Home PublicationsL&LIssuesVolume 29 (2001-2002) May (No. 8)

Grand Challenges: Preparing for the Technological Tipping Point By Glen Bull, Gina Bull, Joe Garofalo, and Judi Harris Includes Vignettes by Chris Dede; Elliot Solloway, Katy Luchini, Chris Quintana, and Cathleen Norris; and Randy L. Bell. To read the online supplement to A fistful of Stars, click here. To read the online supplement to the main article, click here. Thinking carefully about initial educational uses of emerging technologies is important. Experimenting on a small scale before widespread adoption occurs is preferable to adopting innovations wholesale only to find their use cannot be reversed.

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Subject: Ubiquitious Computing, wireless computing
Audience: Teachers, teacher educators, technology coordinators, library/media specialists
Grade Level: K–12 (Ages 5–18)
Technology: Portable wireless devices
Standards: NETS•T I, II (www.iste.org/standards).

A t the beginning of his presidency, John F. Kennedy captured America’s imagination with a bold vision of the future. He delivered the following challenge to a joint session of the U.S. Congress (1961): “I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the Earth.”

Neil Armstrong became the first man to set foot on the moon on July 20, 1969, fulfilling the challenge. Along the way, many of the technological advances we take for granted today were developed. The term grand challenges has become shorthand for fundamental problems in science and engineering with broad economic and scientific impact that can be used to capture our imaginations in the way Kennedy captured America’s imagination with his grand challenge.

The use of portable wireless computers in schools will be widespread before the end of the decade. A future in which every student has a portable wireless device is inevitable and is sometimes termed an era of “pervasive computing” or “ubiquitous computing.”

The transition to pervasive computing will be a disruptive force that will have equally great potential for ill or good. We therefore wish to issue a grand challenge to ISTE members and the larger educational community: We believe that the educational and development communities should begin planning now for the best uses of ubiquitous computing.

The transition to pervasive computing has profound implications for education and may represent as great a paradigm shift as the invention of writing itself. The ancient Greeks viewed writing as the first step in the decline of an educated citizenry. They reasoned that if people could store information in written form, they would no longer need to exercise their mental capacity for memorization.

By the standards of the educated Greek citizenry, our capacity for memorization is insignificant. Nevertheless, once the innovation of writing became widespread, it was not possible to put the genie back in the bottle. A similarly irreversible shift in the educational paradigm is imminent.

Exponential Change
In 1961, the same year Kennedy issued his grand challenge, the first commercial integrated circuit was announced. Gordon Moore, co-founder of Intel, observed that the density of integrated circuits doubles every 18 months, a trend known as Moore’s Law. As a result, the cost of computing has steadily decreased. A graph of cost of computing in millions of instructions per second (MIPS) is logarithmic. (Data documenting the decreasing cost of computing appear in an online supplement to this article at www.iste.org/L&L.)

The consequences over time can be striking. The Eniac computer had the equivalent of 2 KB of memory and weighed 30 tons. In 1949, the editors of Popular Mechanics made the now famous prediction that someday computers might weigh “as little as 1.5 tons (March, 1949).” Today’s musical greeting card that weighs less than an ounce now has greater memory capacity than the Eniac. The cost of a four-function calculator decreased from several hundred dollars in the late 1960s to less than a dollar for solar-powered calculators given away in advertising promotions today.

The Apple II computer introduced in the 1970s had computing capacity equivalent to that of the mainframe computer in mission control that guided Apollo 11 to the first moon landing in 1969. Similarly, today’s Palm m100 handheld computer has about 200 times more memory capacity than the Apple II at 1/20th the cost. Based on these trend lines, we can predict with reasonable certainty that the majority of students in the public schools will have a wireless portable computing device by the end of the decade or sooner.

