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  Reprinted from the May 1991 PHI DELTA KAPPAN  

  Cutting Education's GordianKnot

What has been fundamentally wrong with formal schooling for thousands of years, Mr. Swengel suggests, is its basic instructional unit: teacher-and-class. He proposes mutual instruction as the solution to this knotty problem.


EDWIN M. SWENGEL (San Diego Chapter) spent most of his professional life in classroom teaching, spanning all levels from Montessori preschool through graduate programs in education. A retired professor of education, he now consults with those interested in restructuring the school system and is working on a book on the theory and practice of mutual instruction.

In 333 B.C., Alexander the Great, bent on world conquest, tried to untie a baffling knot in Gordium, capital of Phrygia. Reputedly, only the conqueror-to-be of Asia could unravel this Gordian knot, whose ends were inside it. After futile attempts to get at them, Alexander drew his sword and slashed through the knot - and then went on to conquer a goodly chunk of Asia. For centuries educators have been pulling at the recalcitrant strands of the educational knot. But reformers seem loath to swing a sword that will cut the knot and free the school system to fulfill its cultural responsibilities.

  If we dared to cut, we would find the knot's ends to be "learners" and "learning," not the same as "teachers" and "teaching," two additional strands of institutional wrapping that must be unwound. Teachers need to be freed to teach as individuals, just as learners need to be freed to learn as individuals, not as members of a group of 25 or more same-age classmates, shackled together and clomping along in rigidly scheduled, lock-step curricula.

What has been fundamentally wrong with formal schooling for thousands of years is its basic instructional unit: teacher-and-class. Group instruction has never been even moderately successful for the simple and obvious reason that learners are so different that any large-group lesson is certain to be too difficult for some and too easy for others — and irrelevant to most. Trying to teach and to learn in a system so inherently inefficient demoralizes teachers and frustrates learners.

The radical restructuring that many critics call for must get at the taproot--the uniquely individual learners, who have the right to equal opportunities to develop their unequal abilities and talents. That right cannot be realized optimally under the conditions of group instruction. A system of genuinely personalized instruction must be devised--one that develops the potential of learners, of teachers, of parents, and of administrators and that also meets society's requirements for competent, reliable citizens. These apparently contradictory goals—individual development and social responsibility—can be achieved by cutting through the tough knot that group-centered education has tied itself into.


Fortunately, a very sharp sword is at hand and has been for more than 30 years (actually for millennia): learning with and from other learners. The current pedagogical terms are peer and cross-age tutoring and counseling. A less common but more descriptive term is mutual instruction (MI), a phrase which suggests that tutors and counselors benefit along with their tutees and counselees. Since the early 1960s, thousands of-one-to-one peer assistance programs at all levels from preschool through graduate school have proved successful with all types of learners in all subjects. (Because MI is currently a concept in search of adoption, I cannot describe the features of actual programs. However, to simplify syntax and verb tense. I will describe the potential of MI as if the concept were already in operation.)

Two researchers conducted a meta-analysis of 65 comparative studies of peer tutoring and came to the following conclusion:

Students who participate in tutorial programs--both as tutors and tutees--show greater cognitive growth and attitudinal gains than do students who are not involved in such programs . . . Tutors not only develop more positive attitudes toward the subjects they are teaching, but they also gain a better understanding of these subjects.

However, most peer programs were and still are small-scale remedial or supplemental adjuncts, tacked lightly onto the conventional classroom system of group instruction. Such cross-age programs are sometimes viewed as an added burden placed on already overloaded teachers. The benefits to the few students involved eventually seem not worth the effort to the cooperating teachers.

The often dramatic cognitive and affective gains made by participating tutors and tutees are richly documented, even though they are usually achieved in relatively short time periods and in one subject only, such as 15- or 20-minute tutoring sessions in reading or math that meet three or four times a week during only a part of the school year. The tutors may receive only brief training and little supervision. If so much can be accomplished in so little time and with minimal training and support, should not schools be restructured so that all students could receive these benefits in all subjects at all levels?


An old adage says, "He who teaches is twice taught." A learner needs to "teach" a subject in order to understand it well. Therefore, teaching, in the sense of helping others learn, must be recognized as an essential learning experience for everyone, not just a kindly volunteer service offered by the more able to the less able for the sole benefit of the latter. When a class is divided into tutors and tutees, the tutees often resent their inferior status. All learners need both experiences and in about equal measure.

