P.O. BOX 1586







Dr. James Delisle -- Professor and Co-Director of SENG, Kent State University, Kent, Ohio

Dr. Jerry Flack --Univ. Of Colorado-Colorado Springs

Dr. Howard Gardner -- Professor, Graduate School of Education, Harvard University, Cambridge, Massachusetts

Ms. Diane D. Grybek -- Supervisor of Secondary Gifted Programs (Retired), Hillsborough County Schools, Tampa, Florida

Ms. Dorothy Knopper -- Publisher, Open Space Communications, Boulder, Colorado

Mr. James LoGiudice -- Director, Program and Staff Development, Bucks County, Pennsylvania Intermediate Unit No. 22 and Past President of the Pennsylvania Association for Gifted Education

Dr. Mary Meeker -- President of SOI Systems, Vida, Oregon

Dr. Adrienne O'Neill - Chief Education Officer, Timken Regional Campus, Canton, Ohio

Dr. Stephen Schroeder-Davis -- Coordinator of Gifted Programs, Elk River, Minnesota Schools and Past President of the Minnesota Council for the Gifted and Talented

Dr. Bruce Shore -- Professor and Director, Giftedness Centre, McGill University, Montreal, Canada

Ms. Joan Smutny -- Professor and Director, Center for Gifted, National-Louis University, Evanston, Illinois

Dr. Virgil S. Ward -- Emeritus Professor of Gifted Education, University of Virginia, Charlottesville, Virginia

Dr. Colleen Willard-Holt - Associate Professor, Penn State University, Harrisburg

Ms. Susan Winebrenner -- Consultant, Brooklyn, Michigan

Dr. Ellen Winner - Professor, Boston College

Happy New Year to all of our readers! Beginning with the Winter 2001 issue, we have changed GEPQ from a hard copy format to primarily a web site format on All subscribers and advisory board members will receive an user name and password to access the current and future issues through a password protected web page.

We are making this change because of economic considerations and to expand communication options. First, recent increases in postal rates make it difficult to continue “snail mail” delivery at out low subscription rate. Second, placing GEPQ on a web page will enable us to include more information about the gifted field than is possible with the hard copy version. I hope this transition will proceed smoothly. But with all such changes, some glitches will inevitably occur along the road to improved and wider communication.

I would like to express my sadness concerning the death of Steve Allen -- comedian, entertainer, author and thinker. He was a great friend of gifted education. Several years ago, he wrote a wonderful article for GEPQ (Winter 1994 issue) on his life and views on educating the gifted.

My wife, Eugenia, and I visited Susan Winebrenner in Charlottesville, Virginia in October 2000 where she presented a two-day workshop to a full-house of teachers and administrators. Susan is one of the extraordinary people in the gifted field who knows how to effectively present practical and research-based information on differentiating the curriculum for gifted students in the regular classroom. She has had a tremendous impact on both regular classroom teachers and gifted resource teachers.

The articles in this issue cover a wide range of topics as follows: (1) discussion of mathematics education in China by Andrea Prejean and Lynn Fox; (2) differentiated science curriculum at the upper elementary and middle school levels by Brendan Miller and Colleen Willard-Holt*; (3) A unique program that enables gifted students to solve corporate problems by Dan Holt; (4) review of a book on musical genius; and (5) an article on the life and accomplishments of Thomas Wolfe by Michael Walters. Good reading and see us in hypertext heaven!      

Maurice D. Fisher, Ph.D., Publisher

*Gifted Education Press has recently published a book by these authors on differentiating science curricula.

  Reflections on China: Implications for Gifted Education

Andrea I. Prejean and Lynn H. Fox

American University   Washington, D.C.


We were standing on a college campus looking at a large modern building that cast a shadow over small garden spaces with brightly-colored pagodas.  This was China and we were guests of the State, invited to present papers at the 2nd International Conference on Mathematics Education held in Hangzhou, China in May 2000. The conference was co-sponsored by Hangzhou Teachers College and the California State University at San Marcos. Dr. Fox's paper on the education of mathematically gifted children in the United States and Dr. Prejean's paper on the uses of computer technology in teacher preparation were chosen for the conference.

In this article, we will summarize some of the issues that emerged from the papers presented and from our conversations with conference participants as well as our observations of educational practices in schools in two cities in China -- Hangzhou in the southern part and Xi'an in the more central portion.  We will also share what we have learned about education in present-day China in terms of the historical/political context from which it has evolved. We have extrapolated from all of these experiences our own interpretation of the status of gifted education in China. We conclude with some ideas for connections with China in a number of ways that may be of interest to educators and researchers in gifted education.  

The Conference

The Chinese appreciate the value of ceremony and so the conference opened with very formal presentations by representatives of the co-sponsoring colleges, Hangzhou Municipality, the standing Committee of the National People's Congress of China, and China's Mathematics Association.  The conference culminated in an elaborate banquet and evening of traditional Chinese music and dance performed by students at the host college. Liping Ma gave the keynote presentation.  She was born and raised in China and is now a professor at the University of California at Berkeley, USA.  She recently authored a comparative study of mathematics content knowledge and approaches to mathematics instruction by teachers in China and the United States.

The conference participants included 60 elementary school, high school, and university teachers of mathematics, university mathematics education researchers, and school administrators from the United States of America, Canada, Japan, Austria, South Africa, Malaysia, Singapore, and Hong Kong. Forty of the 60 participants were from China. Conference participants were allowed to observe classes at the high school affiliated with Zhejiang University or at Qui Shi Elementary School in Hangzhou, China.  A small group of teachers and professors from the United States also observed mathematics classes at a junior secondary school (equivalent to our middle school), the Helen Snow School in Xi'an.  

