Defining Giftedness

ERIC_NO: ED262519
TITLE: Defining Giftedness. 1985 Digest.
AUTHOR: McClellan, Elizabeth
PUBLICATION_DATE: 1985
AVAILABILITY: ERIC Clearinghouse on Handicapped and Gifted Children, 1920 Association Dr., Reston, VA 22091 (one free copy).
FULL_TEXT:
WHAT IS GIFTEDNESS?

Historically, giftedness has been closely linked with the concept of genius. This association began around the turn of the century when psychologists developed tests that were designed to measure intelligence (Termam 1925); people who scored on the low end of the scale were labeled retarded, and those who scored on the high end were considered geniuses.

The use of intelligence tests as the single measure of giftedness has been greatly criticized in recent years, primarily because the tests are often biased in favor of the white middle class and because they penalize children with differing linguistic styles.

Also, many researchers and educators have come to believe that giftedness is more than high intellectual ability; it also includes creativity, memory, motivation, physical dexterity, social adeptness, and aesthetic sensitivity.

Dissatisfaction with a limited perspective has led researchers and educators to develop "broadened" definitions. One of the first educators to write about such an expansion was Hollingsworth. Although her research focused on children with IQ's above 170, Hollingsworth believed that children can have other types of gifts, such as mechanical aptitude or artistic ability (Pritchard 1951).

During the 1840s, the conception of giftedness was expanded further when the federal government began to take an interest in the education of gifted and talented children. This federal interest was sparked during and after World War II when policy makers perceived a need for technological advancement in order to maintain the nation's military and political superiority.

By 1950, Congress had passed the National Science Foundation Act which marked the first time the federal government provided funds specifically for the gifted and talented (Zettel 1982). By providing funds for encouraging students to develop their abilities in mathematics and the physical sciences, the Act led, in essence, to the designation of specific academic aptitude as a type of giftedness.

Another significant development in defining giftedness was the publication of Guilford's (1959) studies of the structure of the intellect. As early as 1950, Guilford had urged psychologists to explore the area of creativity, or divergent thinking, but it was his structural model of the 120 theoretical components of intelligence that led to the development of tests to measure intellectual abilties other than those measured by conventional IQ tests.

The development of creativity tests and the results of many studies of the relationship between intelligence and creativity (Getzels and Jackson 1962) have led many educators to include creativity in their definitions. Renzulli (1976), for example, considers giftedness to be a combination of above average ability, creativity, and task commitment.

In 1969, Congress mandated a study by the U.S. Commissioner of Education to determine the extent to which the needs of gifted and talented children were being met (Sisk 1980). The ensuing document, known as the Marland Report (1972), contains a definition of giftedness that has been and continues to be the one most widely adopted or adapted by state and local education agencies. The Report states:

Gifted and talented children are those identified by professionally qualified persons who, by virtue of outstanding abilities, are capable of high performance. These are children who require differential educational programs and/or services beyond those provided by the regular school program in order to realize their contribution to self and the society.

Children capable of high performance include those with demonstrated achievement and/or potential ability in any of the following areas, singly or in combination:

--General intellectual ability

--Specific academic aptitude

--Creative or productive thinking

--Leadership ability

--Visual and performing arts

--Psychomotor ability

Although the definition has been criticized as being limiting (Reis and Renzulli 1982) and of promoting elitism (Feldman 1979), more than 80% of the 204 experts polled for their reactions to the Marland definition agreed with the selection of the categories of high intellectual ability, creative or productive thinking, specific academic aptitude, and ability in visual or performing arts. Approximately half of the experts agreed that social adeptness and psychomotor ability should be included (Martinson 1975).

The federal government has included five broad areas in the definition found in the Omnibus Budget Reconciliation Act of 1981. In this act, block grants for education have been provided to the states; some of these funds may be used for:

special programs to identify, encourage, and meet the special educational needs of children who give evidence of high performance capability in areas such as intellectual, creative, artistic, leadership capacity, or specific academic fields, and who require services or activities not ordinarily provided by the school in order to fully develop such capabilities.

More recently, the Regulations for the Educational Security Act of 1984, which provides grants for strengthening the skills of teachers and instruction in mathematics, science, foreign languages, and computer learning have defined the term "gifted student" as a "student, identified by various measures, who demonstrates actual or potential high performance capability in the fields of mathematics, science, foreign languages, or computer learning." Gifted students may come from "historically underrepresented and underserved groups, including females, minorities, handicapped persons, persons of limited English-speaking proficiency, and migrants.

By placing an emphasis on math, science, foreign languages, and computer learning, this latest federal definition highlights the fact that the ways in which schools operationally define giftedness are often based on the needs of society. Definitions are also influenced by cultural and socioeconomic factors.

As Bernal points out, "what is clever and creative for a child in the barrio or on the reservation, where different value systems are in operation, will not be the same as for the child who grows up in the suburbs" (1974). For economically disadvantaged populations that place a heavy emphasis on preparing students for employment rather than college, a definition might recognize that students can be gifted in areas that are generally nonacademic in nature, such as carpentry or mechanics (McClellan 1984).

WHY DO WE NEED TO DEFINE GIFTEDNESS?

A definition of giftedness is the foundation upon which an educational program for gifted children is built. The specific abilities included in a definition determine the kinds of identification criteria that are used to select children for a program and the kinds of educational services that are provided to those children. The selection of abilities to be included in a definition is, therefore, very important to educators who must determine which children are designated as gifted and what kinds of educational services are provided to them.

For example, a definition that incorporates creativity as a category suggests that schools provide experiences aimed at developing the potential of children who have been identified as being creative; a definition that includes leadership ability suggests other types of identification criteria and educational experiences.

