One size fits all?

Age based tracking versus ability grouping in elementary school mathematics.

Mike Robison

Mathematics Department

Michigan State University

December 1998

"States and Provinces and curricula around the world track students by age. This practice is so common that we do not think of it as tracking. With few exceptions, a six year old must go into first grade even if that six year old is not ready or was ready for the grade one year earlier" (Usiskin 98)

Introduction

One of the many challenges facing schools is the decision on how to allocate students to classrooms. Research confirms the empirical observations of many parents and educators that students learn at greatly varying rates (Walberg 1988). These different learning rates are explained by (among other things) differing learning styles, aptitudes and levels of motivation (NECTL 1994). Unfortunately for visions of "equal outcomes," due to differences in understanding, among other things, these differences in learning rates tend to increase as the child moves through the educational system (Arlin, 1984, P. 67). Given the wide variations in knowledge, motivation, and aptitude, schools must choose methods of allocating students to classes, and curriculum to classes and students.

Unfortunately, school administrators face not only conflicting messages in regard to the educational implications of various decisions, but significant pressure to base decisions either partly or mainly on nonacademic factors⁽¹⁾ (Oakes 1994 a, b and Hastings, 1992 for example). Hastings declares ability grouping to be wrong as a "philosophic absolute" and declares its use to be "totally unacceptable." The National Education Commission on Time and Learning, on the other hand, labels the act of providing the same amount of learning time to students who need varying amounts "inherently unequal" (94). They state "If we provide all students with the same amount of instructional time, we virtually guarantee inequality of achievement" (emphasis in original). The Draft for "Standards 2000' from the NCTM (NCTM 98) calls for increased equity by exposing all students, not just the elite, to challenging mathematics. There is no apparent awareness that many students do not find existing materials, whether consistent with the 1989 standards or not, challenging.

In addition to the variety of factors complicating decisions, schools must decide from a wide range of potential educational structures. Often the same name is applied to different systems, or different names to the same system. In addition, the systems are seldom mutually exclusive and research frequently fails to distinguish which factors cause results (NECTL 1994). This paper focuses mainly on mathematics in elementary schools, "ability grouping," and on highly capable or "gifted" students, although both other educational systems and other categories of student are discussed. This paper's⁽²⁾ definition of ability grouping is adopted from Marshall vs Georgia (1984, 1985). Four features distinguish this system, referred to in Marshall as "achievement grouping" (from Grossen 1996): 1. "A combination of academic factors was taken into consideration with primary emphasis being placed on a child's actual performance in the basal instructional series (18-19)." 2. Students' assignments to levels can vary with subject area and there is some movement between levels. 3. Specialization allows greater individualization of instruction. 4. Performance improves for lower level students.

Literature, Issues, and Analysis

I could not locate any direct reference, favorable or otherwise, to grouping strategies in the NCTM Curriculum Standards (NCTM). There is an acknowledgment in the Teaching Standards (4) that not every child will have the same capabilities in mathematics. Similarly, Standard 8, Learning Environments, calls on teachers to have high expectations for all and extend prior knowledge (Teaching, 115). Finally, the assessment standards argue for "high expectations for all students, envisioning a mathematics education that develops each student's mathematical power to the fullest" [emphasis added] (NCTM 1995). From the NCTM Agenda for action "The student most neglected, in terms of reaching full potential, is the gifted student of mathematics" (NCTM 1980). This all could be read to support grouping of students by ability, although it is clearly not a priority of most of the writers.

Focusing on educational concerns at the expense of socio-political issues still leaves numerous questions about the most effective methods of educating students. There are a vast number of studies of grouping strategies, according to Rogers (98) approximately 750. There are so many in fact that "meta studies" which attempt to summarize and interpret the flood of studies are common (Slavin and Kulik, various), and a literature has developed which compares and contrasts the meta studies (Grossen 1996a, Rogers, 1991, 1998). In general, Slavin is cited by supporters of heterogeneous grouping (not by ability) and Kulik by supporters of homogenous grouping (ability grouping).

