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Don’t give up on schools, there is still much to be done

By Gary Stager

District Administration, Aug 2006

Dear Mr. Gates:

I write with great admiration and appreciation of your remarkable philanthropic efforts on behalf of health, poverty and education. Changing the world is a spectacular goal. Congratulations on your plans to dedicate more of your time to charity and on Warren Buffett’s enormous contribution to the Bill and Melinda Gates Foundation’s efforts.

I know nothing about infectious diseases, vaccines or sustainable agriculture. I defer to you and other experts on those topics. A recent Business Week cover story, Bill Gates Gets Schooled, was eye opening. That article reports the mixed success of your foundation’s efforts in public school reform and your candid admission of disappointing results. It must be depressing to spend a billion dollars on school reform and all you got was a lousy t-shirt. I humbly share the following recommendations to help guide your future initiatives.

Decide what you believe

You and all your advisors should read Seymour Sarason’s book, What Do YOU Mean by Learning? Sarason makes what should be an obvious observation that discussions of learning, teaching and school reform often fail to discuss what the stakeholders mean by learning. Without such a serious ongoing discussion, failure is predictable.

With all due respect, the Gates Foundation needs to decide what it means by learning and stop funding competing organizations. Investing in the Met Schools (see “Radical Reformer,” November 2005, page 46) and Achieve, Inc., simultaneously is like funding both sides of a war.

Apparently it is rocket science

The Business Week article tells the story of a Denver High School that received Gates Foundation funds. The school was broken up into four smaller schools in an attempt to make schooling more personal and have fewer students fall through the cracks. However, the school’s award-winning choir, a perennial source of pride and excellence, crumbled when students were dispersed to four different schools within the building. Surely, some smart adult could have figured out a plan to move children from one corner of a school to another for choir practice?

It must be depressing to spend a billion dollars on school reform and all you got was a lousy t-shirt.

Schools are complex organisms full of unintended consequences

A recent Los Angeles Times article chronicled how the noble goal of breaking large high schools into small, more personal, learning communities does foster school pride. However, it also may cause those communities to become tribes hostile to one another and result in limited elective options for students.

The impossible is easy, the easy is often impossible

This is my axiom to explain the chaotic nature of schools. It may indeed be easier to build a residential campus in Paris for New York City ninth graders than to hire a French teacher for their neighborhood school.

When seeking clarity, ask yourself a simple question: “Would I proudly send my child to this school?”

Drop the business metaphors

Stop talking about schools as businesses and using terms like efficiency, productivity, supply chain and measurable outcomes. Such metaphors are weak and create needless tension among your “partners” in education.

Drop the school metaphors

The clich?s used by educators to describe their practices and objectives can prove just as stifling and counterproductive as business metaphors. Reflexive mantras like “Sage on the stage” and “You must invest in professional development” fail to acknowledge the complexities of education and provide alibis for failure.

Stop talking about results

Such short-term language may be appropriate for quarterly profit statements, but not education. Learning is messy, individual and natural. Schools do not manufacture widgets, but create an environment in which children and teachers may grow.

If you do wish to focus on results, be honest about what works. Education is notorious for having ideology trump evidence. Your talk of “more rigorous curriculum” and scores directly contradicts research funded by your foundation. The Met/Big Picture schools are wildly successful despite the complete absence of any traditional notion of curriculum. If you want results, build a lot more schools like the Met and let go of the fantasy of one-size-fits-all magical curricula.

You need to meddle

If you pay the bills, then you have a right and responsibility to run the school. A hands-off approach to schools you fund creates confusion among the stakeholders. Your support, insight, expertise and clear expectations must be apparent and consistent.

Work with the living and do no harm

You have acknowledged that it is easier and more effective to build new schools than fix some existing ones. Keep creating great schools where children can flourish and building models others can follow.

Solve the college readiness problem

If you find that preparing poor, urban, rural and minority students for college is too difficult, then build some colleges with open enrollment in those communities to offer opportunities students would otherwise be deprived of.

Admit that math education is a disaster

Almost nothing done in the past 50 years has helped students be more numerate. Work with Seymour Papert to invent a mathematics curricula that students could love, rather than coming up with tricks to help a few more memorize algorithms irrelevant to their lives and the complex world in which they learn. Computers have a clear role to play in learning about such sciences of complexity.

Show some courage

You are the richest man in the world. That’s like having tenure. You may work without fear! You and Oprah spent two hours on television alerting the public that too many schools are failing too many children. However, you seem reluctant to discuss the underlying causes of poverty, inequitable funding formulas and the resegregation of our nation’s public schools. The Gates-funded Manual Arts High School in Denver that has now closed was destroyed by the resegregation of the school. Civil rights are critical for students and you need to lend your voice to that struggle.

Education Secretary Margaret Spellings likes to say, “Schools are the same as they were 25 years ago.” That is demonstrably false. I graduated high school 25 years ago and enjoyed a full-range of electives, three music classes per day, great bands, fabulous plays, no AP courses, little tracking and teachers did not soil themselves over the need to raise scores on deeply flawed standardized tests. The climate of fear, name-calling and punishment paralyzing schools today is a recent phenomena produced by those professing to help.

We will have achieved success when all schools are demonstrably great places where children prefer to be and authentic learning exceeds our expectations. I wish you well in your quest to create such a reality.

Gary Stager on International Ed Comparisons

John Dewey is Ours!

By Gary Stager

District Administration, Apr 2005

Put on your dunce caps! It’s international education comparison season again. I know. I know… Eritrea is kicking our butt in long division. If we don’t get tough quickly, all of our best fast-food jobs will be outsourced overseas.

During this somber season of atonement, assorted windbags take to the airwaves to decry the callous incompetence of American teachers and to label our students as fat, lazy and stupid. We learn that country X focuses on the basics; country Y spends more time on fewer topics; while country Z has a longer school year. Don’t you just love how after careful review of the data, the prescription for American public schools is always more testing, increased sanctions, louder name-calling and longer seat-time?

 While there are always lessons to be learned from beyond our daily context, educational innovations abound in classrooms across America. Yet we ignore them. The cynical political forces that scare the populace with annual Sputnik hysteria play upon an unhealthy fear of foreigners and a neurotic national identity.

We know that simplistic proclamations about superior schools far away are incomplete at best, yet we continue to wring our hands about our inferiority. Japan is one of the favorite pedagogical bogeymen, but on a trip to Tokyo I witnessed four people employed to complete every retail transaction and two women required to operate an automatic elevator. I suspect that the four people making change at every department store checkout counter or the two women piloting one elevator did not succeed in calculus class. Like in Houston, students who might lower the average must just disappear.

While others can challenge their validity, the greatest risk posed by the international education comparisons is the underlying assumption that learning is (or should be) uniform. This premise is absurd and destructive for every state engaged in the standardized arms race. No human endeavor can or should be standardized. This is especially true across different cultures with dissimilar needs, goals, motivations, resources and belief systems.

The Stager Perspective
My work in public and private schools across a dozen or so countries entitles me to proclaim myself a scholar on global educational comparisons. My experience and humble analysis leads me to the following conclusion. Schools stink everywhere!

As long as citizens around the world strive to embrace the following myths and practices schools will continue to lose relevance and offer fewer benefits to children.

Artificial curricular hierarchy
The notion that a committee of bureaucrats can prescribe a specific sequence of curricular topics and skills for all learners defies everything we know about learning theory and will always lag behind societal shifts.

Assuming knowledge is static
Just as every learner is different, the nature of knowledge is fluid. Educational success is not measured by recitation and recall.

Testing is not teaching and teaching is not learning
Until we abandon the obsession with quantifying knowledge without even engaging a discussion of, “what we mean by learning,” schools will continue to treat children as rounding errors.

Barbaric conditions
Rows of uncomfortable desks nailed to the floor, bells, grades, age segregation, decontextualized content, sorting by similar levels of incompetence and zero-tolerance policies must give way to more flexible learning environments.

Communication is weak
Parents, still largely unwelcome educational partners, find it increasingly difficult to receive timely answers to simple questions despite enormous investments in data aggregation and school-to-home accountability systems.

It doesn’t ultimately matter if you agree with my hypothesis about the ill-health of schools and schooling. What you must celebrate is that the American ideal is for every child to enjoy a free and excellent K-12 education, followed by unparalleled opportunities for higher education. While our practice does not always measure up to our rhetoric, our democratic ideals are noble and our schools have served many children well. Rather than waste our energy worrying about global competition we should rededicate ourselves to helping every child reach their potential as a well-rounded human with a thirst for knowledge and creative expression.

A Not-So-Funny Thing Happened on the Way to the Future

© 2004 Gary S. Stager

Published by the NECC Daily Leader conference newspaper on June 22, 2004

The computer is not just an advanced calculator or camera or paintbrush; rather, it is a device that accelerates and extends our processes of thought. It is an imagination machine, which starts with the ideas we put into it and takes them farther than we ever could have taken them on our own.”  (Daniel Hillis, 1998)

This is an incredibly dark period for education. Perennial challenges are now accompanied by name-calling and public policy based on “getting tough” with third graders. Perhaps decision-makers just don’t know what learning in the digital age could look like. They need to see how kids not only learn old things in new ways, but construct personal understanding of powerful ideas in a rigorous computationally-rich fashion. Computers are today’s dominant intellectual laboratories and vehicles for self-expression.

Computers offer kids the means of production for learning via previously off-limit domains, including: music composition, filmmaking, robotics, computer science, journalism and engineering.

If only there were a place where compelling models of new educational practice could be shared… Welcome to NECC!

A few years ago, educators ceased talking about computing and started talking about technology. Suddenly computing, this remarkable invention of 20th century ingenuity, capable of transforming every intellectual domain, was dead without so much as an obituary. Conference speakers soon spoke of computers being just technology – like a zipper or Pez dispenser. This rhetorical shift liberated educators from learning to use computers, rethink the nature of curriculum or change practice to embrace the expansive opportunities afforded by computing. Information became the focus, not what kids do with computers.

In the mid-1970s my junior high required every 7th grader to learn to program a computer in nine weeks. The feelings of intellectual elation I experienced programming are indescribable. I didn’t know what was impossible so everything was possible. The computer amplified my thinking and the habits of mind I developed in Mr. Jones’ class serve me every day.

Bill Gates and Steve Wozniak enjoyed similar experiences. Imagine how the world would be different if some smart adults had not procured a mainframe and some terminals and said to Gates and Wozniak, “See what you can figure out. Have fun. Lock up when you’re done.”

How do your children’s school computing experiences compare? Do all students have access to creative tools anytime anyplace? Does the school culture inspire a thirst for knowledge and support authentic project-based work?

We’ve lowered standards when twelve year-olds in my junior high are NOW being taught to find the return key in a mandatory keyboarding class. Someday they may be “taught” to surf a filtered locked-down crippled Web incapable of downloading, rich media or collaboration all in the name of preparing them for the future. Some future.