Educators who are charged with the reponsibility of creating or maintaining programs for gifted children and youth face a different task when they must decide what giftedness is, how gifted children can be identified, and what services schools should provide. The following points are a guide for helping them make those decisions:

--The concept of giftedness is not limited to high intellectual ability. It also comprises creativity, ability in specific academic areas, ability in visual or performing arts, social adeptness, and physical dexterity.

--A program for gifted children should be based on the way in which the school system operationally defines giftedness. A definition should be the basis of decision regarding the selection of identification procedures as well as the provision of educational services for gifted children.

--Definitions of giftedness are influenced by social, political, economic, and cultural factors.

--Giftedness is found among all groups, including females, minorities, handicapped persons, persons with limited English-speaking proficiency, and migrants.

FOR MORE INFORMATION

Bernal, E. M. "Gifted Mexican American Children: An Ethnoscientific Perspective." CALIFORNIA JOURNAL OF EDUCATIONAL RESEARCH 25 (1974):261-273.

Feldman, D. "Toward a Nonelitist Conception of Giftedness." PHI DELTA KAPPAN (1979):660-663.

Getzels, J. W. and P. W. Jackson. CREATIVITY AND INTELLIGENCE. London: John Wiley and Sons, 1962.

Guilford. J. P. "Three Faces of Intellect." AMERICAN PSYCHOLOGIST 14 (1959):469-479.

Marland, S. P. EDUCATION OF THE GIFTED AND TALENTED. Report to the Congress of the United States by the U.S. Commissioner of Education. Washington, DC: U.S. Government Printing Office, 1972.

Martinson, R. A. THE IDENTIFICATION OF THE GIFTED AND TALENTED. Reston, VA: The Council for Exceptional Children, 1975.

McClellan, E. DEFINING GIFTEDNESS: AN ETHNOGRAPHIC APPROACH. Paper presented at the American Educational Research Association Annual Meeting, New Orleans, LA, 1974.

OMNIBUS BUDGET RECONCILIATION ACT OF 1981, Section 582, 42 USC 3842.

Pritchard, M. C. "The Contribution of Leta Hollingsworth to the Study of Gifted Children." In THE GIFTED CHILD, edited by P. Witty. New York: D.C. Heath, 1951.

REGULATIONS FOR THE EDUCATION FOR ECONOMIC SECURITY ACT OF 1984. Part 208, Section 208.3

Reis, S. M. J. S. Renzulli. "A Case for a Broadened Conception of Giftedness." PHI DELTA KAPPAN 63 (1982):619-620.

Renzulli, J. "What Makes Giftedness?" PHI DELTA KAPPAN 60 (1978):180-184.

Sisk, D. "Issues and Future Directions in

Terman, L. GENETIC STUDIES OF GENIUS: VOLUME 1, MENTAL AND PHYSICAL TRAITS OF A THOUSAND GIFTED CHILDREN. Stanford, CA: Stanford University Press, 1925.

Zettal, J. J. "The Education of Gifted and Talented Children from a Federal Perspective." In SPECIAL EDUCATION IN AMERICA: ITS LEGAL AND GOVERNMENTAL FOUNDATIONS, edited by J. Ballard, and others. Reston, VA: The Council for Exceptional Children, 1982.

This Digest was prepared for the Clearinghouse on Handicapped and Gifted Children, 1985.

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This publication was prepared with funding from the Office of Educational Research and Improvement, U.S. Department of Education, under OERI contract. The opinions expressed in this report do not necessarily reflect the positions or policies of OERI or the Department of Education.

ERIC_NO: ED370295
TITLE: Should Gifted Students Be Grade-Advanced? ERIC Digest E526.
AUTHOR: Lynch, Sharon J.
PUBLICATION_DATE: 1994
AVAILABILITY: Council for Exceptional Children, 1920 Association Dr., Reston, VA 22091-1589 ($1 each, minimum order $5 prepaid).
FULL_TEXT:
SHOULD GIFTED STUDENTS BE GRADE-ADVANCED?

Intellectually gifted and academically talented students are able to learn material rapidly and understand concepts deeply. Keeping them challenged and learning to their capacity can require changes in their regular school programs. Education programs for children identified as gifted and talented take many forms: pull-out programs offering educational enrichment, honors classes, afterschool and summer programs featuring special course work, and mentor programs in which children are matched with professionals in the community for special learning experiences.

Sometimes, gifted youngsters may be so advanced in knowledge and so clearly operating at an intellectual level beyond that of their same-age peers that educational acceleration is a realistic and desirable alternative to normal grade-level work. Educational acceleration is often perceived simply as placing a child one or more grades ahead with older children. For instance, a child who has completed the fourth grade may be double-promoted to the sixth, skipping fifth grade entirely. Sometimes, if children are especially talented in one subject area (most often mathematics, science, or English), they may be allowed to take advanced courses with older students in that subject while remaining in their own grade for other subjects. Another alternative is to have gifted children tutored and advanced in given subjects, either individually or in small groups of children with similar talents. For instance, a group of high school students might meet for advanced mathematics classes twice a week with a professor from a local university.

These arrangements are all appropriate for children who are intellectually and academically capable of learning at a faster pace and in greater depth than their same-age peers, and who are motivated to do so. Insisting that gifted and talented students remain with their age-mates at all costs may exact too high a cost from them. It may result in boredom and daydreaming, poor study habits, behavior problems, or school avoidance. But the decision to allow a child to accelerate educationally is one that must be made for each child, taking into account his or her intellectual and emotional needs and the services the school can provide.

IS EDUCATIONAL ACCELERATION HARMFUL TO THE CHILD ACADEMICALLY?

The majority of studies have shown that children who have been educationally accelerated do not suffer academically. Their grades are higher than those of their peers who chose not to accelerate, and they compare favorably with those of older students in their classes. Accelerated students also report heightened interest in and enthusiasm for school.

BUT WON'T THERE BE GAPS IN THE CHILD'S KNOWLEDGE?