Along with her political objections to grouping, Oakes argues that high achieving students benefit from "higher quality" teachers (85). This claim is specifically rejected by Rogers's more recent work (98). Oakes argues, much more credibly, that lower Socioeconomic Status (SES) students are more likely to be assigned to lower tracks/groups, for a given ability level (1994a). This argument at least acknowledges that there is a range of ability among children. The position of this paper is that student ability varies greatly within demographic (racial, gender, or socioeconomic, for example) groups and little between those groups⁽³⁾. The academic skills of disadvantaged gifted children may not be quite as advanced at the time that they start school, but it is quite plausible that the gap between ability and curriculum is even larger. As such, gifted programs are even more important for minority and lower SES children⁽⁴⁾. If the intellectual needs of high SES children are not being met, the parents can always resort to private schools, if pressuring the school to provide appropriate education is unsuccessful. Lower SES families have fewer or no other options and frequently lack the "Cultural Capital" to challenge school authorities. In addition some of these children face peer and family pressures not to achieve in school (Beck).

In National Excellence: A case for developing America's talent, the U.S. Department of Education notes that "The belief espoused in school reform that children from all economic and cultural backgrounds must reach their full potential has not been extended to America's most talented students." They also argue that these problems are most pronounced with disadvantaged and minority students. While the main focus is on upgrading the curriculum across the board, they do focus on the special problems of gifted minority students. According to the Department of Education information, more than 18 percent of Black students who score over 1,400 on the SAT leave school for academic reasons. Hebert discussed the family and social situations of two gifted black males, in an attempt to find explanations and solutions (Hebert). In comparing two gifted back students, he found that two main factors impacted achievement, mainly through their influence on the "sense of self." The successful student had a strong family support system and numerous opportunities to study with other high achievers. This support system allowed him to overcome peer pressure not to study. The second student's family was less supportive of his studies (although certainly he was in a better situation than many children in low SES households). But even more important, he was trapped in a cycle of underachievement and lack of challenge. He was placed in basic level classes, surrounded by students who could not grasp the material as well as he did. Significantly, it was not an issue of being surrounded by bad academic influences. The students in the class put in far more effort than he did (405) but he still dominated the class. The lack of a challenging curriculum was destroying his motivation, while the rest of the students were struggling with the same material.

Slavin (86, 87, 90, 91, 92) discusses "high ability" students, but specifically excludes the top 2-3%. His high ability group is the top third, less the top 2 to 3 percent. He also specifically supports within class ability grouping of elementary students, especially for low ability students. This is consistent with his own studies, as reported by Rogers (98), along with the results of Kulik (82, 84, 84, 91) and Vaughn, Feldhusen and Asher (91) as reported in Rogers. Slavin is sometimes cited in attempts to eliminate ability grouping in general or gifted programs specifically, but there is no support for this position in his analysis. Linchevski and Kutscher report that in their study, ability grouping had no positive impact on high ability students, but the paper has "high ability" defined in practice as approximately the top 40% of students. Their analysis shows statistically insignificant results for this group, along with improvements in achievement for low and middle ability students from mixed ability grouping. Perhaps significantly, they don't say whether the study incorporated official curriculum differentiation, although they mention that the high ability class had superior exposure to mathematical formalism. Their arguments are irrelevant to a gifted and talented program, but do support the non-controversial position of the NCTM and others that low and middle ability students can learn more than they have been.

This introduces another issue that is related to ability grouping, the question of what is being taught. Some structures involve grouping based on ability, but do not adjust the curriculum. Others differentiate the curriculum to varying degrees in an attempt to match content to ability, with or without physically regrouping. In spite of the frequent use of his work to justify elimination or reduction of ability grouping, Slavin concludes that successful ability grouping requires adjusting instruction to student's performance levels (Slavin, cited in Grossen 1996a). Similarly, Kulik concludes "Bright, average, and slow youngsters profit from grouping programs that adjust the curriculum to the aptitude levels of the groups. Schools should try to use ability grouping in this way." (Kulik 98) Rogers concludes that while high ability learners benefit the most from like ability grouping, (since their needs are farthest from the typical teaching) middle and low ability learners also benefit academically from like ability groups (Rogers 98, listing numerous such studies). Rogers also finds that students at all levels generally benefit in regard to socialization and behavior in like ability groups (98, again with numerous sources). Abadzi suggests that there is correlational evidence that "classification in low ability groups is associated with lower self concept, lower achievement motivation . . ." She doesn't claim cause and effect, and there is an obvious potential for low achievement to lead to low ability classification (Abadzi).