Adults talk of how kids know so much about computers, how they are so competent, confident and fluent. Then those kids come to school and are treated like imbeciles or felons. Kid power is a gift to educators. We need to build upon those gifts and channel their students in directions they might not know exist. If kids came to school readers, we wouldn’t grunt phonemes at them. We would read better literature.

When many of us first attended NECC, we viewed the personal computer as not only a window on the future, but a microscope on the past. We knew how all sorts of learners exceed our wildest expectations when equipped with computers and constructionist software. Personal experience illuminated how the existing pencil-based curriculum was failing kids. Optimism filled the air.

Look around and you might conclude that the state-of-the-art includes: classrooms as game shows; data mining to justify standardized testing; reading as a winner-take-all race; and hysterical network security. “Technology” is being touted as a way to centralize control and breathe life into the least effective teaching practices of yore.

Widespread consensus is hard to achieve, especially on complex matters like education. Nonetheless, the educational computing community seems to have decided that our children should look forward to a future filled with testing and Microsoft Office instruction. Tests about Microsoft Office could achieve two national goals.

NECC attendees are pioneers entrusted with helping schools realize the potential of the imagination machine and as Gladwell suggests serve as the 10th Fleet in revolutionizing the context for learning. Go home and share the fabulous ideas you collect here in the Big Easy, but remember that the kids you serve expect big things from you and it won’t be easy.

In Australia…

Laptop Schools Lead the Way in Professional Development

As published in Educational Leadership – October 1995
By Gary S.Stager

Gary S. Stager is a teacher educator and adjunct professor at Pepperdine University. He has spent the past ten years working with a dozen Australian schools in which every student and teacher has a laptop computer.

Educational reform is too often equated with plugging students into anything that happens to plug in. Technology-rich Australian schools lead the way in helping teachers use technology thoughtfully.

Many educators believe that technology alone will lead to innovation and restructuring in schools. Unfortunately, they either do not include staff development in the equation, or they provide programs that do little more than ensure that teachers are able to unjam the printer or use one piece of canned instructional software.

Having developed a number of professional development models for a dozen schools in Australia and more in the United States, I believe computer-related staff development should immerse teachers in meaningful, educationally relevant projects. These activities should encourage teachers to reflect on powerful ideas and share their educational visions in order to create a culture of learning for their students. In brief, teachers must be able to connect their computer experience to constructive student use of computers.

Australian Leadership

In 1989, Methodist Ladies’ College, an independent pre-K-12 school with 2,400 students, embarked on an unparalleled learning adventure. At that time, the Melbourne school made a commitment to personal computing, LogoWriter, and constructivism. The governing principle was that all students, grades 5-12, should own a personal notebook computer on which they could work at school, at home, and across the curriculum. Ownership of the notebook computer would reinforce ownership of the knowledge constructed with it. Approximately 2,000 Methodist Ladies’ College students now have a personal notebook computer.

The school made personal computing part of its commitment to creating a nurturing learning culture. It ensured that teachers were supported in their own learning by catering to a wide range of learning styles, experiences, and interests. All involved agreed that personal computing was a powerful idea, one more important than the computers themselves. What students actually did with the computers was of paramount importance. LogoWriter was the schools’s primary software of choice. (MicroWorlds is now used.)

Dozens of Australian schools (called “laptop schools”) are now in various stages of following the lead of Methodist Ladies’ College in computing and are now using some of the professional development models created during my five years of work there.

Staff Development Innovations

Many schools find the task of getting a handful of teachers to use computers at even a superficial level daunting. The laptop schools expect their teachers not only to be comfortable with 30 notebook computers in their classroom, but also to participate actively in the reinvention of their school. In such progressive schools, staff development does not mean pouring information into teachers’ heads or training them in a few technical skills. Staff development means helping teachers fearlessly dream, explore, and invent new educational experiences for their students.

I have employed three staff development strategies – in-classroom collaboration, “slumber parties,” and build-a-book workshopsæin many laptop schools. All three model constructivism by providing meaningful contexts for learning, emphasizing collaborative problem solving and personal expression, and placing the learner (in this case the teacher) at the center of the learning experience. Each school values and respects the professionalism of the teachers by acknowledging the knowledge, skills, and experience each teacher possesses.

In-Classroom Collaboration

Several Australian laptop schools have used the in-classroom model I developed working in the Scarsdale, New York, and Wayne, New Jersey, public schools. This collaborative form of teacher development places the trainer in the teacher’s classroom to observe, evaluate, answer questions, and model imaginative ways in which the technology might be used. The collaborative spirit and enthusiasm engendered by the trainer motivates the teacher, who feels more comfortable taking risks when a colleague is there to help. Implementation is more viable because this professional development occurs on the teacher’s turf and during school hours.

Residential “Slumber Parties”

This approach allows teachers to leave the pressures of school and home behind for a few days to improve their computing skills in a carefully constructed environment designed to foster opportunities for peer collaboration, self-expression, and personal reflection, and to encourage a renewed enthusiasm for learning. These workshops have taken place at hotels, training centers, a monastery with lodging facilities, even at a school. These learner-centered workshops stress action, not rhetoric. The workshop leader serves as a catalyst, and creates opportunities for participants to connect personal reflections to their teaching. These connections are powerful when they come from the teacher’s own experienceæmuch like the types of learning opportunities we desire for students. The slumber parties use three key activities:

  1. Project brainstorming. Before we are even sure that the teachers know how to turn on their computers, we ask them to identify projects they wish to undertake during the workshop. The projects may be collaborative, personal, or curriculum-related, and they need not relate to the subjects they teach.
  2. Powerful ideas. Each day begins with a discussion of a relevant education issue or philosophical concern. Topics might include the history of Logo and your role in technological innovation (what the school has already accomplished); process approaches to learning; or personal learning stories. The topic for the final day, “What does this have to do with school?” is designed to help teachers reflect on their workshop experiences and make connections to their role as teachers.
  3. Problem solving off the deep end. One or two problem-solving activities are planned to demonstrate how teachers can solve complex open-ended problems through collaborative effort. These exercises help the participants to understand that not every problem has only one correct answer and that some problems may have no answers.

Slumber parties are offered on a regular basis. Because the primary goal of the workshops is to support a learning community, teachers and administrators are encouraged to participate in more than one. Participants gain appreciation for the power and expressive potential of LogoWriter. And, they are reminded that their colleagues are creative, imaginative learners like themselves.

Build-a-Book Residential Workshops

The origin for these workshops is based in the book, Build-a-Book Geometry. The book chronicles the author’s experience as a high school geometry teacher who spent an entire year encouraging his students to write their own geometry text through discovery, discussion, debate, and experimentation. It provides an exciting model for taking what teams of students know about a concept and then giving them challenges built upon their understanding or misunderstanding of it. The teacher then uses the responses to elicit a set of issues to which another team will respond, and so on. Throughout the process, each team keeps careful notes of hypotheses, processes, and conclusions, then shares these notes with the other teams during the process of writing the class book.

Healy’s ideas inspired a format that addresses confusing topics through discussion, problem solving, collaboration, and journal writing. Before the workshop, I ask each participant to identify three LogoWriter programming issues that they do not understand or that they need to have clarified. Small teams of teachers spend hours answering the questions and explaining numerous programming (and often mathematical) issues to one another. This exercise stresses the most important component of cooperative learningæinterdependence. When each group has answered all questions to its collective satisfaction, each teacher meets with a member of another team to explain what his or her group has accomplished.

Participants explore emerging questions through projectsædesigned by the leaderæthat are intended to use increasingly sophisticated skills. For example, teachers discuss the concept of programming elegance as they review student projects, and they keep careful notes of their programming processes, questions, and discoveries. These collective notes are included in the class book (disk). This disk becomes a valuable personal reference that the teachers can use in their own classrooms.

Teacher assessments of the residential workshops have been extremely positive. And, the quality of the experience makes the cost quite low when compared with the cost of providing an ongoing series of two-hour after-school workshops. Schools routinely spend much more time teaching concepts in bite-size chunks, while leaving real learning to chance.

Suggestions for Success

Following are some guidelines for successful technology implementation.

  • Work with the living.
    Because schools have limited technological and teacher development resources, those that do exist should be allocated prudently. If energy and resources are focused on creating a few successful models of classroom computing each year, the enthusiasm among teachers will be infectious. Of course, the selection of models must be broad enough to engage teachers of differing backgrounds and subject areas.
  • Eliminate obstacles.
    It should not be surprising that teachers without sufficient access to computer technology don’t embrace its use. How many workshops must a teacher attend to get a new printer ribbon? How long must a teacher wait to get enough lab time for his or her students to work on a meaningful project? The idea that schools should not buy computers before the teachers know what to do with them must be discarded.
  • Stay on message.
    Administrators must articulate a clear philosophy regarding how the new technology is to be used and how the culture of the school is likely to change. Communication between teachers and administrators must be honest, risk-free, and comfortable. Administrators must constantly clarify the curricular content and traditions the school values, as well as specify the outdated methodology and content that is to be eliminated. Teachers must be confident that their administrators will support them through the transitional periods.
  • Work on the teacher’s turf.
    Those responsible for staff development should be skilled in classroom implementation and should work alongside the teacher to create models of constructive computer use. It is important for teachers to see what students can do; this is difficult to accomplish in a brief workshop at the end of a long workday.
  • Plan off-site institutes.
    Schools must ensure that teachers understand the concepts of collaborative problem solving, cooperative learning, and constructivism. Accordingly, teachers must have the opportunity to leave behind the pressures of family and school for several days in order to experience the art of learning with their colleagues. Off-site residential “whole learning” workshops can have a profoundly positive effect on a large number of teachers in a short period of time.
  • Provide adequate resources.
    Nothing dooms the use of technology in the classroom more effectively than lack of support. Administrators can support teacher efforts by providing and maintaining the technology requested and by providing access to a working printer and a supply of blank disks.
  • Avoid software du jour.
    Many educators feel considerable pressure to constantly find something new to do with their computers. Unfortunately, this newness is equated with amassing more and more software. It is reckless and expensive to jump on every software bandwagon. The use of narrow, skill-specific software provides little benefit to students. Choose an open-ended environment, such as MicroWorlds, in which students can express themselves in many ways that may also converge with the curriculum.
  • Practice what you preach.
    Staff development experiences should be engaging, interdisciplinary, collaborative, heterogeneous, and models of constructivist learning.
  • Celebrate initiative.
    Recognize teachers who have made a demonstrated commitment to educational computing. Free them from some duties so they can assist colleagues in their classrooms; encourage them to lead workshops; and give them access to additional hardware.
  • Offer in-school sabbaticals.
    Provide innovative teachers with the in-school time and the resources necessary to develop curriculum and to conduct action research.
  • Share learning stories.
    Encourage teachers to reflect on significant personal learning experiences. Encourage them to share these experiences with their colleagues and to discuss the relationship between their own learning and their classroom practices. Formal action research projects and informal get-togethers are both effective. Teachers routinely relate that their most beneficial professional development experience is the opportunity to talk with peers.
  • Help teachers purchase technology.
    Schools should help fund 50-80 percent of a teacher’s purchase of a personal computer. This support demonstrates to teachers a shared commitment to educational progress. Partial funding gives teachers the flexibility to purchase the right computer configuration. Consider offering an annual stipend for upgrades and peripherals.
  • Cast a wide net.
    No one approach to staff development works for all teachers. Provide a combination of traditional workshops, in-classroom collaborations, mentoring, conferences, and whole-learning residential workshops from which teachers can choose.