If children skip one or more grades, they may occasionally encounter unfamiliar material from the skipped grade. Therefore, arrangements should be made to allow the children to cover any such material without penalty as it is encountered. Because there is repetition in normal curricula, gaps occur less often than one might think and are seldom a significant problem for the gifted and talented student, who learns quickly and well.

IS EDUCATIONAL ACCELERATION HARMFUL TO THE CHILD

EMOTIONALLY OR SOCIALLY?

This aspect of educational acceleration seems to worry parents and educators most. In general, children who are well-adjusted and socially at ease before accelerating report having two groups of friends--they belong to a circle of older students, but they also retain friendships with children who are the same age.

Children who are socially withdrawn or who have difficulty making friends may experience similar problems when placed with older children. On the other hand, there are cases in which a gifted child is more comfortable with older children than with age-mates. This may be true more often for girls than boys. The receiving classroom teacher in an accelerated setting can help the younger student find a niche among the older students.

WHAT DO EDUCATORS THINK OF THE EDUCATIONAL ACCELERATION

OPTION?

Research about acceleration consistently documents positive effects, both academic and social, for children who have accelerated, but educators have been slow to embrace the option. Fears about social and emotional development problems for these children are common. However, people who specialize in working with gifted and talented children and teachers and parents who have had personal experience with educational acceleration tend to be more positive.

HOW DO PARENTS KNOW IF THEIR CHILD SHOULD ACCELERATE?

If children's standardized test scores, particularly achievement test scores, are many grades above level or off the charts entirely, they are good candidates for acceleration. If a child who was previously an avid student begins to complain of boredom or starts misbehaving in school, it may be an indication that he or she needs additional challenges (but remember that any child may be bored or have behavior problems). Ideally, the decision to accelerate should be mutual--the child, parents, and school officials all agreeing that it would serve the child well. The school psychologist or Individualized Educational Plan (IEP) committee should be consulted early in the process.

WHEN SHOULD ONE BE CAUTIOUS ABOUT ACCELERATION?

If the child under consideration for acceleration is physically or emotionally immature, is pushed into the process by adults, or receives constant negative feedback at school from peers or educators, problems could occur. If the school accelerates students routinely so that an accelerated youngster does not stand out as peculiar and has a small support group of similar youngsters, then chances for an easy adjustment increase.

A child who has been accelerated may find that he or she is no longer the best in the class. Both parents and the child should be ready for this. Parents should be supportive, but never put undue pressure on the gifted and talented child to perform--certainly not when he or she is adjusting to a new environment. The decision to academically accelerate a child may be reversed at any time if it appears not to be working out for the child academically, socially, or emotionally. Adults should help children in this situation understand that the change is not a failure.

WHAT ABOUT ACCELERATION IN A SINGLE SUBJECT?

This option tends to meet with less resistance from educators than grade-skipping because children still take most classes with their age-mates, alleviating concerns about social problems. Here, continuity is crucial. Accelerating students one year, only to have them repeat the material the next, is no solution. Teachers or curriculum specialists can be helpful in determining what aspects of a subject are covered in each grade. Accelerated students may need to make special arrangements to travel to a junior high or high school, or even take a college course before high school graduation. It is important to obtain the cooperation of the school district throughout the child's educational career. Transportation problems may prove more difficult to solve than academic or social ones.

WHAT ARE THE STEPS IN MAKING THE DECISION TO

ACCELERATE?

Assuming that parents and student agree to explore this option, parents might begin by discussing it with the school's coordinator for the gifted and talented, guidance counselor, or principal--whichever person knows the child best. The classroom teachers' opinions also should be sought. Next, the child's academic potential and social and emotional adjustment should be evaluated by a school psychologist. The final decision will probably be made by the school's IEP committee or the principal. It helps to have the enthusiastic support and understanding of the teachers who will be working with the accelerated child, as well as commitments for continuity and coordination from school authorities. Parents considering this option may find it helpful to contact the coordinator for gifted and talented education at their state department of education.

SOURCES

Most of the following references--those identified with an ED or EJ number--have been abstracted and are in the ERIC database. The journal articles should be available at most research libraries. For a list of ERIC collections in your area, contact ACCESS ERIC at 1-800-LET-ERIC (538-3742).

Brody, L.E. and C.P. Benbow (Summer 1987). "Accelerative Strategies: How Effective Are They for the Gifted?" Gifted Child Quarterly, 31 (3), 105-109. EJ 363 446.

Cornell, D.G., C.M. Callahan, L.E. Bassin, and S.G. Ramsey (1991). Chapter 3: "Affective Development in Accelerated Students." In W.T. Southern and E.D. Jones (Eds.), Academic Acceleration of Gifted Children. New York: Teachers College Press.

Davis, G.A. and S.B. Rimm (1989). Education of the Gifted and Talented. Chapter 5: "Acceleration." Englewood Cliffs, NJ: Prentice Hall.

Feldhusen, J.F., T.B. Proctor, and K.N. Black (September 1986). "Guidelines for Grade Advancement of Precocious Children." Roeper Review, 9 (1), 25-27. EJ 343 937.

Kulik, J.A. and C.C. Kulik (October 1984). "Synthesis of Research on Effects of Accelerated Instruction." Educational Leadership, 42(2), 84-89. EJ 308 281.

Lynch, S. (Winter 1990). "Credit and Placement Issues for the Academically Talented Following Summer Studies in Science and Mathematics." Gifted Child Quarterly, 34 (1), 27-30. EJ 408 556.

Southern, W.T., E.D. Jones, and E.D. Fiscus (Winter 1989). "Practitioner Objections to the Academic Acceleration of Gifted Children." Gifted Child Quarterly, 33 (1), 29-35. EJ 392 219.

Tolan, S. (1990). Helping your highly gifted child. ERIC Digest #E477. ED 321 482.