Kulik and Kulik (in Colangelo and Davis) contrast the formal nature of their "meta analysis" with the informal studies of Slavin (87 etc.) and Oakes (85). They also report that Slavin's (87, 88) general and specific conclusions are not supported in their research. Outside of class gifted programs were found to have statistically and educationally significant impacts in 11 of 25 studies, all of which were positive. Although the results involved less data, in-class grouping was also found to be positive. "Positive . . . academic benefits are striking and large in programs of acceleration for gifted students" (190). They specifically contrast these analytic conclusions with the "speculations of Slavin and Oakes." Interestingly, Kulik and Kulik find that impacts of homogenous grouping on self-esteem are slightly negative for high ability students and slightly positive for low ability students. The suggestion is that exposure to peers is reassuring for lower performing students, and exposure to peers is a mild shock to some gifted students. This also contradicts claims of gifted programs necessarily leading to elitism. Based on their vast research into grouping and education, particularly of gifted students, Kulik and Kulik prepared a set of guidelines:

1. Although some school programs that group children by ability have only small effects, other grouping programs help children a great deal. Schools should therefore resist calls for the wholesale elimination of ability grouping.

2. Highly talented youngsters profit greatly from work in accelerated classes. Schools should therefore try to maintain programs of accelerated work.

3. Highly talented youngsters also profit greatly from an enriched curriculum designed to broaden and deepen their learning. Schools should therefore try to maintain programs of enrichment.

4. Bright, average, and slow youngsters profit from grouping programs that adjust the curriculum to the aptitude levels of the groups. Schools should try to use ability grouping in this way.

5. Benefits are slight from programs that group children by ability but prescribe common curricular experiences for all ability groups. Schools should not expect student achievement to change dramatically with either establishment or elimination of such programs.

We note that Kulik's comments on differentiation do not have to conflict with the access to algebra, geometry, etc. called for by the NCTM. All students can be exposed to such topics, with the nature of the material varying with the demonstrated ability of the students (Ideally, not with age, as a classification, as discussed below).

Various examples exist in the literature demonstrating the ability of gifted students to master more advanced material at earlier ages and in more abstract forms than typical students do. Mason used the Van Heile model of Geometric understanding to study gifted Middle School students who had not been exposed to a formal course in Geometry. Some gifted K-8 students were brought to level 3 understanding (in the 1-5 version of the scale) in six hours of instruction. A collection of 6^th to 8^th grade gifted students showed clearly superior Van Heile understanding, in comparison with a comparison group of 10^th graders starting geometry (the comparison group was from Senk). The 6^th graders in the gifted group had clearly superior understanding in comparison to the general group of 10^th graders. In addition to the high knowledge levels, before a formal course, the students often reasoned correctly in cases where they were wrong about definitions. Mason concluded that, based on the data, and using Senk's models to predict success, properly selected middle school students should be successful in a proof oriented geometry class, in some cases with a minor orientation period (Mason).

There are many possible ways to address the different academic needs of gifted elementary school children. One method which has logical merit but which meets with much opposition is acceleration, whether subject or across the board. Critics commonly argue that children need to be with their age mates for social reasons. This argument is rejected by gifted experts, who say that age mates are not really peers for the truly gifted (Winner and von Karolyi). They also reject arguments such as that of Slavin (91) that "gifted kids will be fine no matter what⁽⁵⁾." Winner and von Karolyi discuss several aspects of the social isolation of gifted students in regular settings.