Although many administrators dream of providing only a handful of computers in their schools, the reality of what is happening in schools across Australia requires serious consideration. Universal computing is in our future, and staff development programs must be geared to that fact. Modern staff development must help teachers not only embrace the technology, but also anticipate the classroom change that will accompany widespread use.

We must recognize that the only constant on which we can depend is the teacher. Our schools will only be as good as the least professional teacher. Staff development must enhance professionalism and empower teachers to improve the lives of their students. Our children deserve no less.

The Case for Computing
By Gary S. Stager

A chapter from the book, Snapshots! Educational Insights from the Thornburg Center (2004)

The personal computer is the most powerful, expressive and flexible instrument ever invented. At its best, the PC offers learners a rich intellectual laboratory and vehicle for self-expression. Although computing has transformed nearly every aspect of society, schools remain relatively untouched.

This chapter is not about predicting the future. It is about the learning opportunities that exist today and may be overlooked. Computers and creativity are in dangerously short supply. The dearth of compelling models of using computers in deeper ways has created a vacuum now filled by a Dickensian approach to schooling.

When I read the growing mountain of educational technology standards I can’t help but wonder if these objectives could be satisfied without the use of a computer. The unimaginative use of school computers is symptomatic of larger crises in schooling, including what Seymour Papert calls, “idea aversion.” Over the past few decades I have enjoyed working at key moments in the intersection of learning and computers. My daily work is guided by an optimism rooted in experiences learning with computers and observing children doing the same. As much as this is the story of great promise and great disappointment, the children we serve sustain our enthusiasm to work harder to realize the learning potential of the digital age.

Ancient History – My Early Years of Computing

In 1976 I got to touch a computer for the first time. My junior high school (grades 6-8) had a mandatory computer-programming course for seventh and eighth graders. More than a quarter century ago, the Wayne Township Public Schools in New Jersey thought it was important for all kids to have experience programming computers. There was never any discussion of preparation for computing careers, school-to-work, presentation graphics or computer literacy. Computer programming was viewed as a window onto a world of ideas given equal status as industrial arts, music appreciation, art and oral communications.

The scarcity of classroom computers made programming a highly social activity since we were often leaning over each other’s shoulders in order to get in on the action.

Mr. Jones, the computer programming teacher, was scary in a Dr. Frankenstein sort of way. However, I was attracted by the realization that this guy could make computers do things!

Mr. Jones knew how elaborate computer games worked and would show us the code afterschool if we were interested. Once I understood how to read a computer program, I could THINK LIKE THE COMPUTER! This made me feel powerful.

The feelings of intellectual elation I experienced programming are indescribable. The computer amplified my thinking. I could start with the germ of an idea and through incremental success and debugging challenges build something more sophisticated than I could have ever imagined.

The self-awareness that I was a competent thinker helped me survive the indignities of high school mathematics classes. Mr. Jones helped me learn to think like a computer. The ability to visualize divergent paths, anticipate bugs, and rapidly test mental scenarios is the direct result of computer programming. This gift serves me in everyday life when I need hack my way through a voicemail system to reach a knowledgeable human, or get my car out a locked parking structure.

Perhaps Mr. Jones was such a great teacher because he was learning to program too – maybe just slightly ahead of us. (This never occurred to me as a kid since Mr. Jones knew everything about computers.)

A strong community of practice emerged in the high school computer room. We learned from each other, challenged one another and played with each other’s programs. We altered timeshare games, added ways to cheat and programmed cheap tricks designed to shock classmates. I even ran after school classes in BASIC for kids interested in learning to program.

Computers were to be used to make things at my high school, not as a subject of study. There was never a mention of computer literacy and owning a computer was unthinkable. The school computers were a place to lose our selves in powerful ideas.

We never saw a manual for a piece of software although we treasured every issue of Creative Computing – working hard to meticulously enter hundreds of lines of computer code only to have every single program be buggy. Since we had little idea what was impossible, we thought anything was possible. We felt smart, powerful and creative. We took Fortran manuals out of the public library for no other reason than to hold a connection to a larger world of computing – a world we were inventing for ourselves.

Bill Gates and Steve Wozniak, were involved in similar little ventures at the time. Many of the computing visionaries who changed the world had similar early experiences with computers. I remember the explosion of thinking and creativity I experienced programming computers and try to recreate the spirit of that computer-rich learning culture in every school I visit. Kids deserve no less.

In the mid-80s I was welcomed into the global “Logo community” and asked to present papers at places like MIT. This was pretty heady stuff for a failed trumpet player and mediocre student. Logo programming offered a vehicle for sharing my talents, expressing my creativity and engaging in powerful ideas with some of the leading thinkers in education. Seymour Papert’s scholarship gave voice to my intuitions visa-a-vis the tension between schooling and learning.

To this day, my work with adults and kids is centered around using computers as intellectual laboratories and vehicles for self-expression. To experience the full power of computing, the tools need to be flexible extensible and transparent. The user needs to be fluent in the grammar of the system whether it is text based, symbolic or gestural.

Laptops

In 1989, Methodist Ladies’ College, an Australian PK-12 school already recognized for its world-class music education, committed to every student having a personal laptop computer. By the time I began working with MLC a year later, 5th and 7th graders were required to own a laptop. The “P” in PC was taken very seriously. Personal computing would not only solve the obvious problems of student access, low levels of faculty fluency and the costs associated with the construction of computer labs – the PC would embody the wisdom of Dewey, Vygotsky and Piaget. Logo, because of its open-endedness and cross-curricular potential, was the software platform chosen for student learning. The potential of Logo as a learning environment that would grow with students across disciplines and grade levels could only be realized with access to ubiquitous hardware. This justified the investment in laptops.

MLC principal, David Loader, understood that the personal was at the core of any efforts to make his school more learner-centered. He was not shy in his desire to radically reinvent his school. Bold new thinking, epistemological breakthroughs, sensitivity to a plurality of learning styles, increased collaboration (among teachers and children) and student self-reliance were expected outcomes of the high-tech investment. Teachers learning to not only use, but program, computers would acquaint themselves with the type of “hard fun” envisioned for student learning.

If the computer were to play a catalytic role in this educational shift, it was obvious that the computers needed to be personal. Truly creative and intellectual work requires freedom and a respect for privacy. Quality work is contingent on sufficient time to think, to experiment, to play. The laptop can only become an extension of the child when it is available at all times. Therefore, there was never any debate about laptops going home with students. Time and time again, the most interesting work was accomplished during the student’s personal time.

Laptops were a way to enable student programming “around the clock” and make constructionism concrete.

MLC was a magical place during the early nineties. Every aspect of schooling was open for discussion and reconsideration.

When I expressed concern over the gap between classroom reality and the rhetoric proclaiming the school’s commitment to constructionism, the principal supported my desire to take dozens of teachers away for intensive residential professional development sessions. After all, constructionism is something you DO as well as believe. You cannot be a constructionist who subcontracts the construction. “Do as I say, not as I do,” would no longer cut it.

A renaissance of learning and teaching catapulted MLC and the subsequent Australian “laptop schools” to the attention of school reformers around the world.

We were ecstatic when “laptop” students began to adorn their computers with their names written in glitter paint. This signaled appropriation. The computers mattered. Success.

The early success of MLC and the many other “laptop schools” to follow were a realization of the dream Seymour Papert and Alan Kay held for decades. In 1968, computer scientist Alan Kay visited Seymour Papert at MIT. Papert, a protégé of Jean Piaget, a mathematician and artificial intelligence pioneer was combining his interests by designing computing environments in which children could learn. Kay was so impressed by how children in Papert’s Logo Lab were learning meaningful mathematics that he sketched the Dynabook, a dream of portable computers yet to be fully realized, on the flight home to Xerox PARC, a leading high-tech thinktank.

Kay set out to design a portable personal computer for children on which complex ideas could come alive through the construction of simulations. Dr. Kay recently remembered this time by saying,  “More and more, I was thinking of the computer not just as hardware and software but as a medium through which you could communicate important things. Before I got involved with computers I had made a living teaching guitar. I was thinking about the aesthetic relationship people have with their musical instruments and the phrase popped into my mind: an instrument whose music is ideas.”

Kay’s poetic vision resonated with my memories of Mr. Jones, summer camp and my own experiences programming in Logo.

“One of the problems with the way computers are used in education is that they are most often just an extension of this idea that learning means just learning accepted facts. But what really interests me is using computers to transmit ideas, points of view, ways of thinking. You don’t need a computer for this, but just as with a musical instrument, once you get onto this way of using them, then the computer is a great amplifier for learning.”

At-risk and high tech

For three years, beginning in 1999, I worked with Seymour Papert to develop a high-tech alternative learning environment, the Constructionist Learning Laboratory (CCL), inside the Maine Youth Center, the state facility for adjudicated teens. This multiage environment provided each student with a personal computer and access to a variety of constructive material. The experience of trying to reacquaint or acquaint these previously unsuccessful students with the learning process teaches us many lessons about just how at-risk our entire educational system has become.

The intent of the project was to create a rich constructionist learning environment in which severely at-risk students could be engaged in long-term projects based on personal interest, expertise and experience. Students used computational technologies, programmable LEGO and more traditional materials to construct knowledge through the act of creating a personally meaningful project. The hypothesis was that the constructionist philosophy offers students better opportunities to learn and engage in personally meaningful intellectual development. The computer was the magic carpet that would allow these children to escape their history of school failure.

Students in this alternative learning environment routinely suffered from what Seymour Papert called,“the curious epidemic of learning disabilities.” Kids with low or non-existent literacy skills were able to invent and program robots capable of making decisions and interacting with their environment. Robo Sumo wrestlers, interactive gingerbread houses, card dealing robots, luggage sorting systems and temperature-sensitive vending machines capable of charging a customer more money on hot humid days were but a few of the ingenious inventions constructed with programmable LEGO materials. Students also designed their own videogames, made movies and explored the universe via computer-controlled microscopes and telescopes. They wrote sequels to Othello and published articles in programming journals. These kids proved that computing offered productive learning opportunities for all kinds of minds.

One child, said to be completely illiterate, wrote a page of program code the night before class because an idea was burning inside of him. Another “illiterate” youngster, incarcerated for more than half of his life, was capable of building dozens of mechanisms in the blink of an eye and installing complex software. His ability to program complicated robots presented clues about his true abilities. A week before he left the facility, this child, so accustomed to school failure, sat down and typed a 12,000-word autobiography.

Tony’s adventure is also a tale worth telling. He had not been in school since the seventh grade and indicated that none of his peer group attended school past the age of twelve or thirteen. In the CLL he fell in love with robotics and photography at the age of seventeen.