For more information on this subject, contact:
ERIC Clearinghouse on Disabilities and Gifted Education
Council for Exceptional Children
1920 Association Drive
Reston, VA 22091-1589
(703) 264-9474

Written by Sharon J. Lynch, Ph.D., The George Washington University, School of Education and Human Development.

This publication was prepared by ACCESS ERIC with funding from the Office of Educational Research and Improvement, U.S. Department of Education, under Contract No. RR93002005. The opinions expressed in this brochure do not necessarily reflect the positions or policies of the Department of Education. The brochure is in the public domain. Authorization to reproduce it in whole or in part is granted.

ERIC_NO: ED342175
TITLE: Differentiating Curriculum for Gifted Students. ERIC Digest #E510.
AUTHOR: Berger, Sandra L.
PUBLICATION_DATE: 1991
AVAILABILITY: Council for Exceptional Children, Publication Sales, 1920 Association Dr., Reston, VA 22091-1589 ($1.00 each, minimum order $5.00 prepaid).
FULL_TEXT:
Students who are gifted and talented are found in full-time self-contained classrooms, magnet schools, pull-out programs, resource rooms, regular classrooms, and every combination of these settings. No matter where they obtain their education, they need an appropriately differentiated curriculum designed to address their individual characteristics, needs, abilities, and interests.

DEVELOPING AN EFFECTIVE CURRICULUM

An effective curriculum for students who are gifted is essentially a basic curriculum that has been modified to meet their needs. The unique characteristics of the students must serve as the basis for decisions on how the curriculum should be modified (Feldhusen, Hansen, & Kennedy, 1989; Maker 1982; TAG, 1989; VanTassel-Baska et al., 1988).

It is difficult to generalize about students who are gifted because their characteristics and needs are so personal and unique. However, as a group they comprehend complex ideas quickly, learn more rapidly and in greater depth than their age peers, and may exhibit interests that differ from those of their peers. They need time for in-depth exploration, they manipulate ideas and draw generalizations about seemingly unconnected concepts, and they ask provocative questions.

A program that builds on these characteristics may be viewed as qualitatively (rather than quantitatively) different from the basic curriculum; it results from appropriate modification of content, process, environment, and product (Maker, 1982).

MODIFYING CONTENT

Content consists of ideas, concepts, descriptive information, and facts. Content, as well as learning experiences, can be modified through acceleration, compacting, variety, reorganization, flexible pacing, and the use of more advanced or complex concepts, abstractions, and materials. When possible, students should be encouraged to move through content areas at their own pace. If they master a particular unit, they need to be provided with more advanced learning activities, not more of the same activity. Their learning characteristics are best served by thematic, broad-based, and integrative content, rather than just single-subject areas. An entire content area arranged and structured around a conceptual framework can be mastered in much less time than is traditionally allotted (VanTassel-Baska, 1989). In addition, such concept-based instruction expands opportunities to generalize and to integrate and apply ideas. (See Bruner, 1966, MAN: A COURSE OF STUDY [MACOS] for an example of a thematic, integrated curriculum.)

Middle and secondary schools are generally organized to meet student needs within content areas. Providing an interdisciplinary approach is another way of modifying curriculum . Jacobs and Borland (1986) found that gifted students benefit greatly from curriculum experiences that cross or go beyond traditional content areas, particularly when they are encouraged to acquire an integrated understanding of knowledge and the structure of the disciplines.

MODIFYING PROCESS

To modify process, activities must be restructured to be more intellectually demanding. For example, students need to be challenged by questions that require a higher level of response or by open-ended questions that stimulate inquiry, active exploration, and discovery. Although instructional strategies depend on the age of the students and the nature of the disciplines involved, the goal is always to encourage students to think about subjects in more abstract and complex ways. Activity selection should be based on student interests, and activities should be used in ways that encourage self-directed learning. Bloom's TAXONOMY OF EDUCATIONAL OBJECTIVES (1956) offers the most common approach to process modification. His classification system moves from more basic levels of thought, such as memory or recall, to more complex levels of analysis, synthesis, and evaluation. Parnes (1966), Taba (1962), and others have provided additional models for structuring thinking skills. Every teacher should know a variety of ways to stimulate and encourage higher level thinking skills. Group interaction and simulations, flexible pacing, and guided self-management are a few of the methods for managing class activities that support process modification.

MODIFYING ENVIRONMENT

Gifted students learn best in a receptive, nonjudgmental, student-centered environment that encourages inquiry and independence, includes a wide variety of materials, provides some physical movement, is generally complex, and connects the school experience with the greater world. Although all students might appreciate such an environment, for students who are gifted it is essential that the teacher establish a climate that encourages them to question, exercise independence, and use their creativity in order to be all that they can be.

MODIFYING PRODUCT EXPECTATION AND STUDENT RESPONSE

Teachers can encourage students to demonstrate what they have learned in a wide variety of forms that reflect both knowledge and the ability to manipulate ideas. For example, instead of giving a written or oral book report, students might prefer to design a game around the theme and characters of a book. Products can be consistent with each student's preferred learning style. They should address real problems, concerns, and audiences; synthesize rather than summarize information; and include a self-evaluation process.

ASSESSING CURRICULUM EFFECTIVENESS

In their synthesis of curriculum effectiveness studies and effective practice, VanTassel-Baska et al. (1988) suggested that differentiated curriculum would respond to diverse characteristics of gifted learners in the following three ways:
* By accelerating the mastery of basic skills through testing-out procedures and reorganization of the curriculum according to higher level skills and concepts.
* By engaging students in active problem-finding and problem-solving activities and research.
* By providing students opportunities for making connections within and across systems of knowledge by focusing on issues, themes, and ideas.

Curriculum development is a dynamic, ongoing process. Special attention needs to be paid to articulation, scope, and sequence to avoid gaps and repetition through grade levels; ensure that the understandings and skills we expect children to develop fit together; and assure that children are provided with the knowledge and skills that will prepare them for the future. Periodic evaluations of curriculum effectiveness allow corrections to be made when needed, and they are essential if curriculum is to meet the long-term needs of gifted students for increasingly complex and challenging opportunities.

