruction. Most teachers reported using these practices as a way to deal with individual differences in ability. In addition, elementary school teachers reported grouping students together for reading and for math exercises. Groups were stratified by ability level, allowing each group to receive instruction at its own level and to progress at its own rate. These groups were commonly used in the elementary schools we visited, and previous research has indicated that even in the first grade, more than 90 percent of elementary schools use within class ability grouping for reading and 25 percent use them for math instruction (Entwistle & Alexander 1993).
The transition from elementary to junior high school is one that may have far-reaching consequences. Beginning in junior high, students are no longer with a single teacher the entire day. Instead, they generally move from classroom to classroom to receive instruction in different subjects from different teachers. The school experience becomes more complex: students in junior high school interact with more teachers and more students than do students in elementary school. According to the results of a survey of middle-level school principals, two thirds or more of the nation's middle-level schools use at least some between class ability grouping (Braddock 1990). As we observed, the use of ability groups is especially prevalent in math. According to results from the 1990 National Assessment of Educational Progress (NAEP), school administrators reported 77 percent of eighth-grade students were grouped by ability in math. One-third was grouped by ability in science (National Science Foundation 1993).
In seventh and eighth grade, ability groups involve more than different levels of learning in the same subject. By then, course material is strongly differentiated and students at different levels take different courses. In general, instruction in low-track classes tends to deal with simplified topics and focuses on rote skills. The focus of high-track classes is on understanding of underlying concepts, problem solving, and independent thinking (Oakes et al. 1992).
In mathematics, students are typically assigned to one of three or four groups differing by level of ability, ranging from remedial mathematics to accelerated mathematics. Enrollment in the accelerated track is restricted by an array of school policies. Students in general mathematics are exposed to a curriculum that essentially reviews the content of elementary school courses and provides little challenge for average or above-average students. Because the general mathematics classes cover different topics than the accelerated classes, it is very difficult for students to catch up with the accelerated group and become eligible as 12th-graders to take calculus or other 5th-year secondary mathematics courses (Useem 1991).
Most of the school systems we visited began offering various levels of instruction in core academic subjects to students around the eighth or ninth grade, although a couple began earlier. Scores from standardized tests, past academic performance, and parental wishes were factored into the assignment of students to what were perceived as appropriate levels of instruction. Depending on the school, different weights were given to different factors: some schools emphasized test scores, while others emphasized parental wishes. In other schools the recommendations of individual teachers also had some influence over the tracking decisions.
High schools were organized similarly to junior high schools, with the level of instruction in high school courses being more closely linked with educational and occupational trajectories. To meet the widely differing needs of students, math and science courses were usually offered at different levels of difficulty. This pattern is supported by national data on the practice of tracking by level of ability. According to the 1990 NAEP, school administrators reported that by 12th grade, 74 percent of students were placed in science classes by ability, and 80 percent in mathematics classes (NSF 1993).
At the secondary level there usually are between three and six tracks (Vanfossen, Jones, & Spade 1987). In all tracking systems, judgments about students' academic performance are the basis for group placements. Classes and tracks are labeled in terms of performance levels of the studentssuch as advanced, average, or remedialor according to students' expected postsecondary goals, such as college preparatory or vocational. The resulting groups or tracks are not merely a collection of different but equally valued instructional groups; instead, they form a hierarchy within schools with the most academic or the most advanced tracks considered to be the "top" (Oakes 1987).
Course offerings in the high schools we visited were generally considered either college preparatory, general, or vocational. A student's enrollment or assignment to a particular level course was often determined by their prior course selections, their grades, and their goals for higher education. High school counselors also played a central role in guiding students in making course selections.
In most cases students could take courses from all three of these levels, although students aspiring to attend college generally took courses that were either considered college preparatory or general-level courses, and they often took some of each. However, a national survey showed that 60-70 percent of 10th-graders in honors mathematics were also enrolled in honors English; the degree of overlap is similar in remedial mathematics and English (Oakes et al. 1992).