"Twice taught" also applies to the affective part of the tutorial relationship. We often forget that learning is basically social. Tutoring integrates learning and friendliness; it nurtures patience, tolerance, respect, good humor, and affection. Both tutor and tutee succeed in personal relations and in learning subject matter. These combined successes enhance the self-esteem of both parties.

Most reform-minded critics call for more head learning, i.e. more science and math to make America strong enough to regain world economic leadership. However, our nation's weaknesses are as much moral as mental. The delinquencies that rend the fabric of society are moral: violent crime, drug abuse, irresponsible sex, greed in business and politics, selfish unconcern for the environment present and future, racism, Madison Avenue materialism. People who commit crimes, who exploit and abuse others, lack the most basic of moral values: an equal concern for the rights and welfare of others and for one's legitimate self-interests.

Moral values can and should be learned as directly and consciously as the alphabet, addition facts, and the order of U.S. Presidents. But children learn values and attitudes best from real-life experiences in caring and responsible relationships with persons of all ages, backgrounds, interests, and abilities. Peer and cross-age programs provide ideal learning experiences because they combine intellectual subject matter and human relationships. Tutoring requires tutor and tutee to sharpen and refine their communication skills, to learn to listen and to speak with head and heart.

A humane society grows from and is sustained by a humane school system, whose organizing and directing principle should be: "Learn to teach and teach to learn." This credo weaves moral training into the curricular fabric, giving it extra strength and brighter color.


In 1961 in a landmark book, research psychologist J. McVicar Hunt went out on a pedagogical limb. He predicted that, if "the problem of the match" were solved, the I.Q. of all learners (as measured by standardized I.Q. tests) might conceivably be raised a "substantial degree . . . of the order of 30 points of I.Q." Besides citing extensive research data reporting increases of 30 or more points of I.Q. when learners were put into stimulating environments, Hunt introduced Jean Piaget's concept of the development of intelligence to support his own claim that educational experience, not innate intellectual endowment, is by far the greater determinant of measured intelligence. (The conventional wisdom at the time gave nature about 75 % and nurture about 25 % of the credit.) Hunt issued a challenge to investigate the possibility that I.Q. could be raised, a challenge that educators have not deigned to accept.

The "match" Hunt referred to is between a learner's readiness to learn and an environment that provides the necessary opportunities and support: for example, providing instruments and instruction to develop musical talent, art materials and guidance for artistic interests, gym and playground facilities and coaching for athletics, and creative contacts with interested persons to nurture intellectual interests.

Hunt was especially concerned about intellectual development in the critical years of early childhood. He was pleased to rediscover Maria Montessori's theory and practice of providing a "prepared environment" suited to the varied learning needs, styles, and abilities of children aged 2 to 5. The Montessori method (especially when enriched with more music, art, and large-muscle activities) provides for stimulating interplay between nature and nurture in these early years.

The confidence that an MI system can solve Hunt's "problem of the match" and significantly raise levels of developed intelligence (what I.Q. tests actually measure) is strongly supported by extensive research projects headed by Herbert Walberg and Benjamin Bloom. With colleagues, Walberg reviewed the original studies of productive classroom practices and the syntheses of these studies. The data from thousands of studies yielded four major factors that contribute most to what Bloom terms "mastery learning": reinforcement, acceleration, reading training, and cues and feedback.

The MI system provides all of these elements in a unified, integrated way, so that their combined effect could conceivably raise the mean scores of experimental groups on standardized academic tests by more than three standard deviations above the mean of control groups--an outcome that Walberg suggests is possible. From their peer tutors, learners get immediate reinforcement for their efforts. Students move as fast and as far as their interests and abilities carry them. Tutors are trained to help other students understand the kind of reading (usually the type of thinking) required in each subject area. Tutors provide the necessary cues and immediate feedback that tutees need to stay on course. In tutoring, students are "on task" 90% of the time, in contrast to only 50% of the time under conventional classroom instruction, according to Bloom.