During the spring of 2001, the MYC campus was populated with groundhog holes. To most kids these familiar signs of spring went unnoticed, but not for the “new” Tony.

Tony and his new assistant, “Craig,” spent the next few weeks building a series of what came to be known as “Gopher-cams.” This work captured the imagination of the entire Maine Youth Center. Tony and Craig learned a great deal about how simple unanticipated obstacles like a twig could derail days of planning and require new programming or engineering. These students engaged in a process of exploration not unlike the men who sailed the high seas or landed on the moon. While they never really found out what was down the hole, they learned many much more important lessons.

Robotics gives life to engineering, mathematics and computer science in a tactile form. It is a concrete manifestation of problem solving that rewards debugging, ingenuity and persistence. The LEGO robotic materials promote improvisational thinking, allowing even young children to build a machine, test a hypothesis, tinker, debug, and exceed their own expectations.  As often experienced in programming, every incremental success leads to a larger question or the construction of a bigger theory.  This dialogue with the machine amplifies and mediates a conversation with self.

Digital technology is a critical variable in the transformation of reluctant learners. Self-esteem, or even academic grades, might have been enhanced through traditional activities. However, the availability of computationally-rich construction materials afforded the learners the opportunity to experience the empowerment associated with the feeling of wonderful ideas. For the first time in their lives, these children experienced what it felt like to be engaged in intellectual work. This feeling required a personal sustained relationship with the computer and computationally-rich objects to think with such as LEGO and MicroWorlds. All students deserve the chance to make important contributions to the world of ideas, and must be given the means to do so.

State of the art?

Much needs to be done to ensure that all students enjoy the quality of experience offered by the best laptop schools, online environments and the CLL.

Somewhere along the line, the dreams of Kay, Papert and Loader were diluted by the inertia of school. Detours along the road to the Dynabook were paved by the emergence of the Internet and corporate interest in the laptop miracle.

Until the explosion of interest in the Internet and Web, individual laptops offered a relatively low-cost decentralized way to increase access to computers and rich learning opportunities. The Net, however, required these machines to be tethered to centralized servers and an educational bureaucracy pleased with its newfound control. Computing costs soared, data and children were either menaced or menaces. Jobs needed to be protected. The desires of the many often trumped the needs of the learner.

Microsoft generously offered to bring the laptop message to American schools, but their promotional videos pushed desks back into rows and teachers stood at the front of classrooms directing their students to use Excel to calculate the perimeter of a rectangle. Over emphasis on clerical “business” applications – were manifest in elaborate projects designed to justify (shoehorn) the use of Excel or Powerpoint in an unchanged curriculum. Many of these projects have the dubious distinction of being mechanically impressive while educationally pointless. Our gullible embrace of false complexity increases as the work is projected in a darkened classroom.

I’ve developed Murray’s Law to describe the way in which many schools assimilate powerful technology. “Every 18 months schools will purchase computers with twice the processing power of today, and do things twice as trivial with those computers.”

There is a fundamental difference between technology and computing, which can be seen in the words themselves. One is a noun, the other a verb, What we saw students do with technology at the CCL was active, engaged, compelling, sophisticated learning.  They were computing, and similar experiences for all students can transform the experience of school.

What are you really saying?

I know that many of you must be thinking, “Does Gary really believe that everyone should be a programmer?” My answer is, “No, but every child should experience the opportunity to program a computer during her K-12 education.” Critics of my position will say things like, “Not every person needs to program or will even like it.” To these people I suggest that not every kid needs to learn to write haiku or sand a tie rack in woodshop. However, we require millions of children to do so because we believe it is either rewarding, of cultural value or offers a window onto potential forms of human expression.

Despite our high-tech society’s infinite dependence on programming and the impressive rewards for computing innovation, many people find the notion of programming repulsive. Everyone wants their child to earn Bill Gates’ money, but only if they never have to cut a line of code. Educators especially need to get past this hysteria rooted in fear and ignorance for the sake of the children in our care. (this sentence is optional if you feel it is inflammatory)

I do not understand why anyone would question the value of offering programming experiences to children.

It is unseemly for schools to determine that a tiny fraction of the student population is capable of using computers in an intellectually rich way. The “drill for the test” curriculum of the A.P. Computer Science course serves only a few of the most technically sophisticated students. That is elitism.

Children enjoy programming when engaged in a supportive environment. The study of other disciplines may be enhanced through the ability to concretize the formal. For example, complex mathematical concepts become understandable through playful manipulation, graphical expression of abstractions or the application of those concepts in service of a personal goal. It would be difficult to argue that mathematics education, at the very least, would not be enriched through programming.

Schools need to make a sufficient number of computers with powerful software available for the transparent use of every child across all disciplines. Schools also have an obligation to offer a more inclusive selection of courses designed for a more diverse student body interested in learning with and about computers. Courses in software design, digital communication, robotics, or computer science are but a few options. The Generation Y program, in which students lend their technological expertise to teachers who want to integrate technology into their lessons provides another outlet for authentic practice.

Whither computing?

I wonder when the educational computing community decided to replace the word. computing, with technologyThe Computing Teacher became Learning and Leading with TechnologyClassroom Computer Learning begot Technology and Learning Magazine. Conference speakers began diminishing the power of the computer by lumping all sorts of objects into the catch-all of technology. Computers are in fact a technology, but they are now spoken of in the same breath as the blackboard, chalk, filmstrip projector or Waterpik. Computing was never to be mentioned again in polite company.

I recently read the conference program for a 1985 educational computing conference. The topics of discussion and sessions offered are virtually the same as at similar events today. The only difference is that all mentions of programming have disappeared from the marketplace of ideas.

It seems ironic that educators fond of reciting how kids know so much about computers act as if the computer was just invented. We should be unimpressed by breathless tales of children web surfing or using a word processor to write a school report. My standards are much higher. We will cheat a second generation of microcomputer-age students if we do not raise our game and acknowledge that so much more is possible.

If we concur that kids are at least comfortable with computers, if not fluent, then teachers have a responsibility to build on the fluency of computer-savvy kids. This is a classroom gift, like an early reader, a natural soprano or a six year-old dinosaur expert. It is incumbent on schools and their personnel to steer such students in more challenging and productive directions. Teachers have an obligation to respect the talents, experience and knowledge of students by creating authentic opportunities for growth.

If the youngest children can “play” doctor, lawyer, teacher or fireman, why can’t they imagine themselves as software designers? Open-ended software construction environments designed for children, like MicroWorlds, make it possible for children of all ages to view themselves as competent and creative producers of knowledge. Too few students know that such accomplishments are within reach.  This failure results from a leadership, vision, and professional knowledge deficit.

While school computing fades from memory, keyboarding instruction inexplicably remains a K-12 staple from coast to coast. Computer assisted instruction, schemes designed to reduce reading to a high-stakes race and low-level technical skills dominate the use of computers in schools. In the hands of a clever curriculum committee, “uses scroll bars” can be part of a nine-year scope and sequence.

Examples of kids composing music, constructing robots, or designing their own simulations are too hard to find. More than a quarter century has passed since Mr. Jones taught me to program. Yet, children in that school are now compelled to complete a keyboarding class. There can be no rational justification for so blatant a dumbing-down of the curriculum.

Computing Changes Everything

There are so many ways in which children may use computers in authentic ways. Low-cost MIDI software and hardware offers even young children a vehicle for musical composition. The 1990 NCTM Standards indicated that fifty percent of mathematics has been invented since World War II. This mathematics is visual, experimental and rooted in computing. It may even engage kids in the beauty, function and magic of mathematics.

In Seeing in the Dark: How Backyard Stargazers Are Probing Deep Space and Guarding Earth from Interplanetary Peril, author Timothy Ferris describes how amateur astronomers armed with telescopes, computers and Net connections are making substantive contributions to the field of astronomy. For the first time in history, children possess the necessary tools to be scientists and to engage in scientific communities.

MacArthur Genius Stephen Wolfram has written a revolutionary new 1,280 page book, A New Kind of Science. The book illustrates his theory that the universe and countless other disciplines may be reduced to a simple algorithm. Scientists agree that if just a few percent of Wolfram’s theories are true, much of what we thought we knew could be wrong and many other cosmic mysteries may be solved. Wolfram believes that a human being is no more intelligent than a cloud and both may be created with a simple computer program.

A New Kind of Science starts with very a big bang.

“Three centuries ago science was transformed by the dramatic new idea that rules based on mathematical equations could be used to describe the natural world. My purpose in this book is to initiate another such transformation, and to introduce a new kind of science that is based on the much more general types of rules that can be embodied in simple computer programs.”

You do not have to take Wolfram’s word for it. With the $65 A New Kind of Science Explorer software, you and your students can explore more than 450 of Wolfram’s experiments. The visual nature of cellular automata – the marriage of science, computer graphics and mathematics – allows children to play on the frontiers of scientific thought while trying to prove, disprove or extend the theories of one of the world’s greatest scientists. The intellectual habits required to “think with” this tool are rooted in computer programming.

I recently told Alan Kay that while I was hardly a mathematician, I knew what it felt like to have a mathematical idea. He generously replied, “Then you are a mathematician, you’re just not a professional.” The work of Seymour Papert shows us that through the explicit act of computing children can too be mathematicians and scientists.

“If you can use technology to make things you can make a lot more interesting things. And you can learn a lot more by making them. …We are entering a digital world where knowing about digital technology is as important as reading and writing.  So learning about computers is essential for our students’ futures BUT the most important purpose is using them NOW to learn about everything else. “ (Papert 1999)

We can neutralize our critics and improve the lives of kids if we shift our focus towards using school computers for the purpose of constructing knowledge through the explicit act of making things – including: robots, music compositions, digital movies, streaming radio and simulations. Children engaged in thoughtful projects might impress citizens desperate for academic rigor. Examples of competent children computing bring many current educational practices into question. Emphasizing the use of computers to make things will make life easier for teachers, more exciting for learners and lead schools into what should be education’s golden age.

SIDEBAR

Why Should Schools Compute?

Computing offers an authentic context for doing & making mathematics
Traditional arithmetic and mathematical processes are provided with a genuine context for use. New forms of mathematics become accessible to learners.

Computing concretizes the abstract
Formal concepts like feedback, variables and causality become concrete through use.

Computing offers new avenues for creative expression
Computing makes forms of visual art and music composition possible for even young children while providing a canvas for the exploration of new art forms like animation. A limitless audience is now possible.

Computer science is a legitimate science
Computer science plays a revolutionary role in society and in every other science. It should be studied alongside biology, physics and chemistry.

Computing supports a plurality of learning styles
There are many ways to approach a problem and express a solution.

Computing offers preparation for a plethora of careers
There is a shortage of competent high-tech professionals in our economy

Computing grants agency to the user, not the computer
Rather than the computer programming the child, the child can control the computer.