The form is likely to change over time. Currently, handheld computers are the most affordable portable computing devices. But researchers at the Xerox Palo Alto Research Center (PARC) and the MIT Digital Media Lab have developed prototypes of digital paper—electronic displays about the same thickness as paper. The school personal computer of the future may feature a folding portfolio with a thin-film touch-screen wireless computer on one side and ruled paper on the other side. Every student is likely to have a wireless tablet-sized computer linked to the Internet. For the sake of convenience, we will refer to this class of portable Internet devices that encompass handheld and tablet computers as portable wireless devices (PWDs). Chris Dede (Jump to Vignette 1), Elliot Soloway et al. (Jump to Vignette 2), and Randy Bell (Jump to Vignette 3) have provided vignettes that depict ways PWDs may be used by students in the year 2010. (You can also scroll down to find the Vignettes.)

The Tipping Point
When this transition to ubiquitous computing occurs, it is likely to take place in a relatively short period of time, rather than in a linear progression. Social change often occurs in relatively short periods of time when a critical mass is reached. For example, Sharp introduced the inexpensive FAX machine in 1984 and sold fewer than 100,000 units in the first two years. In the third year, a critical mass was reach-ed as enough businesses had FAX machines to make it worthwhile for all businesses to own one. One million FAX machines were sold in the third year, and two million in the year after. Malcolm Gladwell (2002) refers to this critical transition point when an innovation achieves critical mass and begins to spread rapidly as the tipping point. Interestingly, the mathematics of the growth curve for the spread of both innovations and epidemics is similar—a slow but steady growth until the tipping point is reached, when the innovation or disease explodes throughout a population. The tipping point is associated with the social dynamics underlying mass behavioral change. When a social system is poised at equilibrium, a relatively small force can produce disproportionate changes. Widespread access to PWDs will represent a tipping point in American education. Almost all consumer devices—from microwaves to cell phones—have a price point at which widespread adoption occurs in a short period of time. The same will be true for the spread of PWDs in schools.

The Lesson of the Graphing Calculator
Is it reasonable to expect that every student will someday have a portable computing device? Students in a majority of U.S. high schools use graphing calculators in algebra courses and above, and many middle schools are now following suit. These graphing calculators cost less than $100, slightly less than a lower-end handheld computer. Inclusion of graphing calculator software with equivalent functionality on handheld computers is possible and inevitable.

Graphing calculators are handheld computational devices with software designed primarily for one subject, mathematics. When used appropriately, graphing calculators can assist students in learning, exploring, and applying mathematics. PWDs with wireless connectivity to the Internet will have software for all content areas—word processing for English class, primary source document location and translation for social studies class, and so on. Once handheld computers with the functionality of a graphing calculator are available for the same price, schools will acquire them instead of graphing calculators. Because these devices can be used in all subject areas, teachers of all subjects will be able to use them as extensively as mathematics teachers currently use graphing calculators.

Despite relatively large expenditures on school computing technologies averaging $7 billion per year, the typical amount of student access to school computers nationally is still measured in minutes per week (Becker, 1994; Soloway, 2001). Limited access is one reason the substantive gains in productivity associated with business technology that drove the U.S. economy have yet to be realized in schools. When all students receive their own portable computers with wireless Internet connections, they will shift from a paradigm of minutes of access per week to complete access all day every day. This, in turn, will permit new instructional paradigms and require different classroom management and assessment techniques.

Educational Amplifiers
Soon educators will face a choice. These new technologies will amplify the effect of educational paradigms. Wireless information channels could merely be used as a pipeline to deliver existing curricula, emphasizing tutorial formats. In some cases, this approach can be appropriate, but it would be unfortunate if this were the only use of such enormous capability. Educational activities should take advantage of the capabilities of technology and, hence, should extend or significantly enhance what could be done without technology.

Appropriate use introduces technology in the context of meaningful content-based activities and addresses worthwhile content with sound pedagogy. Emerging educational technologies can enable students to explore topics in more depth and in more interactive ways. Technology also makes previously impractical topics accessible by removing computational constraints. The National Council of Teachers of Mathematics (2001) observes, “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning” (p. 24). New technologies offer opportunities to transform the curriculum through dynamic interactions in place of static pages.