The focus of the conference was on teacher preparation and effective instructional strategies to reach a broad range of students.  Following the Cultural Revolution in China, there were few teachers prepared by colleges and few schools for children.  Thus, there is currently a struggle to create schools and to prepare teachers in a country with only 2% of the population attending college.  Although teaching is a respected profession in China, it is not particularly highly paid.  Most of the new teachers we observed were young women.  The faculties of the colleges, however, were predominately older men.  While much of the teaching, especially at the college level, is traditional lecture, there is a growing concern for changing approaches to teaching, especially at the pre-college level, to include more active learning and technology. Chinese representatives to the conference seemed eager to learn about efforts at educational reform and cognitive constructivism from educators in the United States, Japan, and Singapore. All participants agreed that a mathematically and scientifically literate population was a necessity for promoting social development and raising the quality of life for all persons around the world.  To put the discussion of current Chinese schools in context let us turn for a moment to a brief overview of the history of education in China in the midst of social-political experimentation and change.

History of Chinese Education

We will consider the importance of three distinct waves of educational philosophy and practice in China.  First, the traditional Chinese culture that prevailed prior to 1949 could be described as the Era of Imperial Dynasties.  The second period is marked by the rise of Communism in 1949 that led to dramatic change in philosophy and practice that continued with some variations until the late 1970s.  The most recent era has emerged as the post-Mao Era and continues today with a mixture of reform and restructuring intermingled with some  traditional practices.

Traditional Education

The early Chinese system of education can be traced as far back as the Shang Dynasty (1523 to 1027 B.C.). Education was provided for an elite group, trained for government service.  The curriculum centered around the Six Arts: rites, music, archery, chariot-riding, history and mathematics. This approach to schooling was slightly altered by the teachings of Confucius (551 -479 B.C.) so that the core curriculum focused on the Four Books and Five Classics of Confucius (Surowski, 2000). In the final 100 years of the eras of the imperial rule, the Chinese suffered humiliation and defeat in the Opium war (1840-42) and lost Hong Kong to Great Britain.  This spawned a period of openness to western educational practice, largely through the creation of Christian Missionary Schools.  China, however, still remained a nation with only a small educated elite and massive general illiteracy among the predominantly agrarian population (Hayhoe, 1984; Surowski, 2000).

As early as 1921 the seeds of communism led to some experimentation with the notion of universal education at least at the level of higher education with the creation of Hunan Self-Study University established by Mao Zedong and his supporters.  It was not until 1949, however, that a truly new educational system was fully implemented.

Soviet Influence on Education

With the establishment of the Communist political control of the State came the importation of the Soviet model of education. Most of the early efforts focused on the restructuring of higher education. The majority of primary and secondary-aged children still were not provided much formal schooling. Mao's disenchantment with the Soviets in 1961 led to an attempt to connect the legacy of Confucius with ideas taken from western-style educational practice.  In this period a two-track system was developed.  One track was traditionally academic and led to the possibility of university admission. The second track was vocational and technical. 

The Cultural Revolution era of 1966 to 1976 brought a condemnation of the existing school system as too "bourgeois intellectual."  The Communist Party Central Committee took over the control of education and the curriculum was reconstituted.  The new curriculum focused on practical skills and eliminated subjects such as history and literature.  The higher education community was radicalized by the dramatic changes to the admissions procedures and the focus on admissions of "virtuous" students.  “Virtuous” was defined as being from families of peasants, soldiers or industrial workers in good standing with the party (Hayhoe, 1984; Surowski, 2000).

Modern Day Education

Political changes in 1976 resulted in a reversal of educational policy and practices with the reinstatement of academic standards and a focus on quality over quantity.  This change actually has led to a decline in primary school attendance in rural areas where families find it more prudent to put the children to work than to send them to school.  At the secondary level, the two-track system of vocational and general schools was also reinstated.  Current enrollments are split with nearly 60 percent going to the vocational or technical schools. At present a small percentage of those in the general schools are accepted into universities.  Estimates vary depending on the source.  One college president stated that 10% were admitted, but clearly that is not 10% of the eighteen-year old population, but 10% of those students that have had access to secondary education.

In 1995, the National People's Congress passed the Education Law of the Peoples Republic which shows a commitment to the notion of universal education with a nine-year compulsory education policy and a commitment to produce both scholar/scientists and skilled laborers.  More autonomy is being granted to colleges and universities while at the same time moving to fewer colleges and universities in a more consolidated system.

Descriptions of education in China today emphasize the nine-year compulsory law but the reality is that public education is by no means free.  In the urban areas there are government schools for the academically talented but these charge fairly substantial tuition and are restricted to children whose families are in good standing with the Communist Party.  Although the practice of "streaming" or ability grouping is now being renounced, it still appears to be the norm.  Nor is there any apparent access for children with special needs.  We encountered no discussion of "special education."

Geography dictated educational destiny in China.  What really exists is a rigid dual tracking by geographical district.  Key government schools with the academic curriculums are located in urban areas.  Rural village schools, which constitute the vast majority of schools, offer a more vocational program for producing laborers and industrial workers rather than scholars or teachers.  There is little opportunity for even a very bright student to cross over to an academic school from a village school.

Perhaps because the State provides no funds to village schools, they are not held to the same regulations as the urban key schools.  Thus, they may offer only a half-day program that is not year-round.  This leads to uneven success.  Indeed the village schools face what they call the 3-6-9 situation where 90% of the children are enrolled but only 60% attend regularly and only 30% actually pass the standards to move to the secondary level (Hayhoe, 1984).

What did ring true in our observations was a commitment to the arts and sports as well as academics in the key schools.  At the schools we visited, children came early and stayed late in order to participate in sports and music. The academic work was interspersed throughout the day with breaks for recess, music, and visual arts.  

While primary and secondary schooling are not free, university education is at least for the select few that pass the entrance examinations.  Some students actually receive a stipend to help defray their families’ loss by not having them contributing to the family income.  University housing is run by a student organization rather than by the university administration.