Debugging offers ongoing opportunities to enhance problem-solving skills
Nothing works correctly the first time. The immediacy of concrete feedback makes debugging a skill that will serve learners for a lifetime.

Computing rewards habits of mind such as persistence, curiosity and perspective
Computers mediate a conversation with self in which constant feedback and incremental success propels learners to achieve beyond their expectations.


References

Cavallo, D. (1999) “Project Lighthouse in Thailand: Guiding Pathways to Powerful Learning.” In Logo Philosophy and Implementation. Montreal, Canada: LCSI.

Duckworth, E. (1996) The Having of Wonderful Ideas and Other Essays on Teaching and Learning. NY: Teachers College Press.

Ferris, T. (2002) Seeing in the Dark: How Backyard Stargazers Are Probing Deep Space and Guarding Earth from Interplanetary Peril. NY: Simon and Schuster.

Harel, I., and Papert, S., eds. (1991) Constructionism. Norwood, NJ: Ablex Publishing.

Kafai, Y., and Resnick, M., eds. (1996) Constructionism in Practice: Designing, Thinking, and Learning in a Digital World. Mahwah, NJ: Lawrence Erlbaum.

Levy, S. (2002) The Man Who Cracked the Code to Everything.Wired Magazine. Volume 10, Issue 6. June 2002.

Papert, S. (1980) Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books.

Papert, S. (1990) “A Critique of Technocentrism in Thinking About the School of the Future,” MIT Epistemology and Learning Memo No. 2. Cambridge, Massachusetts: Massachusetts Institute of Technology Media Laboratory.

Papert, S. (1991) “Situating Constructionism.” In Constructionism, in  Harel, I., and Papert, S., eds. Norwood, NJ: Ablex Publishing.

Papert, S. (1993) The Children’s Machine: Rethinking School in the Age of the Computer. New York: Basic Books.

Papert, S. (1996) The Connected Family. Atlanta: Longstreet Publishing.

Papert, S. (1999) “The Eight Big Ideas of the Constructionist Learning Laboratory.” Unpublished internal document. South Portland, Maine.

Papert, S. (1999) “What is Logo? Who Needs it?” In Logo Philosophy and Implementation. Montreal, Canada: LCSI.

Papert, S. (2000) “What’s the Big Idea? Steps toward a pedagogy of idea power.” IBM Systems Journal, Vol. 39, Nos 3&4, 2000.

Resnick, M., and Ocko, S. (1991) “LEGO/Logo: Learning Through and About Design.” In Constructionism, in  Harel, I., and Papert, S., eds. Norwood, NJ: Ablex Publishing.

Stager, G. (2000) “Dream Bigger” in Little, J. and Dixon, B. (eds.) Transforming Learning: An Anthology of Miracles in Technology-Rich Classrooms. Melbourne, Australia: Kids Technology Foundation.

Stager, G. (2001) “Computationally-Rich Constructionism and At-Risk Learners.” Presented at the World Conference on Computers in Education. Copenhagen.

Stager, G. (2002) “Papertian Constructionism and At-Risk Learners.” Presented at the National Educational Computing Conference. San Antonio.

“The Dynabook Revisted” from the website, The Book and the Computer: exploring the future of the printed word in the digital age. (n.d.) Retrieved January 20, 2003 from http://www.honco.net/os/kay.html

Thornburg, D. (1984) Exploring Logo Without a Computer. Menlo Park, CA: Addison-Wesley.

Thornburg, D. (1986) Beyond Turtle Graphics: Further Explorations of Logo. Menlo Park, CA: Addison-Wesley.

Turkle, S. (1991) “Epistemological Pluralism and the Revaluation of the Concrete.” In Constructionism. Idit Harel and Seymour Papert (eds.), Norwood, NJ: Ablex Publishing.

Wolfram, S. (2002) A New Kind of Science. Champaign, IL: Wolfram Media, Inc.

“The Dynabook Revisted” from the website, The Book and the Computer: exploring the future of the printed word in the digital age. (n.d.) Retrieved January 20, 2003 from http://www.honco.net/os/kay.html.

ibid…

In First Chance to Make a Learning Impression, my friend Will Richardson shares his disappointment with the “back-to-school” packets he just received in anticipation of his children’s next school year. Will explains how the focus of the packet is on everything but learning.

Just for fun, I set out to see how long it would take to find the word “learning” somewhere in the mix. Nothing on the first page, or the second, or the third…by the time I finally found the first instance I had stopped counting. It was a buried line in a letter from the principal explaining that due to NCLB, every teacher has to be “highly qualified” and that “every teacher continues life-long learning through professional development activities.”

Will’s 2013 article reminded me of a similar article I wrote for District Administration Magazine way back in 2004. I recommend reading Will’s article as well.

Gary Stager on One-sided Parent Contracts
Here’s a list of promises I think schools should keep
By: Gary Stager
District Administration, Sep 2004

DA Archive

The back-to-school commercials each summer fill me with dreadful flashbacks of my own days as a student. As a parent, the end of summer is signaled by a last-minute desire to squeeze in a bit more family fun and the arrival of a large ominous envelope from the local high school. The package contains countless documents commanding our immediate attention and signatures in triplicate.

This enormous collection of murdered trees contains countless rules, regulations and a list of innumerable sanctions the school intends to visit upon my child. As if this draconian catalogue of crimes and subsequent punishments were not bad enough, I am then expected to sign the documents, implying that I agree with them.

This recent and disturbing phenomenon leaves me with many unanswered questions. What if I don’t sign the forms? When did the local public school become a gulag? Was there a public meeting in The Hague at which these rules and sanctions were compiled and democratically agreed to? Is this the best way to start a fresh school year? Can I have Johnnie Cochran look over the documents before I affix my signature?

If the school expects parents to sign-off on a list of ways school discipline may be enforced, perhaps I can circulate a list of expectations for how I expect the school to educate my child. It only seems fair.

So here’s my list, in no particular order:

  • School to home communications will be proofread and spell-checked
  • Teachers will take reasonable steps to maintain expertise in their subject area
  • Homework will be purposeful and only assigned when necessary to reinforce a concept, engage in a long-term project or as the result of work not completed in-class
  • Children will be encouraged to play
  • Classroom libraries will be stocked with interesting books
  • Students will not be treated as numbers
  • Teachers will discuss current events with their students
  • Students will be encouraged to talk about books they read, not just create mobiles and book reports
  • School personnel will publish their e-mail addresses and respond to e-mail promptly
  • The school district Web site will be updated more often than every five years
  • Class sizes will be 20 or lower
  • Teachers will attend at least one professional learning event outside of the school district per year
  • Teachers will not talk down to children
  • Punishment will be viewed as a last resort
  • The school will offer rich visual and performing arts opportunities for all students
  • Curriculum will endeavor to remain relevant and connected to the world
  • Classroom rules will be developed democratically
  • There will be formal and informal opportunities for parents to interact with teachers
  • The principal will be accessible to students and parents
  • Administrators will make an effort to interact with students in positive contexts
  • Student diversity will be valued and celebrated
  • Cooperation will be valued over competition
  • The school will refrain from sorting, tracking, streaming and labeling children
  • Students will play a large role in all aspects of the life of the school;
  • Authentic forms of assessment will be used
  • A modern functioning computer will be available whenever a child needs one
  • Teachers will embrace opportunities to learn with and from students
  • The school will take teacher input seriously
  • Teachers will feel supported and encouraged to take risks
  • Effective models of professional development will be designed and include the participation of the principal
  • Equal attention and resources will be applied to the arts as to sports
The Coalition of Essential Schools offers 10 common principles for schools concerned with excellence–www.essentialschools.org/pub/ces_docs/about/phil/10cps/10cps.html

Laptops and Learning

Can laptop computers put the “C” (for constructionism) in Learning?
Published in the October 1998 issue of Curriculum Administrator

© 1998 – Gary S. Stager

“…Only inertia and prejudice, not economics or lack of good educational ideas stand in the way of providing every child in the world with the kinds of experience of which we have tried to give you some glimpses. If every child were to be given access to a computer, computers would be cheap enough for every child to be given access to a computer.” - Seymour Papert and Cynthia Solomon (1971)

In 1989, Methodist Ladies’ College (MLC) in Melbourne, Australia embarked on a still unparalleled learning adventure. Eighteen years after Solomon and Papert’s prediction this school made a commitment to personal computing and constructionism. The unifying principle was that every child in the school (from grades 5-12) would own a personal laptop computer on which they could work at school, at home, and across the curriculum with a belief that their ideas and work were being stored and manipulated on their own personal computer. Ownership of the laptop computer would reinforce ownership of the knowledge constructed with it. The personal computer is a vehicle for building something tangible outside of your head – one of the tenets of constructionism. By 1994, 2,000 MLC teachers and students had a personal laptop computer. This school, like most serious workplaces now has a computer ration of more than one computer per worker (teacher & student). Today, approximately 50,000 Australian school children have their own laptop. More and more American schools are embracing laptops as well.

Personal Computing – Personal Learning

Until recently, the notion of the PC and personal computing has escaped schools. Computer labs, special furniture and computer literacy curricula have been designed to make efficient use of scarce public resources. The potential benefits of using a word processor to write, edit and publish are rarely realized when access to the computer is limited and artificially scheduled. Laptops provide a personal space for creating, exploring, and collecting one’s own ideas, work, and knowledge in a more fluid manner. Pioneering schools like MLC adopted laptops for the following reasons:

The laptop is flexible, portable, personal and powerful
Students and teachers may use the computer whenever and wherever they need to. The laptop is a personal laboratory for intellectual exploration and creative expression. Learning extends beyond the walls and hours of the school.

The laptop helps to professionalize teachers
Teachers equipped with professional tools view themselves more professionally. Computers are much more likely to be integrated into classroom practice when every student has one.

Provocative models of learning will emerge
Teachers need to be reacquainted with the art of learning before they are able to create rich supportive learning environments for their students. The computer allows different ways of thinking, knowing and expressing ones own ideas to emerge. The continuous collection of learning stories serves as a catalyst for rethinking the nature of teaching and learning.

Gets schools out of the computer business
Laptops are a cost-effective alternative to building computer labs, buying special furniture and installing costly wiring. Students keep laptops for an average of three years, a turnover rate rarely achieved by schools. Built-in modems provide students with net access outside of school. The school can focus resources on projection devices, high-quality peripherals and professional development.

Since my work with the world’s first two “laptop schools” in 1990, I’ve helped dozens of similar schools (public and private) around the world make sense of teaching and learning in environments with ubiquitous computing. My own experience and research by others has observed the following outcomes for students and teachers.

Learner Outcomes

  • Students take enormous pride in their work.
  • Individual and group creativity flourishes.
  • Multiple intelligences and ways of knowing are in ample evidence.
  • Connections between subject areas become routine.
  • Learning is more social.
  • Work is more authentic, personal & often transcends the assignment.
  • Social interactions tend to me more work-related.
  • Students become more naturally collaborative and less competitive.
  • Students develop complex cooperative learning strategies.
  • Kids gain benefit from learning alongside of teachers.
  • Learning does not end when the bell rings or even when the assignment is due.