For example, The Geometer’s Sketchpad, available on more than one model of handheld computer, allows students to explore mathematical concepts dynamically. Students can visualize effects of geometric transformations in ways not possible with pencil and paper alone, going beyond traditional methods of the existing curriculum.

Wireless access to the Internet further amplifies the educational potential of ubiquitous computing. This model envisions students actively using Internet access both to secure and analyze information and to communicate effectively with others in a wide variety of virtual contexts. Once students make contact with other learners, teachers, content experts, or other community members, they must know how to communicate in productive and appropriate ways, furthering their own learning while contributing meaningfully to others’ growth. This will entail both a technological transformation and, more significantly, a cultural and social transformation in schools. In the near future, such teleresearch and telecollabor-ation can and should be combined to afford students powerful and authentic virtual venues for inquiry.

These experiences assist students in the study of school curricula and prepare them for the postgraduation world. The President’s Committee of Advisors on Science and Technology (1995) identifies technological expertise as the nation’s most important resource: “More than half of U.S. growth in economic productivity and per capita income has resulted from technological advances.”

Consequently, development of technologically competent students may be one of the most important investments we can make in schools. Future students must know how to access information and analyze, interpret, and evaluate it. They can then explore relationships by manipulating data and its representations to generate original solutions to problems. All of these skills require technology-related expertise that must be taught explicitly.

Entrenchment
Everett Rogers (1995) provides the classic summary of the process of innovation in The Diffusion of Innovations. It illustrates that technological and educational futures are not certain progressions, but can tip one direction or another depending on relatively minor factors, often with undesirable outcomes. Once adopted, undesirable uses of technology become entrenched.

Rogers (1995) notes that the mechanical tomato harvester was developed with more than $1 million in public agricultural research funds. Because mechanical harvesters were expensive, costing more than $100,000, only wealthy farmers with large farms could afford them. Consequently, after introduction of the mechanical harvester at the beginning of the 1960s, more than 3,400 of 4,000 tomato farmers were out of business 10 years later. More than 30,000 agricultural jobs were lost.

Rogers (1995) notes that these adverse consequences were not inevitable, and they might have been avoided if the agricultural researchers at the university had possessed the foresight to develop “a smaller machine, one that more of the 4,000 farmers (as of 1962) could have adopted” (p. 154).

Ubiquitous portable computing has the potential to allow reconceptualization of the curriculum supporting learning in new and personal ways. However, some initial uses of this technology are accomplishing just the opposite. One elite private preparatory high school making extensive use of this technology has employed it to monitor teachers and students in a way that would not be possible with-out technology, micromanaging the curriculum on a minute-by-minute basis. Some of the teachers working under this technological regime consider it “confining” and “stifling.” Similarly, several venture capital initiatives are being developed and promoted as ways of raising scores on high-stakes tests through tighter control and management of the curriculum.

The first use of an emerging technology tends to become entrenched. The Sholes typewriter keyboard was designed to slow down the typist to reduce the frequency of jamming. Today’s computer keyboard has no levers to jam, but still uses the keyboard arrangement devised in 1867. Similarly, once the agricultural tomato harvesting innovation was adopted, the bankruptcy of 85% of California’s tomato farmers and the associated loss of thousands of jobs was inevitable. Just as it is not possible to put a scrambled egg back into the shell, it is not easy to reverse or deflect a diffusion path once adopted.

For that reason, thinking carefully about initial educational uses of emerging technologies is important. Experimenting on a small scale before widespread adoption occurs is preferable to adopting innovations wholesale only to find their use cannot be reversed.

The New Digital Divide
Currently there is considerable concern about the Digital Divide that separates rich and poor. A child who has a computer connected to the Internet at home has an academic advantage over a child who does not. However, the hardware Digital Divide is a temporary phenomenon. The threshold of the cost of portable wireless access to the Internet will become so low that PWDs will be available to everyone. Wireless Internet routers capable of supporting access for an entire classroom are already available for less than $200, and emerging low-power, low-cost technologies are just over the horizon. The coming didactic Digital Divide will separate those citizens who know how to use this access and those who do not.