Thus, the notion of education for the masses and education for upward social mobility seems more of an illusion than reality. The current system seems only slightly superior to the very early elite schools of the era of the dynasties or the disaster that occurred during the Cultural Revolution.  Clearly, the system faces problems that go beyond the issue of limited resources.  Teacher shortages are a major issue.  Also, the country is more divided by language and culture than they wish to acknowledge.  For example, oral language is so different between the northern and southern provinces that our guides, one from each area, had to communicate with each other in English.

Conference Theme Highlights

The conference was divided into three themes:

Teaching and  Learning

Teacher Development, and

Mathematics Education Reform

The paper presentations were wide and varied from researchers and teachers from nine countries.  In the next section, we will discuss three of the sessions that seem to have important aspects to American education.  In one session, the long touted mathematics education program in Singapore at Northland Primary School was described.  Several sessions described the value of distance education and the integration of the INTERNET as a teaching tool.  In another session, Liping Ma described her work with Chinese and American teachers and her book Knowing and Teaching Mathematics Elementary Education: Teachers’ Understanding of Fundamental Mathematics in China and the United States (1999).

Paper Session: Singapore

Described by the head of the mathematics department, the program at Northland Primary School seems to emphasize the best practices described and promoted by current American mathematics reform.  The objectives of the program are: “(1) to develop, motivate, and inspire teachers to explore and carry out effective lessons that promote analytical and creative thinking skills in the learning of mathematics; and (2) to enable pupils to appreciate math in everyday life through sound understanding of math concepts, mastery of problem solving skills, application of appropriate processes, and acquisition of metacognitive skills.”  At first glance, these two objectives would seem to have much in common with the goals for mathematics promoted in American schools.  The unique goal established by the Singapore school is the first goal for teachers.  Generally, goals in American schools are written to reflect what the students will do and achieve in mathematics.  The school in Singapore, though, has recognized and acted upon what professional developers have been discussing for ten to fifteen years in American education, but on which little wide-spread action has been seen here.  Without a well-educated and self-directed teaching force that feels some sense of autonomy, our reform efforts in mathematics education in America seem doomed in their attempts to reach their full potential.  The professional development practices in Singapore are well-documented and described.  Staff development consists of three arms: workshops and sharing sessions, demonstration lessons, and learning circles. From these practices come strategies by which teachers are assigned “buddy” teachers and they perform peer observations and team teaching.  From these actions come peer feedback which leads to better teaching and increased student achievement.  

This attention to teacher development in both content and pedagogy contributes to a well-articulated curriculum that has led to high-achieving students.

Paper Session: INTERNET

Several presentations and papers described research into the integration and use of the INTERNET as a means of distance education. The paper Enhancing the Mathematics Curriculum with Web-Based Technology (Bookbinder, 2000) discussed a variety of strategies that would effectively use the WWW.  Use of the Blackboard™ Courseware ( to enhance teacher preparation was described as it was used to facilitate student-led on-line discussions in an elementary education mathematics methods class.  The goal of the activity was to provide a means for continued reflective thought and to provide a situation in which students could take the lead in the reflective process. The paper revealed students’ beliefs about mathematics learning and teaching, students’ attitudes about using this form of communication, and provided thought for a discussion about the use of technology in the preparation of mathematics classroom teachers.   This paper further seems to have implications for gifted education.  

Paper Session: Knowing and Teaching Elementary Mathematics by Linping Ma

A major session revolved around Ma’s (1999) research into the mathematics content knowledge of Chinese and American teachers as it relates to classroom teaching practices.  Her reporting of her research inspired much discussion and debate as we all wrestled with an increasingly serious concern of teachers teaching mathematics without the necessary content knowledge needed to guide students to complete understanding.  Ma (1999) reports that it is Chinese teachers’ rich and deep understanding of the mathematics that contributes to the mathematics achievement of Chinese students.  In her research she concludes that American elementary teachers have not had the in-depth exploration of school mathematics that provides them with the necessary background needed to enrich their students' mathematical education.  Of note, is that even the experienced American teachers that were described as "better" than their counterparts had less understanding than the Chinese teachers in her research.  She suggests that there are three periods that teachers develop their mathematical knowledge: Schooling, Teacher Preparation, and Teaching (Ma, 1999).

The conference papers and presentations revealed the differences and commonalties of American mathematics education with its counterparts around the world.  We are all grappling with the necessity to educate all of our children.  While much was discussed and demonstrated of and about the rich content knowledge of Chinese teachers and their ability to use effective pedagogy, we all recognize that a significantly small number of Chinese students have access to this quality of education.  Unfortunately, it would appear to us that just like the United States, many children do not have the access to quality mathematics instruction in China.

Some Emerging Themes


Attendance rates in village schools are lower for girls than boys.  Parents appear to have different expectations for boys and girls.  In the urban key schools there appeared to be equal numbers of boys and girls in the primary grades.  Our own observations were that school administrators and the university professors were predominantly male while the teachers we observed in the primary grades were young females.

Teaching as a Profession

We were told that teaching was an "honorable" profession but one that was not highly paid. A brief look at the role and status of teachers throughout the history of China shows that this was also the case prior to 1949.  During the early years of the Communist regime, however, many left the profession.  Indeed teachers became the object of much criticism under Mao and were verbally and even physically abused.  Thus, despite more recent efforts by the government to call for respect for teachers, many are reluctant to embark upon a profession that was so reviled in the not so distant past.  

Elitism versus Teaching for Diversity

In the past, Chinese education has focused on educating the elite: children of party members. In the present, the small, but growing wealthy class is managing to find quality education for their children.  At both schools that we visited, though one was technically a state-school, parents were charged tuition. However, Chinese officials (South China Sea Morning Post, May, 2000) like many other governments around the world are recognizing that educating all children is imperative.