Teacher Outcomes

  • The school’s commitment to laptops convinces teachers that computers are not a fad. Every teacher is responsible for use.
  • Teachers reacquaint themselves with the joy and challenge of learning something new.
  • Teachers experience new ways of thinking, learning and expressing one’s knowledge.
  • Teachers become more collaborative with colleagues and students.
  • Authentic opportunities to learn with/from students emerge.
  • Sense of professionalism and self-esteem are elevated.
  • Thoughtful discussions about the nature of learning and the purpose of school become routine and sometimes passionate.
  • Teachers have ability to collaborate with teachers around the world.
  • New scheduling, curriculum and assessment structures emerge.

 

“I believe that every American child ought to be living in the 21st century… This is why I like laptops – you can take them home. I m not very impressed with computers that schools have chained to desks. I m very impressed when kids have their own computers because they are liberated from a failed bureaucracy …

You can’t do any single thing and solve the problem. You have to change the incentives; you’ve got to restructure the interface between human beings. If you start redesigning a learning system rather than an educational bureaucracy, if you have incentives for kids to learn, and if you have 24-hour-a-day, 7-day a week free standing opportunities for learning, you’re going to make a bigger breakthrough than the current bureaucracy. The current bureaucracy is a dying institution.” – U.S. Speaker of the House of Representatives, Newt Gingrich (Wired Magazine, August 1995)

When Seymour Papert and Newt Gingrich are on the same side of an issue, it is hard to imagine an opposing view. The fact that computers are smaller, cheaper and more powerful has had a tremendous impact on society. Soon that impact will be realized by schools. Laptop schools are clearly on the right side of history and will benefit from the experience of being ahead of trend.

Much has been said recently about the virtues of anytime anywhere learning. Laptops certainly can deliver on that promise. Integrated productivity packages may be used to write, manipulate data and publish across the curriculum. However, the power of personal computing as a potential force for learning and as a catalyst for school reform transcends the traditional view of using computers to “do work.” I encourage school leaders considering an investment in laptops to dream big dreams and conceive of ways that universal computing can help realize new opportunities for intellectual development and creative expression.

Coming to a Classroom Near You!

Oneseventh grader’s journey includes learning math through Scooby Doo
©2001 Gary S. Stager/Curriculum Administrator Magazine

A version of this was published in the August 2001 issue of Curriculum Administrator Magazine

At our annual family dinner to celebrate the end of another grueling school year, each of our children reflected upon the lessons learned and the obstacles overcome during the previous ten months. Our seventh-grade daughter, who will be referred to by the top-secret code name of Miffy, shared with us a new pedagogical strategy and use of educational technology not yet conceived of during my school years.

What was this innovation? Was it project-based learning, multiage collaboration, constructionism, online publishing, modeling and simulation? Nope, it was Disney films.

Yup, that’s right. Disney films (and several others too). The following is a partial list of the films shown this year during class time by my daughter’s teachers.

 

1st
period science

2nd
period math

3rd/4th
period language arts

6th
period physical education
(rainy days)

7th
period social studies

8th
period band

Young Frankenstein

 

The Nightmare Before Christmas

 

Contact

 

The Andromeda
Strain

Mulan

 

The Lion King

 

Babe

 

Mighty Joe Young

 

Aladdin

 

Cinderella

 

The Little Mermaid

 

MTV videos

 

VH1 videos

 

Scooby Doo

 

The Nightmare
Before Christmas

Angels in the
Outfield*

 

Little Giants*

 

The Big Green*

 

The Sandlot*

 

Planet of the Apes

 

Mighty Joe Young

 

The Nightmare
Before Christmas

Babe

 

Charlotte’s
Web

 

The Lion King II

 

Aladdin

 

The Road to
Eldorado

 

Dinosaur

A
Touched by an Angel episode dealing with racism & prejudice

 

Remember the Titans

Rocky & Bullwinkle

 

The Emperor’s
New Groove

 

Grease

 

Star Wars: Return
of the Jedi

 

Mr. Holland’s Opus

By now you must be marveling at the interdisciplinary properties of The Nightmare Before Christmas.You may also be wondering why there were no movies shown during fifth period. That’s because they don’t show movies during lunch.
Now I’m as fond of wasting time and goofing-off as the next guy, but Miffy was able to remember watching at least 34 films having no educational value whatsoever in one school year. In case you were thinking that they could be studying film criticism or visual storytelling you should know that they only watched half of most films because the periods are too short. Others were watched over several days.

This remarkable waste of class time occurred in a school where requests for meaningful projects, hands-on experiments, field-trips, drama and other productive learning experiences are abandoned because of an oft-repeated “lack of time.” Sure the standardized tests and top-down curricular pressures wreak havoc with creating a productive context for learning, but we can’t blame this one on Princeton or the President. Somewhere along the line educators determined that the demanding curriculum was elastic enough for the illegal showing of countless commercial films.

My Daughter the Rodeo Clown

Miffy also told me that due to the SAT-9 exams, Career Day had been cancelled. I’m not sure which part of that statement is most tragic, so let’s state it in the form of a standardized test question.

Which is most pathetic?

a)    Canceling Career Day because of SAT-9  (standardized) testing

b)    Career Day

c)    The school’s remedy for having cancelled career day

The ingenious remedy chosen was to spend much of the last week of school watching a series of instructional videos called, “Real Life 101.” While hardly as educational as Mulan, these shows turned out to be far more entertaining. The audience was repeatedly reminded, “you don’t need a college degree for this career, but it wouldn’t hurt! “

The hosts of the series, Maya, Megan, Zooby and Josh (there always seems to be a Josh) introduced exciting career options for the high-tech interconnected global economy of the 21st century. The career options included the following: Snake handler, projectionist, naval explosive expert, skydive instructor, rafting instructor, diamond cutter, roller coaster technician, exterminator, auctioneer, alligator wrestler and my personal favorite growth industry – rodeo clown!

You can’t make this stuff up! The worksheet that followed the Career Day substitute asked each child to rank these careers in order of preference and write a few sentences explaining their number one choice.

If I wanted my children to watch television, I’d let them stay home. At least at home they could watch something educational like “Behind the Music: The Mamas and the Papas”or learn about Beat poetry from the “Many Loves of Dobie Gillis. ”  At least then they would have a chance to learn something more than the unfortunate lessons being modeled by their schools.

*My kid explained that all of these films share the same plot about a group of fat kids working hard together to win the big game – somewhere in there a lesson for us all.

Before accepting overtesting as inevitable, try debating the issue with parents and students
By Gary S. Stager, Ph.D.
Originally published in District Administration Magazine – July 2003

Our schools are in the midst of a mass panic not seen since the swine flu epidemic–standardized testing. We are swept up in a wave of “the tests are important,” “parents demand accountability,” and “they make us do it.” This uncritical groupthink will destroy public education unless we wake up, form alliances and tell the public the truth.

Democrats and Republicans alike caught a bad case of testing fever and voted overwhelmingly for No Child Left Behind, perhaps the greatest intrusion of the federal government into local education in history. NCLB will compel states to test their students every year from grades 2-12 in order to rank schools and shut many of them down. Our Proctor-in-Chief, George W. Bush, is extending the joys of standardized testing into Head Start.

Since many administrators and school board members have no idea how many standardized tests they need to administer, NCLB will undoubtedly add additional tests and draconian consequences to a school year already diminished by weeks of testing and test preparation.

Without so much as a public debate on what we would want for our schools, testing mania has been allowed to spread like a plague on our educational process. If some testing is good, more is better. If the youngest students can’t yet hold a pencil or read, of course they can bubble-in answers to math problems for several hours at a time. Head Start should be a reading program. You got a problem with three-year-olds reading? Why then, you must suffer from “the bigotry of low expectations.” The end of recess does not affect obesity. Replacing art and music with scripted curricula won’t lead to increased school violence or discipline problems. Down is up, black is white.

Education Week’s annual report “Technology Counts,” states an alarming trend–schools are not spending enough money on using computers for the purposes of standardized testing! Apparently, the years I’ve spent helping schools use computers to enhance learning have been wasted. It never occurred to me that computers should be used to replace #2 pencils and scan sheets. Tech-based testing reminds me of the old Gaines Burger commercial that asked, “Is your dog getting enough cheese?”

The Education Week “research” is replete with charts and graphs designed to whip child-centered educators into line. EdWeek loves winners and losers nearly as much as the testing industry. Coincidentally, a giant publisher of standardized tests, textbooks and test preparation systems, funded their “study.”

In such a climate of confusion and hysteria, educators feel powerless. Parents trust that you will do the right thing. Misconceptions about high-stakes testing are amplified by an unwillingness to engage the community in conversation.

Getting Active
Inspired by Juanita Doyon’s terrific new book, Not With Our Kids You Don’t: Ten Strategies to Save Our Schools, and a desire to show my kids that you can make a difference, I decided to try my hand at activism.

I designed a flier answering some of the myths about standardized testing and telling parents that California state law allows them to exempt their child from the STAR tests. Two days before testing was to begin I stood in front of my daughter’s high school and passed out 150 fliers in about 10 minutes. I felt a bit creepy, but the kids told me that I was cool (a first).

I have since learned that 46 students opted out of the tests. That’s a one-third hit-rate. Not since the Pet Rock has a marketing effort been so successful with so little effort Think about it–a kid had to take a piece of paper from a stranger, bring it home, convince his parents to write a letter disobeying the wishes of the school and bring the letter back to school the next day. Perhaps the public isn’t as hungry for increased accountability as we have been led to believe?

One parent said she didn’t know her tax money was spent on standardized testing. Can you imagine the public being less engaged in a matter so important?

It is incumbent upon each of us to tell parents what we know and engage the community in serious discussions about schooling. We may find that we have many more allies than there are politicians telling us what’s best for kids.


I created Pencilsdown.org around 2000, long before today’s opt-out movement. It has been inactive for a number of years, but you may find a copy of the opt-out form I distributed back in 2003 here.

The year following my initial opt-out activism,I wrote a letter to the editor of the local paper urging parents to opt-out. Fearing a loss of federal money as a result of not making AYP due to testing resistance, the Torrance Unified School District lied to parents about the legitimacy of the testing process. I responded with a freedom of information request about funding, personnel, policy, costs and time dedicated to STAR testing. This tied the district office in knots for months. If I can find the request, I will share it.

Here is a list of recommended books for parents and educators interested in opposing standardized testing.

Computationally-Rich Activities for the Construction of Mathematical Knowledge – No Squares Allowed
©1998 Gary S. Stager with Terry Cannings
This paper was published in the proceedings of the 1998 National Educational Computing Conference in San Diego

Based on a book chapter: Stager, G. S. (1997). Logo and Learning Mathematics-No Room for Squares. Logo: A Retrospective. D. L. Johnson and C. D. Maddux. Philadelphia, The Haworth Press: 153-169.