CONCLUSION

The curriculum committee of the Leadership Training Institute (Passow, 1982) developed seven guiding principles for curriculum differentiation that reflect the considerations described in this Digest.
1. The content of curricula for gifted students should focus on and be organized to include more elaborate, complex, and in-depth study of major ideas, problems, and themes that integrate knowledge within and across systems of thought.
2. Curricula for gifted students should allow for the development and application of productive thinking skills to enable students to reconceptualize existing knowledge and/or generate new knowledge.
3. Curricula for gifted students should enable them to explore constantly changing knowledge and information and develop the attitude that knowledge is worth pursuing in an open world.
4. Curricula for gifted students should encourage exposure to, selection, and use of appropriate and specialized resources.
5. Curricula for gifted students should promote self-initiated and self-directed learning and growth.
6. Curricula for gifted students should provide for the development of self-understanding and the understanding of one's relationship to persons, societal institutions, nature, and culture.
7. Evaluations of curricula for gifted students should be conducted in accordance with the previously stated principles, stressing higher level thinking skills, creativity, and excellence in performance and products.

Developing curriculum that is sufficiently rigorous, challenging, and coherent for students who are gifted is a challenging task. The result, however, is well worth the effort. Appropriately differentiated curriculum produces well-educated, knowledgeable students who have had to work very hard, have mastered a substantial body of knowledge, and can think clearly and critically about that knowledge. Achieving such results for one or for a classroom full of students who are gifted will produce high levels of satisfaction, not only for the students who are beneficiaries, but also for every teacher who is willing to undertake the task.

REFERENCES

Bloom, B.S. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook I: Cognitive domain. New York: Longmans, Green.

Bruner, J.S. (1966). Toward a theory of instruction. New York: Norton.

Feldhusen, J., Hansen, J., & Kennedy, D. (1989). Curriculum development for GCT teachers. GCT, 12(6), 12-19.

Jacobs, H., & Borland, J. (1986). The interdisciplinary concept model: Theory and practice. Gifted Child Quarterly, 30(4), 159-163.

Maker, C.J. (1982). Curriculum development for the gifted. Rockville, MD: Aspen.

Parnes, S.J. (1966). Programming creative behavior. Buffalo, NY: The State University of New York at Buffalo.

Passow, A.H. (1982). Differentiated curricula for the gifted/talented. In Curricula for the gifted: Selected proceedings for the First National Conference on Curricula for the Gifted/Talented (pp. 4-20). Ventura, CA: National/State Leadership Training Institute on the Gifted and Talented.

Taba, H. (1962). Curriculum development: Theory and practice. New York: Harcourt, Brace & World.

The Association of the Gifted (TAG). (1989). Standards for programs involving the gifted and talented. Reston, VA: The Council for Exceptional Children.

VanTassel-Baska, J., Feldhusen, J., Seeley, K., Wheatley, G., Silverman, L., & Foster, W. (1988). Comprehensive curriculum for gifted learners. Needham Heights, MA: Allyn & Bacon.

VanTassel-Baska, J. (1989). Appropriate curriculum for the gifted. In J. Feldhusen, J. VanTassel-Baska, & K. Seeley (Eds.), Excellence in educating the gifted (pp. 175-191). Denver: Love.

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This publication was developed by Sandra L. Berger with funding from the Office of Educational Research and Improvement, U.S. Department of Education, under contract no. RI88062007. The opinions expressed in this report do not necessarily reflect the positions or policies of OERI or the Department of Education. ERIC Digests are in the public domain and may be freely reproduced and disseminated.

ERIC_NO: ED441302
TITLE: Teaching Mathematics to Gifted Students in a Mixed-Ability Classroom. ERIC Digest E594.
AUTHOR: Johnson, Dana T.
PUBLICATION_DATE: 2000
AVAILABILITY: ERIC Clearinghouse on Disabilities and Gifted Education, Council for Exceptional Children, 1920 Association Dr., Reston, VA 20191-1589. Tel: 800-328-0272 (Toll Free); e-mail: ericec@cec.sped.org; Web site: http://ericec.org.
FULL_TEXT:
Mathematically gifted students have needs that differ in nature from those of other students. They require some differentiated instruction, defined by Tomlinson (1995) as "consistently using a variety of instructional approaches to modify content, process, and/or products in response to learning readiness and interest of academically diverse students." Yet recent studies have found few instructional or curricular modifications in regular elementary classrooms (Archambault et al., 1993; Westberg, Archambault, Dobyns & Salvin, 1993). In grades 9-12, students may be able to select honors, advanced, and AP courses; however, even in these more homogeneously grouped classes there is a range of differences that need to be acknowledged.

WHY SHOULD WE DO ANYTHING DIFFERENT FOR MATHEMATICALLY

GIFTED STUDENTS?

Gifted students differ from their classmates in three key areas that are especially important in mathematics. These are summarized below.
How Gifted Learners Differ from Classmates:

1. Pace at which they learn

2. Depth of their understanding

3. Interests that they hold (Maker, 1982)
Relationship to Mathematics Learning

1. The sequential nature of math content makes pacing an issue.

2. Deeper levels of understanding and abstraction are possible for most mathematical topics, so differentiation becomes important.

3. If the interest is snuffed out early, the talent may not be developed.

Mathematically gifted students differ from the general group of students studying math in the following abilities: spontaneous formation of problems, flexibility in handling data, mental agility of fluency of ideas, data organization ability, originality of interpretation, ability to transfer ideas, and ability to generalize (Greenes, 1981). No list of characteristics of the mathematically gifted includes "computational proficiency," and yet at levels prior to Algebra I, this is commonly used as the criterion that determines who gets to move on to more interesting material. Furthermore, there is a myth that gifted students don't need special attention since it is easy for them to learn what they need to know. On the contrary, their needs dictate curriculum that is deeper, broader, and faster than what is delivered to other students.