Walberg also points out that these combined effects on learning are nearly 15 times more powerful than the effect of socioeconomic status. The problem of providing high-quality schooling in depressed and minority areas need not wait for the elimination of poverty. Through the learners' own abilities to help one another, MI can provide high-quality schooling at any socioeconomic level.

Some critics complain that MI wastes students' time in teaching what they have already learned. However, Bloom's extensive five-year study of individuals highly talented in athletics, the arts, and research found that repeated drill on the fundamentals---overlearning--is essential in developing talent. He optimistically concluded that "each society could vastly increase the amount and kinds of talent it develops"--but not under the usual classroom conditions.

From results of another major study comparing a variety of classroom teaching techniques to one-to-one tutoring (considered the most effective teaching/learning situation), Bloom became convinced that, given time and competent individual assistance, all students but those with severe mental disabilities can achieve mastery levels in required curricula, as Walberg's findings also suggest.

However, Bloom is wrong in stating that cost prevents schools from providing one-to-one tutoring for all students. He studied tutoring by paid adult teachers. But other studies have shown that peer tutors can be as effective as professional teachers in tutoring." Because all MI students learn to be tutors, a school using MI always has a one-to-one "teacher"/pupil ratio, with the tutors backed by professional teachers who would be available for tutoring beyond the students' expertise.


The following elements are not unique to MI. What is unique is the way they are organized and integrated around the central principle that peer teaching is an essential part of learning, both social/psychological and intellectual. MI is flexible and open-ended, but it is not an eclectic hodge-podge of "good ideas." Any effective teaching/learning materials and techniques can be incorporated into MI, if they can be adapted to one-to-one and small-group learning.

To offer a wide variety of subjects and to ensure a stimulating variety of talents and personalities among the learners, teachers, and aides, the optimal size for an MI school is 1,000 to 1,200 students, ranging in age from 2 to 18. All would be housed on the same campus, staffed with 40 to 50 teachers and 40 to 50 aides. Aides handle the logistics of room management, do routine supervision, and give some instructional assistance. Computer programs facilitate record keeping to chart individual student progress.

Include early childhood education. Public schooling should be extended to include 2- to 4-year-olds. MI schooling is continuous, not divided into separate age-and grade-level schools. All learners have access to all teachers and all subjects. The MI school is a real-life microsociety, in which all members are available to one another for help and companionship as needed and desired.

Early childhood education belongs in the public school, though it need not be compulsory. Even very good homes cannot provide all the intellectual and social experiences that children need in their critical early years. Given the probably irreversible trend toward full-time careers for both parents in most families, competent early care and education will become a public responsibility equal to that of educating older children.

Provide pre-parenting experience. Another compelling reason for schools to have an early childhood program on site is the opportunity it provides for older students to observe and work with young children. Parenting skills in humans are not instinctive; they must be learned. On-the-job training is usually too little and too late, even when one parent can be at home full-time. To strengthen home life, present and future, all students need some experience, under professional instruction and supervision, in dealing constructively with a variety of young children at work and at play. Having preschoolers on campus facilitates these important cross-age intellectual and social contacts.

Grades and grading out; mastery learning in. Age-graded classes and any kind of system of letter grades should be eliminated. Learners in an MI school move at their own pace through developmental programs geared to their abilities and achieve required levels of competence, with peer and teacher assistance as needed. Thus, students cannot fail a course or a grade.

Fear of failure or of a poor showing is a powerful deterrent to learning. Confidence in one's abilities, coupled with tutorial support, can be a powerful stimulus to learning. Moreover, success in learning breeds more success, especially when learners have some freedom of choice in what, when, how, and with whom they learn.

"Enjoy your preschool days while you can."

Professional associations are developing comprehensive K-12 curricula that concentrate on basic concepts and thinking skills—teaching less but in greater depth. This can best be accomplished if developmental programs are cast in forms that support self-instruction and peer tutoring. Learners tackle a program when they have the requisite entering knowledge and skills. Knowing that they can get all the individual help they may need, learners have no fear of failure.