The School Visits

Our Observations 

The visits to the schools were for the authors the most interesting aspects of our entire visit.  Although it was clear to us that what we were seeing was "the best" and not the "norm" for China, it helped to confirm the rhetoric of the meetings in terms of commitment to change in instructional strategies.  Although class sizes were very large by U.S. standards with 48 students to a class, the technology we saw in use was very advanced.  We watched two different elementary mathematics teachers in a large room designed for demonstration teaching at Qui Shi Elementary School.  The school is part of the Zhejiang University and classes for teachers are routinely held there.  We also each observed a different middle school class in Xi’an.  All four of these classes included good examples of constructivist pedagogy: active teaching and learning.  Our review will focus on the most interesting of the two elementary school teachers we observed.  

The room had a very large screen connected to a computer that the teacher used like an electronic blackboard.  We were told that the teachers developed their own lessons for this computer, not "commercial" pre-programmed software.  It appeared to be some type of authoring software on the order of HyperStudio. At first glance and observation, the primary class seated in a lecture format with the teacher behind a podium, seemed to have little in common with reform mathematics educational theories. Upon reflection, the class was interactive, with activities and a format that attended to a variety of intelligences and learning styles.                                          

The goal of the lesson was to investigate the area and perimeter of regular rectangles.  Students were asked to find all the arrays possible if the area was 12 square units. After a brief introduction and review of the meaning of area and perimeter, students gathered together in groups of 4 to work on the problem.  Using 1cm paper squares, students worked together to find all the possible arrays.  Quickly, at the call of the teacher, the students returned to their seats and shared their answers to the investigation.  As students shared their answers, the instructor displayed their answers in a computer program for the whole class to see.  From this activity, the students and teacher developed the formula for finding the area of regular rectangles (l x w = a).  At the conclusion of this part of the lesson, students were instructed to choose any rectangle shaped spot in the classroom and measure and find the area of their chosen spot.  After a discussion designed to bring all the pieces together, the students filed out and another class filed in.

Our Analysis

The lesson observed in this Chinese Primary School demonstrated “best practices” as described by leading mathematics educators, mathematicians, and recent reform efforts (NCTM, 2000). The teacher displayed a deep understanding of mathematics, the problem was interactive and open-ended, students clustered together to work, and technology was integrated into the lesson.

While American elementary classrooms traditionally have teachers who are generalists with little in-depth mathematics content, this Chinese teacher taught mathematics exclusively.  Her education included in-depth study of mathematics as well as appropriate pedagogy.  To be effective, teachers must know and understand deeply the mathematics they are teaching and be able to draw on that knowledge with flexibility in their teaching tasks (NCTM, 2000, p. 17).  The lesson, tasks, and discussion facilitated by the teacher demonstrated a deep understanding of the content.  This understanding provides teachers with the confidence needed to allow children to explore the content that is most meaningful for them and leads to students who own the content for a lifetime, instead of renting it for a short while.

The problem that the students solved is not a new one.  Demonstrating an understanding of area is a common outcome for intermediate students.  However, students were encouraged to solve the problem in their own way and to offer support to each other as they solved the problem.  Through their own exploration, students developed the mathematical formula for finding area and added to their conceptual understanding of area.  Through this activity not only did students learn the formula, but because they helped develop it, they can recreate the formula when they need it.

The pattern of teaching that emerged in almost all of the classes we observed was "teacher talks and interacts with entire class (about 48 students) for 10 minutes" followed by some type of "hands on or problem-solving activity" completed in groups of 4 or 6 children.  In one class, children, working in pairs, went all over the room measuring angles on walls, doorways, and desks.  This pattern would be repeated three to four times during one class.  The teacher was always on her feet, moving around the room and talking with children.  Most of the teachers had some form of checking the work or having the groups go to the chalkboard or white board to share their work at the end of each "mini-lesson activity."

In several classrooms for middle school age children (12-14 year olds), the classes were involved in games, working in pairs or foursomes.  Some of the games had been demonstrated to us by one of the teachers at a session at the conference the day before.  We found this interesting given our own use of games with junior high school students and the emphasis on games at the Key School in Indianapolis, USA, which is based on the theory of Multiple Intelligences proposed by Howard Gardner (Gardner, 1983).

Ideas for Gifted Education Collaborations

As China opens it doors to the influx of visitors and ideas, it opens the lines of communication between teachers and students in both countries.  Teachers of gifted programs can now create a new form of "pen pal" by having reading circles or book buddies via email.  More elaborate exchanges can be facilitated by using webpages, authoring programs like HyperStudio, and other communication software that allows for video transmissions.  Teachers in two schools can have their classes work on projects with teams created across classes, or students in one class can teach students in the other class about their culture and history.  Some of these projects could culminate in delegations of teachers and students from one school visiting the other school in person.


While the United States may be more evolved than China in terms of providing free schooling for the majority of its children, there are still many lessons to be learned from China's educational system and cultural changes.  For example, Liping Ma's study suggests that the preparation of elementary teachers in China is more effective than in the U.S. in terms of mathematics content knowledge and understanding.  This in turn produces young students who have a strong conceptual foundation.  Also China has, in a very short time, produced a new crop of teachers who seem to have embraced the new pedagogy of active and collaborative learning despite their own more traditional training.  China also seems to have convinced a huge segment of the population to learn English as their second language and they seem to tackle this task with more humor and enthusiasm than is typically seen in the U.S. classes studying a "foreign" language.

China in turn hopes to learn from other nations including the United States as it searches for models for a more democratic system of compulsory schooling.  This includes the notion of teaching for diversity within the regular classroom and providing better access to education for children with disabilities.  Although a few model schools have been developed that use constructivist instructional strategies, there is some concern among educators that China is not prepared for the outcomes of an educational system that fosters creative and independent thinking and learning.