The proportions of students taking advanced-level courses varied from school to school. For example, at one of the high schools we visited most students were preparing for college by taking advanced-placement or honors-level courses, while at another school the majority of students were enrolled in general- or vocational-level courses. Most high school students were enrolled in general-level courses in math and science. These courses were not at the level of advanced-placement or college-preparatory courses, which would involve a year of calculus, nor were they at the basic level generally found in a vocational curriculum. Since most colleges will admit students who have a general education background, many students taking general-level courses aspired to attend college. Vocational courses were taken by students who intended to go directly into the workforce, but a number of students in vocational courses also had college aspirations.
Most selective colleges in the United States require for admission a minimum number of credits in core academic subjects and give extra points for advanced courses. For students with aspiring to these selective colleges, college-preparatory level courses were perceived as essential. Also available in some of the high schools were advanced-placement courses that allowed students who completed the requirements and passed the examinations to receive credit for college-level work before high school graduation. Only a small proportion of the students at the high schools we visited were taking advanced-placement courses.
These findings are in line with data published by the National Center for Education Statistics based on a national survey of 912 secondary schools. According to this survey of grades 10-12, 86 percent of these schools reported offering courses in their core curriculum that are differentiated in terms of content, quantity, or intensity of work, or expectations regarding independent work. In addition, these schools indicated that during the 1993 fall, term 14 percent of all 10th-graders took math courses designed for students of widely differing abilities (28 percent did so for English courses). The remaining 10th-graders were in math or English courses designed for more discrete levels of abilities. In math, 27 percent of students were enrolled in courses designed for students of higher abilities, 47 percent took courses for students of average abilities, and 16 percent took courses for students of lower abilities. In English, 23 percent of students were enrolled in courses designed for students of higher abilities, 39 percent took courses for students of average abilities, and 9 percent took courses for students of lower abilities. A majority of these schools also indicated that there was some movement of students between ability levels in math and English courses after 10th grade, with students moving up as well as down (USDE 1994).
In sum, we found considerable flexibility and variation in the way schools met the needs of students with differing levels of ability. Few restrictions were placed on whether tracking or ability grouping could be practiced at any grade level; consequently, most school districts that we visited were practicing some form of ability grouping and tracking, whether at the elementary, junior, or senior high level. As the student moves up in grades, tracking and ability grouping practices of schools become more numerous. However, these tracks were not widely perceived as limiting students' opportunities to attend college or to enter high status occupations.
Reactions among respondents to tracking and ability grouping were mixed. Some respondents believed that tracking is useful, while others said that tracking was inappropriate for certain age groups or even harmful at any age. The beliefs were strongly held and some of our most lively discussions centered on the appropriateness of tracking. Among teachers and administrators, there was a clear demarcation between those who supported tracking and those who did not, and some respondents noted this as a source of friction. Parents, on the other hand, generally tended to support tracking and ability grouping.
The depth of feeling that we encountered about tracking is illustrated in a comment by the mother of a student at King Junior High School, a middle-achieving school in Metro City. The mother was describing her reactions after being told that her son would not be placed in a high-level math course.
It's the public schools' responsibility to educate my child with respect to his ability. I told them, I come from a family of lawyers. If he tests for scholar's math, you have to put him there. You put him there today or I'll see you in court tomorrow. That evening the principal called me and said he was put in scholar's math.
Further conversations at King Junior High School revealed that the local school board was attempting to reduce the number of students in the high-level math classes in order to implement a detracking program. The parents with whom we talked did not support the detracking philosophy. A parent had this to say about the school board's policy regarding tracking and ability grouping:
The present superintendent . . . . I don't think he has done much good for the district, frankly. My kids are out of that district and I'm very glad that they are out of there. The present board is very much against ability grouping. The board has this feeling that all kids are equal, all kids should be treated equal, and gotta be very sensitive to their needs, their social and emotional needs, and somewhere their academic needs gets left out. And to our minds, that has hurt a lot of kids because they aren't challenged. What they've done in the junior high system (King) was to take away all advanced classes except for math. My three younger children have gone through that system (King) and have not been adequately prepared for high school.