Abstract
The NCTM Standards state that fifty percent of all mathematics has been invented since World War II. (National Council of Teachers of Mathematics, 1989) Few if any of these branches of mathematical inquiry have found their way into the K-12 curriculum. This is most unfortunate since topics such as number theory, chaos, topology, cellular automata and fractal geometry may appeal to students unsuccessful in traditional math classes. These new mathematical topics tend to be more contextual, visual, playful and fascinating than adding columns of numbers or factoring quadratic equations. Logo provides a powerful medium for rich mathematical explorations and problem solving while providing a context in which students may fall in love with the beauty of mathematics. The examples in this paper are intended to spark the imaginations of teachers and explore several mathematical areas ripe for Logo-based investigations.

Introduction
While it may seem obvious to assert that computers are powerful computational devices, their impact on K-12 mathematics education has been minimal. (Suydam, 1990) More than a decade after microcomputers began entering schools, 84% of American tenth graders said they never used a computer in math class.(National Center for Educational Statistics, 1984) Computers provide a vehicle for “messing about” with mathematics in unprecedented learner-centered ways. “Whole language” is possible because we live in a world surrounded by words we can manipulate, analyze and combine in infinite ways. The same constructionist spirit is possible with “whole math” because of the computer. In rich Logo projects the computer becomes an object to think with – a partner in one’s thinking that mediates an ongoing conversation with self.

Many educators equate Logo with old-fashioned turtle graphics or suggest that Logo is for the youngest of children. Neither of these beliefs is true. Although traditional turtle graphics continues to be a rich laboratory in which students construct geometric knowledge, Logo is flexible enough to explore the entire mathematical spectrum. Logo continues to satisfy the claim that it has no threshold and no ceiling. (Harvey, 1982) Best of all, Logo provides a context in which children are motivated to solve problems and express themselves.

The National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics recognizes Logo as a software environment that can assist schools in meeting the goals for the improvement of mathematics education. In fact, Logo is the only computer software specifically named in the document.

The Goals of the NCTM (1984) Standards for All Students

  1. learn to value mathematics
  2. become confident in their ability to do mathematics
  3. become mathematical problem solvers
  4. learn to communicate mathematically
  5. learn to reason mathematically

The NCTM Standards state that fifty percent of all mathematics has been invented since World War II. (National Council of Teachers of Mathematics, 1989) Few if any of these branches of mathematical inquiry have found their way into the K-12 curriculum. This is most unfortunate since topics such as number theory, chaos, topology, cellular automata and fractal geometry may appeal to students unsuccessful in traditional math classes. These new mathematical topics tend to be more contextual, visual, playful and fascinating than adding columns of numbers or factoring quadratic equations. Logo provides a powerful medium for rich mathematical explorations and problem solving while providing a context in which students may fall in love with the beauty of mathematics.

Computer microworlds such as Logo turtle graphics and the topics of constructions and loci provide opportunities for a great deal of student involvement, In particular, the first two contexts serve as excellent vehicles for students to develop, compare and apply algorithms. (National Council of Teachers of Mathematics, 1989, p. 159)

The examples in this paper are intended to spark the imaginations of teachers and explore several mathematical areas ripe for Logo-based investigations. The project ideas use MicroWorlds, the latest generation of Logo software designed by Seymour Papert and Logo Computer Systems, Inc. MicroWorlds extends the Logo programming environment through the addition of an improved user interface, multiple turtles, buttons, text boxes, paint tools, multimedia objects, sliders and parallelism.

Parallelism allows the computer to perform more than one function at a time. Most computer-users have never experienced parallelism or the emergent problem solving strategies it affords. MicroWorlds makes this powerful computer science concept concrete and usable by five year-olds. The parallelism of MicroWorlds makes it possible to explore some mathematical and scientific phenomena for the first time. Parallelism also allows more conventional problems to be approached in new ways.

Euclidian Geometry
One source of inspiration for student Logo projects is commercial software. Progressive math educators have found software like The Geometric Supposer and the more robust Geometers’ Sketchpad to be useful tools for exploring Euclidian geometry and performing geometric constructions. I noticed that while teachers may use these tools as extremely flexible blackboards, kids can pull down a menu and request a perpendicular bisector to be drawn without any deeper understanding than if the problem was solved with pencil and paper.

Could middle or high school students design collaboratively their own such tools? If so, they would gain a more intimate understanding of the related math concepts because of the need to “teach” the computer to perform constructions and measurements. Throughout this process, teams of students are asked to brainstorm questions, share what they know and define paths for further inquiry. Students as young as seventh grade have developed their own geometry toolkits in MicroWorlds.

Much of learning mathematics involves naming actions and relationships. Logo programming enhances the construction of mathematical knowledge through the process of defining and debugging Logo procedures. The personal geometry toolkits designed by students are used to construct geometric knowledge and questions worthy of further investigation. As understanding emerges the tool can be enhanced in order to investigate more advanced problems.

At the beginning of this project students are given a few tool procedures to start with. These procedures are designed to:

  1. drop a point on the screen (each point is a turtle and in MicroWorlds every turtle knows where it is in space)
  2. compute the distance between two points


With these two sets of tool procedures students can create tools necessary for generating geometric constructions, measuring constructions and comparing figures. MicroWorlds’ paint tools may be used to color-in figures and to draw freehand shapes. The procedural nature of Logo allows for higher level functions to be built upon previous procedures. Figures 1a, 1b & 1c are screen shots of one student’s geometry toolkit.

Probability and Chance
Children use MicroWorlds to explore probability via traditional data collection problems involving coin or dice tosses and in projects of their own design. Logo’s easy to use RANDOM function appears in the video games, races, board games and sound effects of many students.

Perhaps the best use of probability I have encountered in a MicroWorlds project is in a project I like to call, “Sim-Middle Ages.” In this project a student satisfied the requirements for the unit on medieval life in a quite imaginative fashion. Her project allows the user to specify the number of plots of land, number of seeds to plant and the number of mouths to feed. MicroWorlds then randomly determines the amount of plague, pestilence, rainfall and rate of taxation to be encountered by the farmer.

On the next page there are two buttons. One button announces if you live or die in the middle ages and the other tells why, based on the user-determined and random variables. You may then go back and adjust any of the values in an attempt to survive. (figures 2a, 2b and 2c)




Things happen in the commercial simulations, but users often don’t understand the causality. In student-created simulations, students use mathematics in a very powerful way. They develop their own algorithms to model historical or scientific phenomena. This type of project can connect mathematics with history, economics, physical science and life science in very powerful ways.

Number Theory
“Number theory, at one time considered the purest of pure mathematics is simply the study of whole numbers, including prime numbers. This abstract field, once a playground for a few mathematicians fascinated by the curious properties of numbers, now has considerable practical value… in fields like cryptography.”(Peterson, 1988) Software environments, such as MicroWorlds, provide a concrete environment in which students may experiment with number theory. “Experimental math” projects benefit from Logo’s ability to control experiments, easily adjust a variable and collect data. Kids control all of the variables in an experiment and can swim around in the beaker with the molecules. Intellectual immersion in large pools of numbers is possible due to computer access. The scientific method comes alive through mathematical experimentation.

A fascinating experimental math problem to explore with students is known as the 3N problem. The problem is also known by several other names, including: Ulam’s conjecture, the Hailstone problem, the Syracuse problem, Kakutani’s problem, Hasse’s algorithm, and the Collatz problem. The 3N problem has a simple set of rules. Put a number in a “machine” (Logo procedure) and if it is even, cut in half – if it is odd, multiply it by 3 and add 1. Then put the new value back through the machine. For example, 5 becomes 16, 16 becomes 8, becomes 4, 4 becomes 2, 2 becomes 1, and 1 becomes 4. Mathematicians have observed that any number placed into the machine will eventually be reduced to a repeating pattern of 4…2…1…

While this is an interesting pattern, what can children explore? Well, it seems that some numbers take a long time to get to 4…2…1… I call each of the numbers that appear before 4, a “generation.” I often expose students to this problem by trying a few starting numbers and leading a discussion. Typing SHOW 3N 1 takes 1 generation to get to 4. Students may then predict that the number 2 will take two generations and they would be correct. They may then hypothesize that the number entered will equal the number of generations required to get to 4. However, 3N 3 takes 5 generations! I then ask, “how can we modify our hypothesis to save face or make it look like we were at least partially right?” Kids then suggest that the higher the number tried, the longer it will take to get to 4…2…1… They may even construct tables of the previous data and make numerous predictions for how the number 4 will behave only to find that 4 takes zero generations (for obvious reason that it is 4).

I then tell the class that they should find a number that takes a long time to get to 4…2…1… I do not specify what I mean by a “long time” in order to let the young mathematicians agree on their own limits. The notion of limits is a powerful mathematical concept which helps focus inquiry and provides the building blocks of calculus. Students often test huge numbers before realizing that they need to be more deliberate in their experimentation. The working definition of “long time” changes as the experiment continues. Eleven generations may seem like a long time until a group of kids test the number 27. Gasps and a chorus of wows can be heard when 27 takes 109 generations. Then I ask the class to tell me some of the characteristics of 27. Students often list some of the following hypotheses:

Its factors are 1, 3, 9, 27
It’s odd
It’s 3 * 3 * 3 (an opportunity to introduce the concept of cubed numbers)
The sum of the digits = 9
The number is greater than 25
 

We then test each of the hypotheses and discard most of them. The cubed number hypothesis is worthy of further investigation. If we test the next cubed number, 4, with SHOW 3N 4 * 4 * 4 we find that it does not take long to get to 4. One student may suggest that only odd perfect cubes take a long time. I then suggest that the other students find a way to disprove this hypothesis by finding either an odd perfect cube that doesn’t take a long time or an even cube that does. Both exist.

to 3n :number
print :number
ifelse even? :number [3n :number / 2] [3n (:number * 3) + 1]
end

to even? :number
output 0 = remainder :number 2
end

A simple tool procedure may be added to count the number of generations for the “researcher.” The more you play with this problem, the more questions emerge. A bit more programming allows you to ask the computer to graph the experimental data or keep track of numbers that take longer than X generations to reach 4…2…1… Running such experiments overnight may lead to other interesting discoveries, like the numbers 54 and 55 each take 110 generations. What can adjacent numbers have in common? 108, 109 and 110 each take 111 generations. Could this pattern have something to do with place value? How could you find out? (see figures 4a & 4b)

The joy in this problem for kids and mathematicians is connected to the sense that every time you think you know something, it may be disproven. This playfulness can motivate students to view mathematics as a living discipline, not as columns of numbers on a worksheet. For many students, problems like 3N provide a first opportunity to think about the behavior of numbers. “For the most part, school math and science becomes the acquisition of facts that have been found by people who call themselves scientists.” (Goldenberg, 1993) Logo and experimental math provides another opportunity to provide children with authentic mathematical experiences.

Fractal Geometry and Chaos Theory
The contemporary fields of fractal geometry and chaos theory are the result of modern computation. Many learners find the visual nature of fractal geometry and the unpredictability of chaos fascinating. Logo’s turtle graphics and recursion make fractal explorations possible. The randomness, procedural nature and parallelism of MicroWorlds brings chaos theory within the reach of students.