Helping others learn what one has become competent in oneself is an ideal way to achieve a broader, deeper grasp of essential information and concepts. Repetition is necessary for mastery and for long-term memory. Tutors creatively review what they know as they repeatedly reconstruct their own understanding to fit the growing understanding of their tutees. Instruction in how to tutor and how to be tutored emphasizes ways to ask penetrating questions and to evaluate answers. All the higher-level thinking skills are used in tutoring and collaborative learning. Moreover, these skills cannot be practiced nearly as intensively in teacher-led group discussions and are difficult to practice alone. (However, many tutors testify that they often converse with themselves when studying independently, quizzing themselves as if in a tutorial session.)

Harness pupil power for personalized learning. Obviously, this is the central distinctive feature of MI. The failure to recognize and fully use students' creative energies and abilities in helping to solve academic and personal problems is the main reason that other reform efforts have failed to achieve genuinely individualized instruction, which requires personalization.

There is nothing wrong with giving a child a worksheet of challenging problems. But it is wrong to give a child a worksheet that is too hard or too easy. And it is worse to fail to give immediate feedback in an effort to find out how a child arrived at correct answers and why he or she made errors. It is still worse to fail to go back and fill in the gaps in learning, "picking up the dropped stitches" that weren't knit into a particular academic garment. The critical teaching/learning interchanges required for mastery demand the kind of one-to-one attention that a single classroom teacher lacks the time to give to every student every day.

The critical elements in peer-tutoring programs are adequate training and ongoing supervision of tutors. These are major responsibilities of an MI teacher, but many well-developed, field-tested training programs are available. The training of tutors soon becomes automatic and self-instructional, and tutees learn how to tutor by working with well-trained tutors.

MI solves two of the most intractable problems of conventional schooling: motivation and discipline. Very little of what schools demand that students learn has any immediate value in their daily lives, so they have little desire to learn it. However, learning in order to help others learn provides an attractive and realistic external motivation that is rooted in our social instinct to share knowledge. After all, why are secrets so hard to keep?

This motivation to learn, coupled with success as tutor and tutee, leaves students without a reason to "buck the system." They ally themselves with teachers: they assume the responsibility of being dependable role models for their tutees, who in turn work hard to please their tutors. Those who work in tutoring and peer-counseling programs are nearly unanimous in asserting that discipline problems are infrequent, mild, and practically nonexistent--even when "problem pupils" are in the program.

Provide study rooms and learning labs, not classrooms. Some young, timid, and insecure children need a homeroom, which MI provides. However, most learners enjoy going to departmental study rooms and learning labs for instruction by specialists in each discipline.

Large study rooms can comfortably accommodate 40 or more students. They are distinctively furnished and decorated so that students "breathe" the different air of each discipline. Young children need and deserve the stimulation of such environments as much as do older students. Language arts, literature, social sciences, and mathematics are not taught in the same drab rooms, as is common in junior and senior high schools. Neither should all subjects be presented in all purpose, self-contained, age-graded K-6 elementary classrooms.

Two teachers and two trained aides staff each room. Each teacher/aide team specializes in either the introductory or advanced levels of a discipline, but all staff members get to know all students of all ages as they intermingle in their rooms. Interested older students become influential models and mentors for younger ones. The specialist teachers help students plan their individual research projects and pair them with tutors. Students who wish to work together voluntarily form small study and research groups.

Give teachers professional status. Other professionals deal with their clients largely on a one-to-one basis. Why not teachers? Freed from nonteaching duties and large-group instruction, MI teachers work professionally with individual students and with small groups. Teachers have time to study available programs and to adopt, adapt, and design specialized work units to suit students' special needs. Teachers have time to confer with their colleagues and with parents about individual students' specific and general progress. Teachers cooperate in designing interdisciplinary programs that integrate student learning.

Develop a sense of community. Although MI emphasizes the primary importance of one-to-one and small-group relationships, these need to be supplemented with a sense of membership in a larger group. The whole school is too large, and the succession of contacts with fellow students and teachers in the departmental rooms is too diverse and unconnected to serve as a "home base." The concept of the MI "family" provides a solid sense of being a valued member of a permanent, ongoing community.

About 25 students, equally distributed across an age range of 5 to 18, are designated as a "family." Each such family is headed by a teacher and an aide (preferably of opposite sexes, for a "father/ mother" pair). They serve as primary counselors to these students as long as they are in school, providing continuing oversight of each child's total progress. This arrangement facilitates contacts with parents, who need not establish a new rapport with a different teacher every year. Each MI family stays together year after year, adding new members as some graduate or move away or as a need for a special personal relationship is accommodated by assignment to a different family. Except for the oldest and the youngest, each family member is a big brother/sister to a younger member and also a little sister/brother to an older member.