Kathleen Fulton, former director of the U.S. Office of Technology Assessment (personal communication, December 2001), comments, The new Digital Divide is a didactic divide. Students from wealthy schools and poor schools often have different experiences with technology even when the hardware in disadvantaged schools is comparable to or better than wealthier counterparts.

The social dynamics of our society will change in unforeseen ways. A new generation is using instant messenger and chat services in ways that are incomprehensible to many in the generations before them. Such tools and techniques are developing at an accelerated rate, a rate that calls for an effective response—the preparedness of educators in schools with technology integrated into all subject areas. The initial applications of these technologies have predominantly focused on more efficient delivery of existing curricula. These include online tutorials, integrated learning systems, and related assessment mechanisms that parse the existing curriculum more and more finely. The potential for transformation of the curriculum can alter our very conception of schools and learning—therefore, it is important to go beyond today’s obvious uses.

A Call to Action
The educational community has engaged in a number of efforts of this kind—classrooms of the future and test beds—but such efforts have had arguably limited effect on prevailing educational practice. Exploring the potential of ubiquitous computing is important, but this exploration must be approached thoughtfully and employ sophisticated research models to have the needed effect on education. Therefore, we are calling for a national dialogue on this important subject.Several different avenues should be pursued in parallel. Approaches to establishment and support of a nation-al research and development agenda should include a leadership retreat to address this topic, establishment of communities of interest, and small-scale pilot studies.

Leadership retreat. A leadership retreat on the topic of ubiquitous computing in schools should include researchers and others already involved in PWD integration as well as interested foundations. The retreat should also include teachers who are now using PWDs. As a preliminary step, the National Technology Leadership Summit, underwritten by the U.S. Department of Education, brought together representatives of the national teacher educator associations representing the core content areas (see sidebar inset below).

Communities of interest. Forums for interaction and discussion among those interested in classroom PWD implementation are also needed. These could facilitate informal conversations among and provide support to those who are interested in advancing research and development into classroom use. (We invite you to participate in an interactive series of scholarly commentaries addressing this issue at the Cite Journal Grand Challenges Web page, www.citejournal.org/grandchallenges.)

Collaborative design. Educators and developers should collaborate to develop technological products that best meet the needs of schools. This collaboration should begin during the design phases and continue through introduction into schools.

Pilot studies. It is important to initiate many small-scale pilot studies to explore effective ways to employ PWDs in schools before the tipping point.

A variety of scenarios should be explored under different circumstances and conditions to ensure that PWDs are used effectively, without entrenching adverse or suboptimal uses on a widespread scale. The university researchers who developed the mechanical tomato harvester were not concerned about the effects of this innovation on human lives. Friedland and Barton (1975) consequently described these researchers as social sleepwalkers. We have a responsibility to think about the societal effects of educational innovations before their consequences are similarly irreversible.

Introduction of PWDs into schools creates extensive classroom management issues. It becomes difficult to ensure that students are attending to the subject at hand without becoming unduly restrictive. Some schools have even banned their use because of an inability to manage the consequences.

As costs drop and technological power increases, educational content and training for appropriate use do not make comparable gains. In fact, they typically lag far behind. It is important to place emerging technologies into the hands of teachers (and teacher educators, principals, and school board members) from the start so they understand the power and can dream the dreams the new technological capacity makes possible. This will ensure that when the technological capability arrives, we will be able to use it effectively to transform education. This will require collaboration among educators, hardware designers, and software developers to create capabilities designed explicitly to address curricular needs.

Summary
The few minutes of weekly access to school computers currently allowed the average U.S. student are not enough to change the overall curriculum in a fundamental way. When students have access 24 hours a day, seven days a week, the opportunity will exist to reexamine and enhance school curricula. This transition will represent a watershed event in education. The grand challenge will be to realize the educational and social potential of ubiquitous computing by the time this new era arrives. In a follow-up to his “urgent national needs” address to Congress, President Kennedy (1962) foretold innovations that would affect all Americans in the coming age:

The growth of our science and education will be enriched by new knowledge of our universe and environment, by new techniques of learning and mapping and observation, by new tools and computers for industry, medicine, the home as well as the school.