Fractals are self-similar shapes with finite area and infinite perimeter. Fractals contain structures nested within one another with each smaller structure a miniature version of the larger form. Many natural forms can be represented as fractions, including ferns, mountains and coastlines.

Chaos theory suggests that systems governed by physical laws can undergo transitions to a highly irregular form of behavior. Although chaotic behavior appears random, it is governed by strict mathematical conditions. Chaos theory causes us to reexamine many of the ways in which we understand the world and predict natural phenomena. Two simple principles can be used to describe Chaos theory:

  1. From order (a predictable set of rules), chaos emerges.
  2. From a random set of rules, order emerges.

MicroWorlds may be used to explore both chaos and fractal geometry simultaneously. Figure 3shows two similar fractals called the Sierpinski Gasket. The fractal on the left is created by a complex recursive procedure. The fractal on the right is generated by a seemingly random algorithm discovered by Michael Barnsley of Georgia Institute of Technology. The Barnsley Fractal is created by placing three dots on the screen and then randomly choosing one of three points, going half way towards it and putting another dot. This process is repeated infinitely and a Sierpinski Gasket emerges. In fact, if you grab the turtle from the “chaos fractal” and move it somewhere else on the screen, it immediately finds its way back into the “triangle” and never leaves again. The multiple turtles and parallelism of MicroWorlds makes it possible to explore the two different ways of generating a similar fractal simultaneously. Experimental changes can always be made to the procedures and the results may be immediately observed.

Animation
One of the most attractive aspects of MicroWorlds is its ability to create animations. Students are excited by the ease with which they can create even complex animations. MicroWorlds animations require the same mathematical and reasoning skills as turtle graphics. The difference is that the turtle’s pen is up instead of down and the physics of motion comes into play. Multiple turtles and “flip-book” style animation enhance planning and sequencing skills. Even the youngest students use Cartesian coordinates and compass headings routinely when positioning turtles and drawing elaborate pictures.

Perhaps the best part of MicroWorlds animation is that the student-created animation and related mathematics are often employed in the service of interdisciplinary projects. Using animation to navigate a boat down the ancient Nile, simulate planetary orbits, design a video game or energize a book report provides a meaningful context for using and learning mathematics.

Functions and Variables
Logo’s procedural inputs and mathematical reporters give kids concrete practice with variables. Functions/reporters/operations are easy to create in MicroWorlds and can even be the input to another function. For example, the expression SHOW DOUBLE DOUBLE DOUBLE 5 or REPEAT DOUBLE 2 [fd DOUBLE DOUBLE 20 RT DOUBLE 45] are possible by writing a simple procedure, such as:

to double :number
output :number * 2
end

Many teachers are unaware of Logo’s ability to perform calculations (up through trigonometric functions) in the command center or in procedures. SHOW 3 * 17 typed in the command center will display 51 and REPEAT 8 [fd 50 rt 360 / 8] will properly draw an eight-sided regular polygon.

A favorite project I like to conduct with fifth and sixth graders creates a fraction calculator. First we decide to represent fractions as a (Logo) list containing a numerator and a denominator. Then we write procedures to report the numerator and denominator of a fraction. From there, the class can easily collaborate to write a procedure which adds two fractions. Some kids can even make the procedure add fractions with different denominators. From there, all of the standard fraction operations can be written as Logo procedures by groups of children. The next challenge the kids typically tackle is the subtraction of fractions.

One day, a fifth grader, Billy, made an interesting discovery while testing his subtraction “machine.” Billy typed, SHOW SUBTRACT [1 3] [2 3] (meaning 1/3 – 2/3), and -1 3 appeared in the command center. I noticed the negative fraction and mentioned that when I was in school we were taught that fractions had to be positive. Therefore, there is no such thing as a negative fraction.

Billy exclaimed, “Of course there is! The computer gave one to us!” This provoked a discussion about “garbage in – garbage out,” the importance of debugging and the need for conventions agreed upon by mathematicians and scientists. We even discussed the difference between symbols and numbers. Billy listened to this discussion impatiently and announced, “That’s ridiculous because I can give you an example of a negative fraction in real-life.”

Billy said, “I have a birthday cake divided into six slices and eight people arrive at my party. I’m short two sixths of a cake – negative 2/6!” He went on to say, “If the computer can give us a negative fraction and I can provide a real-life example of one, then there must be negative fractions.” The hazy memory of my math education diminished the confidence required to argue with this budding mathematician. Instead, I agreed to do some research.

I looked in mathematics dictionaries, but found more ambiguity than clarity. I also spent several weeks consulting with math teachers. Most of these people either dismissed the question of negative fractions as silly or complained that they lacked the time to adequately deal with Billy’s dilemma. After a bit more time, I ran into a university mathematician at a friend’s birthday party. Roger did not dismiss Billy’s question. Instead he asked for my email address. The next morning the following email message awaited me.

Date: Sun, 06 Nov 1994 09:52:44 -0400 (EDT)
Subject: fractions
To: gstager@pepperdine.edu

Dear Gary,

It was fun to have a chat at Ihor’s party. This morning I got out my all time favorite source of information on things worthwhile, the Ninth Edition of the Encyclopedia Britannica. (With its articles by James Clerk Maxwell et al.) It is very clear. Fractions come about by dividing unity into parts, and are thus by definition positive.

Interesting.
Yours,
Roger


Now what should a teacher tell Billy? In the past, you might hope that he forgot the matter. Today, Billy can post his discovery on the Internet and engage in serious conversation – perhaps even research with other mathematicians. Access to computers and software environments like MicroWorlds makes it possible for children to make discoveries that may be of interest to mathematicians and scientists. It is plausible that kids can contribute to the construction of knowledge deemed important by adults.

New Data Structures
MicroWorlds has two new data structures that contribute to mathematical learning. With the click of the mouse, sliders and text boxes can be dropped on the screen. As input devices, sliders are visual controls that adjust variables. Each slider has a name and a range of numbers assigned to it. Like a control on a mixing board the slider can be set to a number in that range. The slider’s value can then be sent to a turtle whose speed or orientation is linked to the value of the slider. The slider can also be used to set the values of variables used in a simulation.

Sliders may also be used as output devices. A procedure can change the value of a slider to indicate an experimental result. If a slider named, counter, is in a MicroWorlds project then the command, SETCOUNTER COUNTER + 1, can be used to display the results of incrementing the counter.

MicroWorlds text boxes also function as both input and output devices. A text box is like a little word processor drawn on the MicroWorlds page to hold text. Text boxes also have names that when evoked report their contents. If a user types the number 7 in a text box named FOO, then typing SHOW FOO * 3 will display 21 in the command center. FD FOO * 10 will move the turtle forward 70 steps. The command, SETFOO 123 will replace the contents of the text box, FOO, with 123. Therefore, text boxes may be used as experimental monitors or calculator displays. Constructing a garden-variety calculator with a text box and MicroWorlds buttons or turtles is deceptively simple, but provides one illustration of how text boxes could be used in a mathematical context.

A basic spreadsheet can be built in MicroWorlds with just one line of Logo code. If three text boxes are named, cell1, cell2 and total, then a button with the instruction, SETTOTAL CELL1 + CELL2, will put the sum of the first two cells in the third. Making the button run many times will cause the “spreadsheet” to perform automatic calculations. A bit more programming will allow you to check for calculation efforts, graph data or cause a turtle to change its behavior based on the result of a calculation. Building a model spreadsheet helps students understand how a commercial spreadsheet works, develop computation skills and add automatic calculation to their Logo toolbox.

Instructional Software Design
Children can use Logo as a design environment for teaching others mathematical concepts. Idit Harel’s award-winning research (Harel, 1991) and the subsequent research by her colleague, Yasmin Kafai (Kafai, 1995), demonstrated that when students were asked to design software (in LogoWriter or MicroWorlds) to teach other kids about “fractions” they gained a deeper understanding of fractions than children who were taught fractions and Logo in a traditional manner. These students also learn a great deal about design, Logo programming, communication, marketing and problem solving. Harel and Kafai have confirmed that children learn best by making connections and when actively engaged in constructing something meaningful. Their research provides additional evidence of Logo’s potential as an environment for the construction of mathematical knowledge.

Conclusion

Increased access to computers and imaginative teachers will open up an infinite world of possibilities for Logo learning. Software environments, such as MicroWorlds provide children with an intellectual laboratory and vehicle for self-expression. MicroWorlds inspires serendipitous connections to powerful mathematical ideas when drawing, creating animations, building mathematical tools or constructing simulations.

Excursions into the worlds of number theory, fractal geometry, chaos and probability rely on MicroWorlds’ ability to act as lab assistant and manager. Paul Goldenberg suggests that it is difficult to test out ideas unless one has a slave stupid enough not to help. (Goldenberg, 1993) The computer plays the role of lab assistant splendidly, yet the student still must do all of the thinking. MicroWorlds makes it possible to manage large bodies of data by running tedious experimental trials millions of times if necessary, collecting data and displaying it in numerical or graphical form. The procedural nature of MicroWorlds makes it possible to make small changes to an experiment without having to start from scratch.

MicroWorlds provides schools with a powerful software package flexible enough to grow with students. In days of tight school budgets it is practical to embrace a software environment with which students can address the demands of numerous subject areas. The sophistication with which students confront intellectual challenges improves along with their fluency in MicroWorlds.

Seymour Papert was horrified at how the simple example of commanding a turtle to draw a house, depicted in Mindstorms, became “official Logo curriculum” in classrooms around the world. However, providing students with a rich “mathland” in which to construct mathematical knowledge has always been one of the goals in the design and implementation of Logo. This paper attempts to provide simple examples of how MicroWorlds may be used to explore a number of mathematical concepts in a constructionist fashion. Those interested in additional ideas should read (Abelson & diSessa, 1981), (Cuoco, 1990), (Clayson, 1988), (Goldenberg & Feurzeig ,1987), (Lewis, 1990) and (Resnick, 1995). More detailed examples and teacher materials related to this paper are available on my World-Wide-Web site at: http://moon.pepperdine.edu/~gstager/home.html.

References

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  19. Silverman, B. (1987). The Phantom Fishtank: An Ecology of Mind. Montreal: Logo Computer Systems, Inc. (book with software for Apple II or MS-DOS)
  20. Stager, G. (October, 1988). “A Microful of Monkeys.” The Logo Exchange .
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  22. Stager, G. (1991). “Becoming a Scientist in a Logo-based Environment.” Proceedings of the Fifth International Logo Conference. San José, Costa Rica: Fundacion Omar Dengo.
  23. Suydam, M. N. (1990). Curriculum and Evaluation Standards for Mathematics Education. (ERIC/SMEAC Mathematics Education Digest No. 1, 1990) Columbus, OH: ERIC Clearinghouse for Science, Mathematics and Environmental Education. (ERIC Document Reproduction Service No. ED319630 90).