Each family meets daily for 45 minutes or so, primarily for socializing, for getting to know one another well, and for learning about out-of-school activities. "Show and tell" is appropriate for family gatherings. The family occasionally lunches together and attends some school-wide meetings as a unit. Each family "adopts" four or five preschoolers and gives them special attention, frequently bringing them to family meetings.

The families sing traditional songs together, read some of the classic poetry and stories that help shape our national psyche, and make preparations for and celebrate national holidays. Students plan and direct most of the family meeting activities, which provide social and learning experiences that supplement and complement other school activities and fill in any academic or social gaps in their more individualized programs.

As primary counselors for each of the "children," the family teachers help plan the students' total program so that it is reasonably well-balanced between required subjects and individually chosen projects.

Lay a solid foundation for literacy and build on it. Success in MI depends as heavily on proficiency in reading and writing as does conventional schooling. However, MI strives to guarantee that every student not only becomes literate but also enjoys all the activities that involve literacy.

Many years ago, one of the first encouragements I received in my beginning pursuit of the then-embryonic concept of MI came from a professor of education at the University of Illinois. He knew of no formal research on the subject, but he warmly reminisced: "When I started my teaching career in a one-room country school, we'd never heard of a 'nonreader.' The other kids would take the little ones into their seats and just wouldn't give up till they taught them to read." Dolores Durkin found evidence aplenty that older children are efficient tutors of beginning readers.

Because the preschoolers are on campus, older children can read to them individually and talk with them about the stories and about themselves. The older children can print the stories that the youngsters tell and compile them into bound booklets to put in the class library. Older children can help the beginners write their own stories as they learn to print and read. Through such continuing personalized, unpressured tutorial attention, every child can become a confident, competent reader and writer.

Learning to read is not nearly as complicated and tortuous as the reading "experts" have made it. Of all the basic skills, reading and writing most need truly individualized, personalized instruction of the quantity and quality that only a well-organized, comprehensive cross-age tutoring program can provide. Moreover, such an individualized program can begin around age 2. The aim is not to rush preschoolers into reading, but to develop their verbal competence and their interest in all the things they will hear and read about.

Once a child has started reading, by whatever method, "reading" problems are mostly comprehension (thinking) problems, frequently exacerbated by psychological hang-ups spawned by pressure to "keep up with the class" and fear of failure. The tyranny of age-based expectations that drive the standardized basal reading programs is the single greatest cause of functional illiteracy. This is the major "pedagogenic" disorder caused by the age-graded, group teaching/learning system.


Once the school knot begins to unravel, freeing students to learn as unique individuals and teachers to teach as unique individuals and to serve as resource persons and facilitators, other knots, large and small, almost untie themselves. MI gives us a hold on the "learner" and "learning" ends of the educational rope. But it can also untangle most of the persistent subknots that have always frustrated attempts to improve schooling significantly.

Flexible scheduling. With MI there is no need for daily, quarterly, semester-long, or yearly course scheduling that prevents students from covering all the subjects they wish to study when they want to study them. All required courses are available in a variety of programs that individuals and small groups study according to their individually planned schedules. Teachers schedule planning, instructional, and evaluation meetings as needed with individual students and small study groups.

Instead of operating as year-round schools that schedule students and teachers to be in school or out for blocks of time, MI schools can require students to put in the state-mandated number of school days and hours in whatever patterns suit their own and their families' work and vacation schedules. When students are out of school for any reason, they do not "miss out" or have to "make up" work. On their return, they simply pick up where they left off in their own study programs.

Invest time in leisure. Most observers, along with frustrated students and teachers, agree that group instruction is highly inefficient, wasting half or more of students' learning time. Personalized MI programs cut in half the time most learners need to master the required curriculum. Students invest this saved time in developing personal interests and hobbies to fill their leisure time in creative, satisfying ways.

One's sense of self is often based more on productive use of leisure time than on one's job or profession. There aren't enough self-fulfilling jobs for everyone, so students should use school time to develop skills and interests to occupy their leisure time. The school provides facilities and opportunities to develop these skills and interests in arts and crafts, in music, in drama, in sports, in reading, and in subject areas not included in the regular curriculum.