New educational technologies can generate both positive and negative consequences. Educators have a responsibility to avoid becoming educational sleepwalkers, blindly implementing this emerging technology in the most expedient way. The opportunity to undertake the requisite research and experimentation before the tipping point arrives will occur only once.

Acknowledgements
We appreciate the numerous individuals who have provided suggestions, recommendations, and feedback on this article as it evolved. John Mergendoller contributed significantly to the final form in which the concept was expressed. Kathleen Fulton, Margaret Riel, Gerald Bracey, Steven Rasmussen, Joel Gingold, Jolaine Harbour, Beverly Hunter, and Bob Tinker contributed comments that were incorporated into the final draft, and many others provided helpful insights. Finally, as always, Anita McAnear provided significant guidance, for which we are grateful.

Resource
Cite Journal Grand Challenges Web page: www.citejournal.org/grandchallenges

References
Becker, H. J. (1994). Analysis and trends of school use of new information technologies [Online]. Available: www.gse.uci.edu/doehome/EdResource/Publications/EdTechUse/TEXTCH4.HTM.

Friedland, W. H., & Barton, A. (1975). Destalking the wily tomato: A case study of social consequences in California agricultural research (Research Monograph 15). Santa Cruz: University of California, Santa Cruz.

Gladwell, M. (2000). The tipping point: How little things can make a big difference. New York: Little, Brown and Co.

Kennedy, J. F. (1961, May 25). Special message to the Congress on urgent national needs [Online]. Available: www.cs.umb.edu/jfklibrary/j052561.htm.

Kennedy, J. F. (1962, September 12). Address at Rice University on the nation’s space effort [Online]. Available: www.cs.umb.edu/jfklibrary/j091262.htm.

Moore, G. (n.d.). The continuing silicon technology evolution inside the PC platform [Online]. Available: http://developer.intel.com/update/archive/issue2/feature.htm.

National Council of Teachers of Mathematics. (2001). Principles and standards for school mathematics. Reston, VA: Author.

President’s Committee of Advisors on Science and Technology (1995). Statement of principles [Online]. Available: www.ostp.gov/PCAST/principles.html.

Rogers, E. (1995). Diffusion of innovations (4th ed.). New York: Free Press.

Soloway, E., Norris, C., Blumenfeld, P., Fishman, B., Krajcik, J., & Marx, R. (2001). Log on education: Handheld devices are ready-at-hand. Communications of the ACM, 44(6), 15–20.

Vignette 1: Augmented Reality through Ubiquitous Computing
By Chris Dede

Alec and Arielle strolled through Harvard Yard on the way to the museum to collect data for their class assignment. Each carried a handheld device that pulsed every time they walked past a building. This signaled that the building would share information about its architecture, history, purpose, and inhabitants using interactive wireless data transfer. Alec usually stopped to use his handheld to ask questions about an interesting looking location. Today, he was in a hurry and ignored the pulses.

Inside the museum, they split up to work on their individual assignments. When Alec typed his research topic into the museum computer, it loaded a building map into his handheld device, with flashing icons showing exhibits on that subject. At each exhibit, Alec could capture a digital image on his handheld device, download data about the artifacts and links to related Web sites, and access alternative interpretations about the exhibit. To ensure that the server sends him information tailored to his native language, reading level, and learning style, his handheld device automatically supplies information about Alec’s age and background.

Though the museum-supplied information was interesting, Alec always enjoyed the comments posted about each exhibit by other kids. Sometimes, he added a few remarks of his own to the ongoing discussion. Seeing a cool artifact related to Arielle’s topic, Alec paused to link to her handheld device, sending a digital image of the exhibit and information on its location.