The most exciting possibilities for gifted education for both countries come from the emerging opportunities for cultural exchange.  Many Chinese students come to the United States for graduate studies and China is now currently open to accepting students and visiting professors from other countries. Although exchange programs that provide for extended visits in another country are the ideal, the INTERNET and other supporting technology creates new possibilities for the exchange of ideas and information on a regular basis.  


        Bookbinder, J.S. (2000).  Enhancing the Mathematics Curriculum with Web-Based Technology.  Paper presented at the 2nd International Conference on Mathematics Education in Hangzhou, China, May 2000.

        Gardner, H.  (1983).  Frames of Mind: The Theory of Multiple Intelligences.  New York: Basic Books.

        Hayhoe, R.  (1984). Contemporary Chinese Education.  London: Croom Helm.        

        Ma, L.  (1999).  Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States.  Mahwah, NJ: Lawrence Erlbaum Associates.

        National Council for Teachers of Mathematics (2000).  Principles and Standards for School Mathematics.  Reston, VA: National Council for Teachers of Mathematics.

        South China Morning Post (2000).  Chinese Officials Rethink Education. Hong Kong.

        Surowski, D.B. (2000).  History of the Educational System of China.  Projects for International Education Research.


Differentiating Instruction for Gifted Middle School Students in Heterogeneous Science Classes*

Brendan D. Miller                                                Colleen Willard-Holt

Elizabethtown Area School District                        The Pennsylvania State University

Elizabethtown, Pennsylvania                                  Middletown, Pennsylvania

 The heterogeneity of many American classrooms has created a demanding environment for teachers. The various academic needs of a wide range of students must be met simultaneously in this type of setting. Students with learning disabilities are frequently provided with curriculum adaptations while the special needs of gifted students are often neglected because of their high level of ability. Therefore, a differentiated curriculum is also imperative for gifted students who are expected to reach their maximum potential within a heterogeneous classroom.

To provide for the academic needs of gifted and talented students in my heterogeneous science classes, I have created an enriched unit which utilizes the concepts of curriculum compacting and independent study. The enriched unit on invertebrate animals was planned for gifted and high-ability students who were selected from heterogeneous, middle school life science classes. The purpose of the differentiation was to compact the content for students who are able to learn at a quicker pace. Because science is a highly content-based subject, I did not believe that the selected students would have the material pre-mastered upon entry into my class. Therefore, I provided these students with a guided worksheet packet which supplemented their independent reading of the invertebrate chapters from the textbook. These students were given time in class to learn the concepts on their own by reading the chapters and examining the provided specimens on display. The students were then tested to determine their proficiency concerning invertebrate phyla. Students who scored above 80% were then eligible for the independent study projects which included one teacher-selected project and one student-selected project. Because the students spent less time on grade-level material, they gained time to work independently on alternate activities that explored a greater scope and depth of invertebrate concepts. This enriched unit created a more challenging learning opportunity for student-selected study.

Teacher-selected Independent Study Project

After approximately one week of class time, the students had completed the guided worksheet packet and had prepared for the test of content proficiency. The students who passed the test of content proficiency with at least an 80% were eligible to continue with the teacher-selected independent study project. The students were required to use the library to complete a research guide about an invertebrate phylum. Then, they had to create their own invertebrate which matched the characteristics of the phylum that they chose to research. They also had to create a three-dimensional model of their invertebrate and then write a creative story about the animal. When students submitted their completed invertebrate projects, I assessed the projects with a rubric.

Student-selected Independent Study Project

Upon completion of the teacher-selected project, the enriched students were permitted to select their own topic and project on invertebrates. I had compiled a topic menu and a project menu to provide students with ideas for developing their own independent study. Although students were allowed to develop an idea that was not listed, all students opted to select a topic and project from the menus. Students were required to describe their proposed projects on their contracts so that I could approve them. Although the students had been informed that their projects would receive feedback on an evaluation form instead of a grade, they became intrinsically motivated to complete the work to the best of their abilities. Upon evaluating the projects, I was very satisfied with the overall quality that was exhibited by the students. Examples of student-selected projects follow:

● Starfish: One student chose to research the anatomy of starfish. After having completed thorough research, he was permitted to dissect a specimen during class using a student dissection manual.  Then, he created a three-dimensional, clay model of a dissected starfish arm with color-coded parts to display the internal anatomy.

● Spider Myths: The Greek myth of Arachne was read by a student. He then summarized the myth and created his own spider myth called, “The True Story of Spider Man.” Finally, he compared and contrasted his myth with the Greek myth of Arachne.

● Spider Webs: Another arachnid project was completed by a student who researched the various designs of webs constructed by different types of spiders. Then, he created models of those webs by using hot glue.

● Insect Display: Five insects were researched in-depth by a student. This student then created a three-dimensional clay model of each one which displayed its physical characteristics. He also described the characteristics and life style of each insect on note cards which accompanied each model.

● Bug Book: Another student researched a wide variety of insects and created an alphabetical bug book which included colored, hand-drawn pictures of the bugs as well as an informative sentence about each one. He then presented this elementary level book to his younger brother.

Management Considerations

Selected students were given a contract that explained the requirements, expected working conditions, and assessment for the independent study. Each student received a folder which included all of the independent study materials. Along with the contract, the folders included a laminated pass to the library, daily progress sheets, a fifteen-page guided worksheet packet to be completed while independently reading the two chapters on invertebrates in the textbook, and an invertebrate research guide to be completed while working in the library. The folders were periodically checked for students’ progress. The enriched students were permitted to use the library as needed for quiet study and research. Students used their laminated passes to allow for unrestricted access to the library. When students were working within the classroom, they were seated at lab tables in the back of the room. They were permitted to leave their seats to get materials as needed. Students left and entered the room through the back door of the classroom so that all movement would occur without disturbing the class.