Mathematics can be the gatekeeper for many areas of advanced study. In particular, few gifted girls recognize that most college majors leading to high level careers and professions require four years of high school math and science (Kerr, 1997). Students may drop out of math courses or turn toward other fields of interest if they experience too much repetition, not enough depth, or boredom due to slow pacing.

An Agenda for Action: Recommendations for School Mathematics of the 1980s (NCTM, 1989, p. 18) says, "the student most neglected, in terms of realizing full potential, is the gifted student of mathematics. Outstanding mathematical ability is a precious societal resource, sorely needed to maintain leadership in a technological world." By 1995, when the NCTM created a Task Force on the Mathematically Promising, not much had changed (Sheffield et al., 1995).

WHAT DO THE CURRICULUM STANDARDS OF THE NATIONAL COUNCIL OF TEACHERS

OF MATHEMATICS (NCTM) SAY WE SHOULD DO ABOUT MATHEMATICALLY GIFTED

STUDENTS?

The NCTM Standards do not mention gifted students explicitly but recognize that students are not all the same. For all students, the Standards place a greater emphasis on areas that traditionally have been emphasized for the gifted. All students are now expected to complete a core curriculum that has shifted its emphasis away from computation and routine problem practice toward reasoning, real-world problem solving, communication, and connections. "The Standards propose that all students be guaranteed equal access to the same curricular topics; it does not suggest that all students should explore the content to the same depth or at the same level of formalism" (NCTM, 1989, p. 131). At the high school level, additional topics are suggested for "college-intending" students. The Report of the Task Force on the Mathematically Promising recognizes that there are special issues relating to the education of the mathematically promising student (Sheffield et al., 1995) and has made recommendations that include the development of new curricular standards, programs, and materials that encourage and challenge the mathematically promising.

WHAT SHOULD BE DONE TO DIFFERENTIATE CURRICULUM, INSTRUCTION AND

ASSESSMENT FOR THE MATHEMATICALLY GIFTED IN THE REGULAR CLASSROOM?

Historically there has been debate about the role of acceleration versus enrichment as the differentiation mode for mathematics. Most experts recommend a combination. The following are suggestions for differentiating for the mathematically gifted by using (1) assessment, (2) curriculum materials, (2) instructional techniques, and (4) grouping models. These opportunities should be made broadly available to any student with interest in taking advantage of them.

* Give pre-assessments so that students who already know the material do not have to repeat it but may be provided with instruction and activities that are meaningful. In the elementary grades, gifted learners still need to know their basic facts. If they do not, don't hold them back from other more complex tasks, but continue to work concurrently on the basics.

* Create assessments that allow for differences in understanding, creativity, and accomplishment; give students a chance to show what they have learned. Ask students to explain their reasoning both orally and in writing.

* Choose textbooks that provide more enriched opportunities. Unfortunately, curriculum in this country is mainly driven by textbooks, which are used about 80% of the time (Lockwood, 1992). Math textbooks often repeat topics from year to year in the grades prior to algebra. Since most textbooks are written for the general population, they are not always appropriate for the gifted. Several series that hold promise for gifted learners have been developed recently under grants from the National Science Foundation; they emphasize constructivist learning and include concepts beyond the basics.

* Use multiple resources. No single text will adequately meet the needs of these learners.

* Be flexible in your expectations about pacing for different students. While some may be mastering basic skills, others may work on more advanced problems.

* Use inquiry-based, discovery learning approaches that emphasize open-ended problems with multiple solutions or multiple paths to solutions. Allow students to design their own ways to find the answers to complex questions. Gifted students may discover more than you thought was possible.

* Use lots of higher-level questions in justification and discussion of problems. Ask "why" and "what if" questions.

* Provide units, activities, or problems that extend beyond the normal curriculum. Offer challenging mathematical recreations such as puzzles and games.

* Provide AP level courses in calculus, statistics, and computer science or encourage prepared students to take classes at local colleges if the supply of courses at the high school has been exhausted.

* Differentiate assignments. It is not appropriate to give more problems of the same type to gifted students. You might give students a choice of a regular assignment; a different, more challenging one; or a task that is tailored to interests.

* Expect high level products (e.g., writing, proofs, projects, solutions to challenging problems).

* Provide opportunities to participate in contests such as Mathematical Olympiads for the Elementary School (grades 4-6), Math Counts (grades 7-8), and the American Junior High School Mathematics Exam (grades 7-8) or the American High School Mathematics Exam (grades 9-12). Give feedback to students on their solutions. After the contests, use some of the problems as the basis for classroom discussions.

* Provide access to male and female mentors who represent diverse linguistic and cultural groups. They may be within the school system, volunteers from the community, or experts who agree to respond to questions by e-mail. Bring speakers into the classroom to explain how math has opened doors in their professions and careers.

* Provide some activities that can be done independently or in groups based on student choice. Be aware that if gifted students always work independently, they are gaining no more than they could do at home. They also need appropriate instruction, interaction with other gifted students, and regular feedback from the teacher.

* Provide useful concrete experiences. Even though gifted learners may be capable of abstraction and may move from concrete to abstract more rapidly, they still benefit from the use of manipulatives and "hands-on" activities.

HOW CAN TECHNOLOGY SUPPORT THE NEEDS OF THE GIFTED?