Alec’s favorite exhibits were those augmented by virtual environments. For example, at a panorama showing the bones found at a tar pit, Alec’s handheld device depicted a virtual reconstruction of the dinosaurs that were trapped at that prehistoric location. In the virtual environment, he could assume the perspective of each species and walk or fly or swim through its typical habitat. Other types of exhibit-linked virtual environments enabled “time travel” to show how a particular spot on the earth’s surface had changed over the eons. For each epoch, Alec used virtual probes on his handheld device to collect data about temperature, air pressure, elevation, and pollutants.

Walking back from the museum, Arielle and Alec shared what they had found. Both wondered what learning was like before augmented reality and ubiquitous computing, when objects and locations were mute and inert. How lifeless the world must have been!

Chris Dede is the Timothy E. Wirth professor of learning technologies at Harvard’s Graduate School of Education. He is also chair of the Learning and Teaching Area in the school.

Vignette 2: Which Scenario Is Better for Learning?
By Elliot Soloway, Katy Luchini, Chris Quintana, and Cathleen Norris

Scenario with Handheld Technology
Group A starts by using the handheld version of the Artemis Digital Library on their handhelds to do some initial online research about water pollution. Amy and Bob find a Web site about pH levels and bookmark it to use as a reference and then go outside to test the pH level of the stream.

Carl and Diana stay inside and continue using Artemis Digital Library. When they find a Web site about water pollution from sewage they use their handhelds to send an instant message to Amy and Bob outside to ask them to look for signs of sewage contamination.

Outside, Amy and Bob test the pH level of the water and record the data using a spreadsheet program on their hand-helds. They get a pH level of 17 and think that this reading is odd, so they check the Web site they’ve bookmarked and find out that 17 isn’t within the range of possible pH values. They notice a flashing light on the front of the pH meter and use the handheld’s Web browser to go to the Web site of the company that makes the testing equipment. They find out that the light means that their meter is miscalibrated, so they send an instant message to another student downstream asking to borrow her pH meter. While they wait for the meter, they receive the message from Carl and Diana about looking for sewage and use the camera attachment for their handhelds to take pictures of potential pollutants in the stream.

Once they come back inside the classroom, they beam the data they’ve collected to the rest of their group. All four students then use their handhelds to collaboratively create a PiCoMap (concept map) and use Model-It Express on their handhelds to collaboratively build a model of their findings and theories about pollution in the stream. Once they finish their map and model, they upload them to the class’s Co-Web (a shared online discussion space) about water quality.

As they ride home on the bus that afternoon, Bob and Diana work on incorporating the images from the stream into another PiCoMap about visible water pollutants, using reference materials they downloaded to their handhelds using Fling-It.

In class the next day, Group B goes to the Co-Web and downloads the PiCoMap that Group A created about water pollution. Group B uses the Critique-It tool on their hand-helds to analyze Group A’s PiCoMap and compare it to the one they created about the sewage treatment process. They notice that the pH level recorded by Group A is higher than the levels of the purified water they found on the Web site for the sewage treatment plant. So Group B puts a comment on Group A’s PiCoMap about the differences and includes a URL to a Web site about sewage treatment and pH levels. Once Group B has finished critiquing the PiCoMap, they re-post the map and their comments to the class Co-Web.

Amy, Bob, Carl, and Diana then download the comments that Group B has made about their PiCoMap. Amy decides to use her handheld to e-mail the experts at the sewage treatment plant to find out more about the pH levels of the treated water. The experts reply via e-mail that the water treated at their plant has a pH of 7 when it’s put back into the stream. The group finds this interesting because the pH levels they found behind the school were higher, so Bob decides to use Artemis Digital Library on his handheld to look for more information about what could cause changes in pH levels. The other group members revise their original PiCoMap to include information about the water from the sewage treatment plant and highlight the fact that they found a higher pH level in their stream. Carl suggests that they make a new PiCoMap about the factors that could have caused higher pH levels and link this more specific map to their larger map about the stream.