Work pertaining to the regular curriculum was graded. The guided worksheet packet used while reading the textbook was graded for accurate completion. The proficiency test was graded to determine eligibility for continuation in the enrichment program. The teacher-selected independent study was graded because it was completed in place of the normal invertebrate project which was assigned to the regular education students. The student-selected independent study did not receive a letter grade. Instead, an evaluation form was used to provide feedback.


Through the course of implementing a differentiated curriculum for gifted and high-ability students, I encountered many challenges as well as successes. Initially, I struggled with selecting students for enrichment. I was not able to use a pre-test for this purpose because the enrichment program was designed to allow the students to learn the invertebrate content at a quicker pace before being tested. Without pre-test scores, I relied upon prior academic achievement to determine which students would be most capable of independent learning. These students were then provided with the opportunity to apply for the enrichment program. From the applicants, I made the final selections. The purpose of the application process was to ensure that the most committed students would be selected. After making the selections, the enrichment program ran smoothly until some students lost eligibility due to low test scores. Therefore, these students were placed back into the regular class to ensure their success with the required content. Eventually, I discovered that tracking the progress of the remaining students was quite challenging as a result of their different paces and the need to take their work folders home. To resolve this problem, I periodically told students that they must leave their folders in the room for my review. Then, I recorded their progress on a master tracking sheet.


When students submitted their teacher-selected projects, I was pleased with the quantity of the research and the quality of their models. I was also very satisfied that many of the student-selected projects were creative and displayed quality work. I think the program was a positive learning experience for the students and myself.

During the final week of the independent study program, I provided a questionnaire to the enriched students to evaluate the program and their own work. The responses on the questionnaire affirmed my belief that gifted and high-ability students appreciate the opportunity to learn  the  content  at  a quicker pace so that they can be provided with a more challenging and self-directed learning environment. Upon final reflection of my experience with implementing a differentiated curriculum for gifted and high-ability students, I have realized that the success of the enrichment program depended not only on the effort of the participating students, but also on my organization, flexibility, and preparation. I have learned valuable skills through this experience which will help me to better meet the needs of students with high ability levels. Therefore, I have evolved into a more adept teacher. Hopefully, the process used to design this invertebrate unit will enable other teachers to successfully implement a differentiated curriculum in their own classrooms.

*In this article Mr. Miller presents his experiences with differentiated curriculum in his classes. The role of Dr. Willard-Holt was to assist in developing the curriculum unit and in preparing the manuscript for publication.


Let’s Get Real*: An Innovative Problem-Based Learning Program

Dan G. Holt, Ph.D.

Hummelstown, Pennsylvania

Problem-based learning arises from the constructivist perspective of education, which in turn has its roots in the thinking of John Dewey and Jean Piaget.  Dewey advocated immersion of students in hands-on, real-life problem solving as a way of making meaning (1916).  Piaget posited that learning occurs when one is puzzled by a situation. Working through that puzzle leads to cognitive change (1985).  More recently, Brooks and Brooks stated that “posing problems of emerging relevance is a guiding principle of constructivist pedagogy” (1993, p. 35).  Savery and Duffy (1995) stated that problem-based learning may be one of the best exemplars of a constructivist learning environment.  The strategy has gained nationwide popularity, as evidenced by the promulgation of several PBL networks (Torp & Sage, 1998), and credibility through a number of studies demonstrating its positive effects on student achievement and motivation (Gallagher, Stepien, & Rosenthal,1992; Stepien & Gallagher,1993; Stepien, Gallagher, & Workman,1993; Torp & Sage, 1998).

Let’s Get Real, a competitive problem-solving program now in its sixth year, exemplifies problem-based learning and authentic outcomes in the context of a business-school partnership.  Let’s Get Real (LGR) challenges teams of sixth through twelfth grade students to solve actual business problems posed by corporate co-sponsors.  In this way it seeks to prepare students for employment and furnish corporate co-sponsors with an untapped resource.  Teams of two to six students submit written solutions to be judged by corporate executives, scientists and engineers. Solutions are judged based on practicality or implementation potential, effectiveness of the solution, the cost and benefit of the solution, creativity/originality, development of the idea, and documentation of the development of the solution.  Teams advancing to the finals present their solutions orally at each sponsor’s corporate headquarters.

Topics for problems may include, but are not limited to, the following: environmental issues, manufacturing, distribution, product formulation, chemistry, software creation, facilities design, engineering, marketing, personnel issues, etc.  An example of a successful problem from Hershey Foods Corporation follows: “Hershey receives cocoa beans in burlap bags, yielding over one million pounds of empty bags per year.  The most efficient way to empty the bags is to split them down the front, making the burlap unusable as bags.  Previously, the used burlap had been sold to a carpet company to be used as backing.  The carpet company has discovered a cheaper, cleaner material to use for backing.  Taking the burlap to a landfill will cost the company $40,000 annually, in addition to being harmful to the environment. What are other cheaper, environmentally friendly ways for Hershey to dispose of the burlap?”  The winning team for this problem consisted of four seventh graders (who beat teams of high school seniors).  This team appeared at the oral presentation wearing burlap vests and ties, toting burlap toys, with a Power Point presentation.  They had investigated a number of possibilities, with the most fruitful appearing to be a landscaping company who would shred the burlap and use it for mulch.  Although Hershey did not use the solution precisely as presented, the team’s research led Hershey to another alternative that resulted in a significant cost avoidance.

Teams may consist of students from different grades and/or different schools.  Sixth through twelfth grade students from all school settings (public, private, parochial, charter, vocational, alternative, or home schooling) are eligible.  Even students in mentoring programs or scouting programs are eligible to enter. Each team must have an adult coordinator, and coordinators may facilitate multiple teams.  No entry fees are charged and students from anywhere in the United States are eligible to enter.