Technology can provide a tool, an inspiration, or an independent learning environment for any student, but for the gifted it is often a means to reach the appropriate depth and breadth of curriculum and advanced product opportunities. Calculators can be used as an exploration tool to solve complex and interesting problems. Computer programming is a higher level skill that enhances problem solving abilities and promotes careful reasoning and creativity. The use of a database, spreadsheet, graphic calculator, or scientific calculator can facilitate powerful data analysis. The World Wide Web is a vast and exciting source of problems, contests, enrichment, teacher resources, and information about mathematical ideas that are not addressed in textbooks. Technology is an area in which disadvantaged gifted students may be left out because of lack of access or confidence. It is essential that students who do not have access at home get the exposure at school so that they will not fall behind the experiences of other students.

WHAT IS THE RESPONSIBILITY OF SCHOOLS AND TEACHERS IN

DEVELOPING GIFTEDNESS IN MATHEMATICS?

Classroom teachers and school districts share the responsibility of addressing the needs of gifted students.

* Teachers need training and support in recognizing and addressing the needs of the mathematically gifted.

* Teachers who teach mathematics to gifted learners need a strong background in mathematics content. If the school has only a few students with special needs and does not have such a teacher, a mentor from outside the school should be located to work with individuals.

* A coordinated curriculum plan needs to be in place so that the mathematical experiences for students are not duplicated or interrupted from one year to the next.

* The school should have an organized support system that includes resource books, technology, and human resources.

Regular mathematics classrooms that offer sufficiently challenging and broad experiences for gifted students have the potential to enrich the learning community as a whole since other students will be interested in attempting, perhaps with help, some of the more challenging tasks. If math classes offer diversity in assignments, products, and pacing and monitor student needs, all students will be able to work at their own challenge level.

REFERENCES

Archambault, F. X., Westberg, K. L., Brown, S. W., Hallmark, B. W., Zhang, W., & Emmons, C. L. (1993). Classroom practices used with gifted third and fourth grade students. Journal for the Education of the Gifted, 16, 103-119.

Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28, 14-18.

Lockwood, A. T. (1992). The de facto curriculum. Focus in Change, 6.

Maker, J. (1982). Curriculum development for the gifted. Rockville, MD: Aspen Systems Corporation.

Kerr, B. A. (1997). Developing talents in girls and young women. In N. Colangelo & G. A. Davis (Eds.), Handbook of gifted education (2nd ed., pp. 483-497). Boston: Allyn & Bacon.

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

Sheffield, L. J., Bennett, J., Berriozabal, M., DeArmond, M., Wertheimer, R. (1995) Report of the task force on the mathematically promising. Reston, VA: National Council of Teachers of Mathematics.

Tomlinson, C. A. (1995). Deciding to Differentiate Instruction in Middle School: One school's journey. Gifted Child Quarterly, 39, 77-87.

Westberg, K. L., Archambault, F. X., Dobyns, S. M. & Salvin, T. J. (1993). The classroom practices observation study. Journal for the Education of the Gifted, 16, 120- 146.

Dana Johnson is a mathematics instructor at the College of William and Mary and also teaches enrichment classes through the Center for Gifted Education at the College.

ERIC Digests are in the public domain and may be freely reproduced and disseminated, but please acknowledge your source. This digest was prepared with funding from the Office of Educational Research and Improvement (OERI), U.S. Department of Education (ED) under Contract No. ED-99-CO- 0026. The opinions expressed in this publication do not necessarily reflect the positions or policies of OSEP or the Department of Education.

ERIC_NO: ED389141
TITLE: Differentiating Instruction for Advanced Learners in the Mixed-Ability Middle School Classroom. ERIC Digest E536.
AUTHOR: Tomlinson, Carol Ann
PUBLICATION_DATE: 1995
AVAILABILITY: ERIC Clearinghouse on Disabilities and Gifted Education, Council for Exceptional Children, 1920 Association Dr., Reston, VA 22091-1589 ($1 each, minimum order $5 prepaid).
FULL_TEXT:
A particular challenge for middle school teachers is being able to differentiate or adapt instruction to respond to the diverse student needs found in inclusive, mixed-ability classrooms. This digest provides an overview of some key principles for differentiating instruction, with an emphasis on the learning needs of academically advanced learners.

WHY DIFFERENTIATE INSTRUCTION?

A single seventh grade heterogeneous language arts class is likely to include students who can read and comprehend as well as most college learners; students who can barely decode words, comprehend meaning, or apply basic information; and students who fall somewhere between these extremes. There are students whose primary interests lie in science, sports, music, or a dozen other fields. There are students who learn best by working alone and those who are most successful working in groups. Further, the learning profiles of young adolescents often change rapidly as they develop. There simply is no single learning template for the general middle school class. If middle school students differ in readiness, interest, and learning profiles, and if a good middle school attempts to meet each student where he or she is and foster continual growth, a one-size-fits-all model of instruction makes little sense. Rather, differentiated instruction seems a better solution for meeting the academic diversity that typifies the middle school years.

WHAT DIFFERENTIATION IS--AND IS NOT

A differentiated classroom offers a variety of learning options designed to tap into different readiness levels, interests, and learning profiles. In a differentiated class, the teacher uses (1) a variety of ways for students to explore curriculum content, (2) a variety of sense-making activities or processes through which students can come to understand and "own" information and ideas, and (3) a variety of options through which students can demonstrate or exhibit what they have learned.

A class is not differentiated when assignments are the same for all learners and the adjustments consist of varying the level of difficulty of questions for certain students, grading some students harder than others, or letting students who finish early play games for enrichment. It is not appropriate to have more advanced learners do extra math problems, extra book reports, or after completing their "regular" work be given extension assignments. Asking students to do more of what they already know is hollow. Asking them to do "the regular work, plus" inevitably seems punitive to them (Tomlinson, 1995a).