Costs. The administrative bureaucracy is the only segment of the traditional system that will bleed when the MI sword cuts into its stout ropes. But the question must be asked: Since private schools flourish without central office supervision and support, why can't public schools do likewise? The current trend in school restructuring is toward decentralized control and local school empowerment. This approach can save substantial administrative costs, which can be invested in trained aides (the equivalent of nurses for doctors), the only extra cost associated with MI.


Vastly improved teacher training is built into the MI system. Teachers tend to teach as they were taught. After 12 to 15 years of mutual instruction, graduates who opt to continue their teaching careers as professionals - or as aides and/or parents — will know how to work in and improve an MI system. Professional training at the college level would expand their knowledge in content areas and deepen their understanding of MI theory and practice and so help to make the system ever more responsive to the needs of individuals and of society.


Regardless of its political and economic system, any society will fail unless its members become competent and caring citizens. The usual system of group instruction has trouble attracting and holding skilled and dedicated teachers and eager and industrious students. The current dropout rate is about the same for both. (About 20% of teachers "drop out" within their first five years.)

Empirical evidence from more than 30 years and tens of thousands of limited, small-scale projects in tutoring and counseling strongly support the belief that a comprehensive Ml system as sketched herein would produce far cooler heads and much warmer hearts than any system has yet achieved. Because the effects of MI are cumulative, the overall impact of mutual instruction cannot be fairly determined in less than a full school generation of MI experience - 12 to 15 years.

However, the varied evidence now available justifies the belief that, through mutual instruction, every student can develop a high level of intelligence and character that will sustain a firm sense of security, a well-earned feeling of self-worth, and a dedication to lifelong learning. These traits will carry over into adult life and contribute to the development of a cultured society that will guarantee not only the survival but the continued growth of democracy, "the last, best hope of earth."

  Peer and cross-age tutoring projects were widespread during the experiment-oriented 1960s and '70s. No other innovations proved as consistently successful in improving students' academic learning and attitudes. Unfortunately, as with many other promising innovations, peer helping programs were down-sized or discontinued in the back-to-basics pendulum swing of the 1980s.

However, further development and refinement of peer programs have continued. Current data bases contain around 1500 reports of successful peer programs covering the curriculum at all levels from early childhood through graduate school. This literature amply supports the following—and many other—claims about peer helping:
  • one-to-one tutoring improves learning for both tutor and tutee significantly beyond the levels they achieve under classroom instruction;
  • all children can learn to give and receive one-to-one help effectively;

  • most students are eager to give and receive individual help, and take their tutor and tutee roles seriously—and creatively;
  • the help that most children need to solve garden-variety learning problems can usually be efficiently given by trained peer tutors, freeing teachers to work with students needing help beyond tutors' capabilities;
  • tutors' self-concept improves almost instantly when they start to tutor;

  • "bad kids" behave responsibly and conscientiously while tutoring, and their overall behavior and attitudes gradually improve as they continue to get and give more individual help;
  • average and below-average students learn to be competent tutors, often more patient and understanding than academically more proficient students;

  • gifted students need both the tutor and tutee experience to develop their communication and social skills, especially with slower-learning schoolmates;
  • special education students can learn to tutor their classmates successfully;

  • emotionally-disturbed teen-agers improve their learning and general behavior as a result of doing tutoring.
A peer program has no financial cost. It takes initially only interest and some dedicated effort from teachers, administrators, and students to get a program started. Once under way and with continuing expert guidance and support, peer programs become largely self-governing, self-perpetuating, and self-correcting. Tutors and tutees ally themselves with the adult staff.

A comprehensive peer helping program can solve or greatly ameliorate most of the problems that frustrate students, teachers, administrators, and parents. In any school, the students themselves are a rich and largely untapped resource that can and should be used to raise the learning and behavior of all students to levels that cannot be reached under traditional methods of group instruction.

Mutual Instruction --
Learn to teach. Teach to learn.

[Note: If you would like the original version with all the footnotes with sources,
please write to Marcia Swengel Powell at marpo3344@gmail.com and she will email it to you.]

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Copyright © 2010 by E.M Swengel