There are a number of benefits for students and corporate sponsors.  Let’s Get Real is an opportunity for students to apply their problem-solving skills to authentic business situations, to work together in teams, to become better acquainted with and prepared for the business world, to make individual impressions on a major corporation, and to have fun!  Regarding benefits for corporate sponsors, Let’s Get Real provides an opportunity for businesses to become directly involved with young people, to encourage them to study in fields of interest to the corporation, to gain appreciation for the accomplishments of young people, and to derive benefits from the solutions generated by minds not constrained by “the box.” Corporations also benefit by publicly supporting education in their own communities.   

The following quotes are representative of participants’ reactions to the program:

                "Let’s Get Real is an exciting program that can provide several benefits to the sponsoring company at a very low cost. The company contributes to a better educated student who is more aware of the types of opportunities in Corporate America. The company also receives valuable PR and good will. If the problems for the competition are well chosen and presented, the competition also represents a chance of immediate payback of magnitudes higher than the cost of the program. But, perhaps most importantly, meeting bright enthusiastic students and listening to their outstanding presentations is inspiring and provides motivation for the employees who are lucky enough to attend the competition (Corporate sponsor)."

                "The Let’s Get Real program has become an academic competition that brings authenticity to the performance-based activities that I do in my classroom....[It] allows businesses to bring realities to the life of my students.  Grade is still important to my students, but when they tackle the actual corporate problems, they also know that the problem is real and their proposed solution could be implemented.  They know that corporate and business executives will be looking over their problems.  This becomes a driving force to my students...[They] understand that what they did meant something beyond a grade; professionals looked at what they did and gave it value (Teacher)."

Although not limited to gifted students, LGR is particularly appropriate for them.  The program embodies a number of the NS/LTI Principles for Differentiated Curriculum.  LGR involves interdisciplinary content; analyses reveal that teams have integrated language arts, technology, mathematics, economics, science, social studies, and the visual arts in their solutions. Problem solving and higher order thinking form the entire basis of the program. The problems by nature are complex; otherwise, corporate specialists would have already solved them.   Inquiry and in-depth research are involved as the students investigate their solutions and verify them through experimentation. The students are expected to work independently in creating their solutions, with the coordinator playing a strictly facilitative role.  The written solutions and oral presentations are high level products which are evaluated by multiple audiences, including the teams themselves, the coordinator, and possibly peers.  Ultimately these products are judged by corporate employees embodying authentic audiences. These factors interplay synergistically to create rich and challenging learning experiences for gifted students.

Information on entering the competition or becoming a corporate sponsor may be found at or by emailing Dr. Dan Holt at:

*Trade Mark


        Brooks, J.G. & Brooks, M.G. (1993).  In search of understanding: The case for constructivist classrooms.  Alexandria, VA: ASCD. 

        Dewey, J. (1916).  Democracy and education: An introduction to the philosophy of education.  New York: Macmillan.

        Gallagher, S.A., Stepien, W.J., & Rosenthal, H. (1992). The effects of problem-based learning on problem solving.  Gifted Child Quarterly, 36(4), 195-200.

        Piaget, J. (1985).  The equilibration of cognitive structures.  Translated by T. Brown and K.J. Thampy.  Chicago: University of Chicago Press.  (Original work published in 1975).

        Savery, J.R. & Duffy, T.M. (1995).  Problem-based learning: An instructional model and its constructivist framework.  Educational Technology, 35(5), 31-35.

        Stepien, W.J., Gallagher, S.A., & Workman, D. (1993). Problem-based learning for traditional and interdisciplinary classrooms. Journal for the Education of the Gifted, 16(4), 338-357.  

        Stepien, W. & Gallagher, S. (1993, April). Problem-based learning:  As authentic as it gets. Educational Leadership, 25-28.     

        Torp, L. & Sage, S. (1998).  Problems as possibilities: Problem-based learning for K-12 education.  Alexandria, VA: ASCD.



Musical Prodigies: Perilous Journeys, Remarkable Lives by Claude Kenneson (1998). Amadeus Press, Portland, Oregon.

"My earliest musical memories are from the time when I was a baby and crawled under my dad's piano. While he played I remember lying there looking up at the struts and sounding board, and the sound would come down and envelope me. I loved being there under the piano while he practiced. . . ." (Bejun Mehta, p.336, from Musical Prodigies (1998) by Claude Kenneson).

The author makes clear throughout this fascinating examination of the development of musical prodigies that family environment interacting positively with the unfolding of the child's natural abilities are the most important factors in developing young, highly gifted musicians. But the individuals Kenneson discusses are beyond giftedness. They are so extraordinary as to defy current explanations from developmental and educational psychology. The early lives and precocious achievements of many of the great ones are discussed here -- Mozart, Paganini, Clara Schumann, Heifetz, Casals, Piatigorsky, Rubinstein, Gould, Argerich, Cliburn, du Pré, Yo-Yo Ma and other concert artists of the violin, piano, cello, string bass and guitar. Precocious composers (e.g., Mozart, Samuel Barber), conductors (e.g., Pierino Gamba, Lorin Maazel) and a singer (Bejun Mehta) are also included. 

Kenneson, a music professor emeritus at the University of Alberta (Canada) attempts to make sense of these "miraculous" early achievements by describing his experiences in teaching two young children to play the cello -- Eric Wilson and Shauna Rolston. In the chapter entitled, "Reader's Guide," Kenneson discusses some of the common features of the prodigies he has taught and studied for his book, such as: early rapid development, intensive encounters with music in a family environment that supports musical accomplishment, the nurturing influence of families that rearrange their lives and work to foster their child's musical development, and the importance of using music in a playful manner during the early years. What is clear to this reviewer is that successful musical accomplishment at a young age (beginning at three or four years) requires intensive early exposure to musical performance, primarily through at least one parent who is a skilled musician. Additionally, music teachers other than the parent(s), come into the picture early in the young prodigy's musical life beginning at three to eight years. These teachers appear to be almost as important (or in later years, more important) than parental influences. The combined influences of parents and private music teachers produce a synergy effect in these precocious children's lives that advances their musical accomplishments to the highest possible levels.