In fact the idea that all students of a certain age should learn the same thing at the same pace is relatively new, having been developed in the mid 19^th century for administrative, not educational reasons (Bacharach, Hasslen, and Anderson; Daniel and Cox). As discussed above and in Prisoners of Time (National Education Commission on Time and Learning) these writers argue for learning environments where age doesn't limit opportunity. While Bacharach et. al. are not focused on gifted children, they make a good argument for grouping students of differing ages together. Since the literature discussed above demonstrates the value of grouping students by ability, while few if any studies support restricting grouping to common ages, it is ironic that so many schools are moving from the former to the latter.

Daniel and Cox classify flexible pacing as "any provision that places students at an appropriate instructional level . . . and allows them to move forward in the curriculum as they achieve mastery" (2). "High ability students are the most likely to be frustrated in the generalized age-in-grade lockstep that characterizes most schooling in this country." (3). Daniel and Cox report on several flexible pacing and continuous progress systems. EQUIP, in Salt Lake City, Utah, for example, is a large gifted program which focused on Problem Solving, and thinking and writing skills. There were significant successes, including a fifth grader successfully doing traditional high school Geometry. In addition, while some students were the sort of high achieving gifted that opponents of gifted programs want to keep in heterogeneous classrooms as good examples, "many of these students did not fare well in traditional classrooms" (12). Daniel and Cox also report that many flexible pacing programs, which are originally introduced in limited circumstances, such as gifted programs or math only, were often expanded to the whole school due to their success. The EQUIP school had a similar program for regular students, and some children moved into the EQUIP program as the years passed. The superintendent of one school reports that all students share an improved sense of achievement. Slower students aren't formally held back, removing the potential stigma, and students who learn faster are allowed to keep learning. Also, since, as Bachman notes, older students in a group are more likely to fill leadership roles, slower students grouped with younger, faster learning students, experience leadership opportunities.

Conclusions

As indicated above, children learn at widely varying rates. Obviously, not all six year olds are at the same level in learning, but most schools continue to act as though they are, or insist that they should be. The literature clearly demonstrates the educational advantages of ability grouping for gifted students, and strongly suggests that students in other categories also benefit, given appropriate curriculum. I suggest a model of elementary mathematics education that moves rapidly away from age grouping, to grouping students by ability. Initially, students with less outside enrichment, for a given level of ability, might start at a more basic level. The elimination of provisions restricting access to material to certain age groups would allow highly capable disadvantaged youngsters to move up, based on ability, as illustrated by the Salt Lake example of Daniel and Cox (18).

All students would pass through a similar curriculum⁽⁶⁾, with some allowances for enrichment. The primary difference would be pace. While some writers argue the need to keep gifted students around as "good examples" and others argue that this is both pointless and unfair (NECTL, Kulik, Silverman, Rogers, etc.) Bacharach, Hasslen and Anderson argue that older children in mixed age groups tend to take on leadership roles (15). It seems clearly unfair and unjustified to limit a child's opportunity to learn for adult's political goals, and to serve as some sort of example for other students. Since the groups consist of students at similar levels, this process counteracts the tendency for the outgoing gifted child to dominate cooperative group arrangements. Quoting M. Hunter (1964) from Daniel and Cox "Expecting all children the same age to learn from the same materials is like expecting all children the same age to wear the same size clothing."

Bibliography:

1.

^0. The supposed merits of basing educational decisions on sociopolitical factors will not be discussed here. The educational merits of ability grouping or not ability grouping, for various categories of students, are discussed.

2.

^0. As distinguished from tracking, which features, among other things, "permanent, comprehensive" decisions about placement and no "compensatory provisions." Tracking is also commonly associated with placements based on racial or socioeconomic factors unrelated to educational achievement.

3.

^3. Sowell discusses the varying IQ scores of different immigrant groups, showing that it is common for groups which are outside the mainstream to score lower (as a group) on IQ tests and the like. These same groups have moved to at least average levels as they adapted to American society (Sowell 1995). The presence of students with high intellectual ability under less than ideal socioeconomic conditions is dramatically illustrated in Jenkins.

4. For an example of a program to expand (demographically) the range of students participating in a Gifted and Talented program, see Keynes.

5. A similar argument is noted, and rejected, by the President of the American Psycological Association, Martin Seligman (Seligman).

6. Aside form this issue, the Standards 2000 documents provide an excellent model for such a curriculum.