CHARACTERISTICS OF A DIFFERENTIATED CLASS

Four characteristics shape teaching and learning in an effective differentiated classroom (Tomlinson, 1995a):

1. "Instruction is concept focused and principle driven." All students have the opportunity to explore and apply the key concepts of the subject being studied. All students come to understand the key principles on which the study is based. Such instruction enables struggling learners to grasp and use powerful ideas and, at the same time, encourages advanced learners to expand their understanding and application of the key concepts and principles. Such instruction stresses understanding or sense-making rather than retention and regurgitation of fragmented bits of information. Concept-based and principle-driven instruction invites teachers to provide varied learning options. A "coverage-based" curriculum may cause a teacher to feel compelled to see that all students do the same work. In the former, all students have the opportunity to explore meaningful ideas through a variety of avenues and approaches.

2. "On-going assessment of student readiness and growth are built into the curriculum." Teachers do not assume that all students need a given task or segment of study, but continuously assess student readiness and interest, providing support when students need additional instruction and guidance, and extending student exploration when indications are that a student or group of students is ready to move ahead.

3. "Flexible grouping is consistently used." In a differentiated class, students work in many patterns. Sometimes they work alone, sometimes in pairs, sometimes in groups. Sometimes tasks are readiness-based, sometimes interest-based, sometimes constructed to match learning style, and sometimes a combination of readiness, interest, and learning style. In a differentiated classroom, whole-group instruction may also be used for introducing new ideas, when planning, and for sharing learning outcomes.

4. "Students are active explorers." "Teachers guide the exploration." Because varied activities often occur simultaneously in a differentiated classroom, the teacher works more as a guide or facilitator of learning than as a dispenser of information. As in a large family, students must learn to be responsible for their own work. Not only does such student-centeredness give students more ownership of their learning, but it also facilitates the important adolescent learning goal of growing independence in thought, planning, and evaluation. Implicit in such instruction is (1) goal-setting shared by teacher and student based on student readiness, interest, and learning profile, and (2) assessment predicated on student growth and goal attainment.

HOW TO THINK ABOUT DIFFERENTIATING INSTRUCTION

There are many ways to shake up the classroom to create a better fit for more learners--including those who are advanced. In general, "interest-based adjustments" allow students to have a voice in deciding whether they will apply key principles being studied to math-oriented, literature-based, hobby-related, science-oriented, or history-associated areas. For example, in studying the American Revolution, one student might opt to write a short story about the life of a teenager during the Revolutionary period. Another might elect to apply key ideas about the American Revolution to an investigation of heroes then and now. Yet another might prefer to study ways in which the Revolution affected the development of science.

"Adjustments based on learning profile" encourage students to understand their own learning preferences. For example, some students need a longer period to reflect on ideas before beginning to apply them, while others prefer quick action. Some students need to talk with others as they learn, while others need a quiet work space. Some students learn best as they tell stories about ideas being explored, others as they create mind maps, and still others as they construct three-dimensional representations. Some students may learn best through a practical application of ideas, others through a more analytical approach.

"Readiness-based adjustments" can be created by teachers offering students a range of learning tasks developed along one or more of the following continua:

1. "Concrete to abstract." Learners advanced in a subject often benefit from tasks that involve more abstract materials, representations, ideas, or applications than less advanced peers.

2. "Simple to complex." Learners advanced in a subject often benefit from tasks that are more complex in resources, research, issues, problems, skills, or goals than less advanced peers.

3. "Basic to transformational." Learners advanced in a subject often benefit from tasks that require greater transformation or manipulation of information, ideas, materials, or applications than less advanced peers.

4. "Fewer facets to multi-facets." Learners advanced in a subject often benefit from tasks that have more facets or parts in their directions, connections within or across subjects, or planning and execution than less advanced peers.

5. "Smaller leaps to greater leaps." Learners advanced in a subject often benefit from tasks that require greater mental leaps in insight, application, or transfer than less advanced peers.

6. "More structured to more open." Learners advanced in a subject often benefit from tasks that are more open in regard to solutions, decisions, and approaches than less advanced peers.

7. "Less independence to greater independence." Learners advanced in a subject often benefit from greater independence in planning, designing, and self-monitoring than less advanced peers.

8. "Quicker to slower." Learners advanced in a subject will sometimes benefit from rapid movement through prescribed materials and tasks. At other times, they may require a greater amount of time with a given study than less advanced peers so that they may explore the topic in greater depth and/or breadth.

STRATEGIES FOR MANAGING A DIFFERENTIATED CLASSROOM

Among instructional strategies that can help teachers manage differentiation and help students find a good learning "fit" are the following:

* use of multiple texts and supplementary materials;

* use of computer programs;

* interest centers;

* learning contracts;

* compacting;

* tiered sense-making activities and tiered products;

* tasks and products designed with a multiple

intelligence orientation;

* independent learning contracts;

* complex instruction;

* group investigation;

* product criteria negotiated jointly by student and

teacher;

* graduated task- and product-rubrics.

FINAL THOUGHTS

Teachers moving toward differentiated instruction in an inclusive, integrated middle school classroom find greater success if they (1) have a clear rationale for differentiation, (2) prepare students and parents for a differentiated classroom, (3) attend to issues of classroom structure and management as they move toward more student-centered learning, (4) move toward differentiation at a pace comfortable to both teacher and learners, and (5) plan with team members and other colleagues interested in differentiation (Tomlinson, 1995b).

REFERENCES

Tomlinson, C. (1995a). How to differentiate instruction in mixed-ability classrooms. Alexandria, VA: Association for Supervision and Curriculum Development.

Tomlinson, C. (1995b). Deciding to differentiate instruction in middle school: One school's journey. Gifted Child Quarterly, 39, 77-87.

A companion digest, Gifted Learners and the Middle School: Problem or Promise (E535), is available.

Carol Ann Tomlinson is Assistant Professor, Curry School of Education, the University of Virginia, Charlottesville.

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ERIC Digests are in the public domain and may be freely reproduced and disseminated. This publication was prepared with funding from the Office of Educational Research and Improvement, U.S. Department of Education, under contract no. RR93002005. The opinions expressed in this report do not necessarily reflect the positions or policies of OERI, or the Department of Education.