Kenneson has done a great service to educators and parents by writing this excellent book. What positive use can they make of his pertinent descriptions and insightful conclusions? First, it is clear that numerous opportunities for the growth of these extraordinary children must be provided through schools of music, music teachers and music programs in public and private schools. Unfortunately, the public schools of America are currently ignoring their music education programs to the detriment of children who range from very capable to highly gifted to extraordinary accomplishment. In most cases, the burden must therefore fall on perceptive parents and teachers who are sensitive to musical ability at an early age, and to great music institutions such as Juilliard and the Curtis Institute.

For many years, this reviewer has been concerned with the role of children's sensibility levels in their mental development as expressed through heightened awareness and responsiveness to particular aspects of their environment such as tones, rhythms, melodies and musical performances. Clearly, musical prodigies have sensibility levels to musical sounds and rhythms that are far beyond those of average children. In addition, they are endowed with advanced sensori-motor abilities that enable them to use a violin bow or strike piano keys in a coordinated and rhythmical manner. Their accelerated cognitive development also leads to facility in reading music notations. Can children's interest in and responsiveness to music be enhanced by the proper types of exposure to music at a young age?  From reading Musical Prodigies and other related works (described below), it appears that young children benefit from organized music programs. But the rare musical brilliance described by Kenneson is a different story -- unique types of mental development must also be present (as a result of the child's genetic, psychological and physiological makeup) to bring musical aptitude to the level of a prodigy. Other books that will help to illuminate the reader's understanding of musical prodigies are as follows:

Developing Talent in Young People by Benjamin Bloom (1985, Ballantine Books) and Music Talks by Helen Epstein (1987, McGraw-Hill).

Both of these books emphasize the role of music education during the child's formative years. Bloom's book (based on psychological studies and interviews) has several chapters on the lengthy and arduous music education of concert pianists. Epstein has interviews with many outstanding musicians such as Itzhak Perlman, Cho-Liang Lin, Midori and Yo-Yo Ma. She also describes the work of the violin teacher Dorothy DeLay (Juilliard School of Music) with violin prodigies.

Isaac Stern: My First 79 Years by Isaac Stern, written with Chaim Potok (1999, Knopf).

Here is the extraordinary life and professional career of this joyous, world-renowned musician. Stern's family immigrated from Russia to San Francisco where he began his accelerated progress and success on the violin starting at about eight years.

Thomas Wolfe (1900-38): An Appreciation on His Centennial

by Michael E. Walters  Center for the Study of the Humanities in the Schools

The United States celebrated the centennial of the birth of Thomas Wolfe in October 2000 when a commemorative stamp was issued in his honor from his hometown in Asheville, North Carolina. (He died tragically of tuberculosis of the brain at thirty-eight years.) The original completed manuscript of his masterpiece, Look Homeward Angel (1929), as he wrote it without editing has been published by the University of South Carolina Press under the direction of Arlyn and Matthew Bruccoli. This Centenary Edition (2000) uses the original title, O Lost: A Story of the Buried Life. The manuscript and notebooks related to the creation of this masterpiece were recently displayed in the New York Public Library's main building on 42nd Street where I had the wonderful opportunity to visually experience the creative artistry of a major American literary genius.

Look Homeward Angel has been described as the classic book of an American who is coming-of-age, and a novel for gifted and sensitive adolescents similar to Catcher In the Rye (1951) by J.D. Salinger. Upon re-reading Look Homeward Angel, I find it is also a novel concerning the development of a gifted individual. Throughout the book, the author describes how the main character, Eugene Gant, becomes interested in and devoted to the craft of writing.  In 1929, when Wolfe’s book was published, the written word and reading were considered to be more important human activities than they are today. Wolfe composed this book in the same format as Virgil (Aeneid), Dante (The Divine Comedy) and Milton (Paradise Lost), all epics of the human condition. The epic that Wolfe authored was about the self, and how it interacts and relates to the American experience. It is simultaneously an autobiographical and national epic that describes the positive and negative qualities of the American psyche -- the ability to transcend one's environment, and to express the democratic and progressive spirit of the United States.

His writing style (poetic prose) was as important as its content, and it is obvious that he was influenced by Walt Whitman's Leaves of Grass (1855). This poetic prose enables the reader to share Wolfe's perceptions and visions by means of various literary techniques such as reminisce, repetition and rhythmic patterns of expression.  In addition, his style throughout the book was the print version of techniques used by French Impressionist painters. By giving readers mental images of past experiences, they almost believe these events are happening to them. Another writer who influenced Wolfe was the French author, Marcel Proust (Remembrance of Things Past, 1913-27).  Like Proust, he makes the reader a part of his personal memory, an excellent example of literary genius at work. By reading  Look Homeward Angel gifted students can learn how Wolfe made his artistic craft appear so effortless and unique.

The citizens of his hometown were upset with Look Homeward Angel because Wolfe described the social reality of Asheville, North Carolina with honesty. He wrote about anti-semitism, racism, sexism, homophobia and class attitudes that were part of the mental fabric of his environment. For Wolfe, the biblical injunction, "The truth shall set you free" (John 8:32), was a personal code of behavior. In 1998, the childhood home he wrote about was seriously damaged in an apparent arson attack. However, his classic of the American experience, Look Homeward Angel, will always be with us like a lighthouse for the American soul.



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