Although a number of teachers and administrators supported detracking, many favored tracking as a way to deal with individual differences in ability. In fact, one teacher at South Central Vocational High School argued for earlier tracking of students, especially for those from disadvantaged backgrounds, who are unlikely to attend college:
I think somewhere in the sixth grade we should start molding these kids. I'm talking about channeling these kids. We are gonna say, you are going to be a carpenter. You see that's your first source. That's your creativity. To develop yourself. No one says you're going to be a carpenter your whole life. But there you have a position that gives you some self worth.
The following comment from a middle school teacher in West City was perhaps most representative of the majority of math and science teachers we interviewed. "Oh yes, it is a must. You have to separate students by ability."
In sum, reactions to the practices of tracking and ability grouping were quite varied. Parents tended to support tracking and ability grouping. Several administrators expressed preference for diverse classrooms, but many tended to support tracking and ability grouping. Most math and science teachers reported that it is difficult to teach classes with students who vary greatly in aptitude and interest in these subjects. Hence, they tended to support ability groupings, though with ambivalence.
Ambivalence over tracking and ability grouping was also apparent in the ways counselors and teachers provided career guidance. While recognizing the need to provide realistic career guidance, counselors and teachers acted in ways that are consistent with ambivalence about closing doors of opportunities for students based on their past academic performance. Their focus seemed to be on encouraging current interests and desires.
Many students had high educational and occupational aspirations, regardless of socioeconomic background. One junior high school student with failing grades wanted to be a lawyer. Some high school students wanted to be athletes, doctors, and engineers. Many cases of similar optimism about career goals were found at schools in all areas at all research sites.
One student who was taking several vocational courses in math and science at Uptown High School in Metro City was enrolled in the metal works program for 11th-grade students. In addition to drafting, gym, and trigonometry, she was taking technical math, technical English, and machine shop. Her grades were average. Although these courses were not at the college preparatory level, she was planning to attend a 4-year college to become an electrical engineer. When we asked about the level of her course selections, she said that her schedule was rigorous enough to prepare her for college. In reality, the courses she was taking probably would not prepare her for the academic rigor of most engineering programs, which typically require high-level math and science skills.
In fact, like most students at most of the high schools we visited, the majority of students at Uptown High School were not taking courses that were sufficiently rigorous for selective 4-year colleges and universities. As the student described above, many students reported high educational and occupational aspirations, but these aspirations were not matched by an appropriate selection of academic classes or by their success within these classes. In contrast, students in affluent districts with similarly high aspirations were more likely to be taking rigorous courses. A number of these students were taking calculus and other advanced math courses during their senior year.
Encouraging students to hold high aspirations may have an important function. One parent of a low-achieving student encouraged her daughter's high aspirations as a way of maintaining commitment to school. Although her daughter was doing poorly in school, the mother of a girl attending Metropolitan School talked to us about how she encouraged her daughter's occupational aspirations:
I told her she got to go to school, finish the eighth grade and go to high school. She got to finish high school. I told her don't be like your mother who dropped out. She tells me when she gets old she wants to be a doctor or a lawyer. I say you got to go for it. If that's what you want, you gonna have to stay in school. You have to go to high school and you have to go to college. I want her to have a college degree. I don't want her having babies.
Some of the educators we interviewed pointed to an acute need for career guidance for students who do not plan to go to college or who do not have special talents. In their opinion, schools need to provide more career guidance than is currently available to address the issue of individual differences. The principal of South Central, for example, argued that the low-achieving students at his school need to learn the value of regular occupations, so that they can learn to hold realistic aspirations:
I know of a bus driver who sent five kids to college. He worked and was careful about spending his money. Most of the kids here think that driving buses is not where the money is at. They think of all the glitz and glamour.
The stories we heard illustrate how Americans value optimism, choice, and opportunity. This was manifested in the school setting in various ways, most notably in the area of college and career counseling. In the context of career guidance, this means that many Americans encourage aspirations for highly competitive occupations and are uncomfortable with programs that limit educational and occupational opportunities based on the economic background, achievement level, or the ability and talent of students. Many parents, as well as teachers, did indeed encourage high occupational aspirations in their children and minimized the role of individual differences in ability as an impediment to achieving these aspirations. Others, however, seemed to suggest that more realistic preparation for low-profile careers might serve the needs of some students better.