Once the group members have finished their revisions, they post their PiCoMaps to the class’s Co-Web and use the classroom desktop to look at all of the PiCoMaps produced by the different student groups in their class. They notice that their PiCoMap is related to the ones created by Group B as well as to another group’s PiCoMap about fecal coliform. While Diana uses the desktop to look at the class’s maps, Amy uses her handheld to post a comment to the class’s discussion space (on the Co-Web) about the similarities in the different groups’ maps. The next day in class these three groups of students work together to combine their individual PiCoMaps into a larger map that is relevant to the entire class’s driving question about the quality of water in their community. They use the handhelds to beam the individual PiCoMaps to each other and then connect and revise them into a larger map, which they then post on the Co-Web.

Scenario without Handheld Technology
Group A goes upstairs to the library to research water pollution. Amy and Bob find a book with a detailed table about pH levels. There’s too much information to copy into their science notebooks, so Amy and Bob just list what seems like the most important information and then go outside to test the pH level of the stream behind their school.

Meanwhile, Carl and Diana wait their turn to use the library desktop to look up information online about water pollution. They want to print out a Web site they find about sewage contamination, but the library printer is out of paper so they have to go downstairs to get more. Once they get the Web site printed, Carl takes the paper outside to try and find Amy and Bob and ask them to look for sewage in the stream.

Outside, Amy and Bob measure the stream and get a pH reading of 17. Amy thinks this is strange because she wrote down that pH levels range from 0 to 14, but Bob didn’t copy that part of the book and doesn’t think the reading is unusual. They decide to keep going and record the pH test results in their notebooks. On their way back, they run into Carl, who has been wandering around for 15 minutes looking for them. It’s too late now to ask Amy and Bob to look for sewage contamination in the stream so they go back into the classroom.

Inside, Amy and Bob read off the test results they collected so that Carl and Diana can copy them into their own science notebooks. Bob, Carl, and Diana stand behind Amy as she uses a desktop computer and the Model-It software program to build a model of the stream’s ecosystem. Diana mentions that the pH readings seem strange, and the four students go back upstairs to the library to check the reference book. They discover that a few of their test results are outside of the possible range of pH values, but because class is about to end, they decide to just ignore the anomalous readings. They don’t have time to work on their concept map about the stream’s water quality in class, so they quickly divide the work to do at home. On the bus ride home, Bob and Diana decide to do their homework together and make a single concept map including both of their assigned parts. The next day at school they discover that the map they’ve created doesn’t quite fit with the maps Amy and Carl made, but they just scribble out the parts that don’t match and combine the rest to turn in.

The teacher gives each of the completed concept maps to a different group to comment on, and Group B receives Group A’s map. Group B doesn’t quite understand Group A’s map because there are a lot of scribbled-out sections, but they think there’s a discrepancy between the pH levels Group A reported in the stream and the levels for purified water that Group B found on the sewage treatment plant’s Web site. Group B isn’t sure what this difference means, so they raise their hands and wait for the teacher to come around and help them. When the teacher gets to them, she suggests that they make a note for Group A with their question and recommend that Group A try and figure out why different parts of the stream might have different pH levels.

When Group A gets their map back, they read the comment from Group B about the pH levels at the sewage treatment plant. Group A decides to ignore this note because they think there was something wrong with their pH readings from the stream to begin with. Anyway, Group A’s concept map is already pretty messy and complicated, and they don’t feel like trying to revise it to include more information about sewage treatment. So they just post their map on the bulletin board where they can look at all of the class’s maps together.

In looking at the entire class’s concept maps, Group A notices that two other groups also talked about water pollution and pH levels. Group A would like to be able to combine these three maps into a single concept map that relates to the class question about water quality, but there isn’t any easy way to combine the paper maps. They think about using string to link nodes in the maps, but that doesn’t let them add notes about the relationship between the groups’ work and the class’s question. And if they combine the maps on the bulletin board, then the individual groups can’t take their maps down to continue working on them, and no one can have a copy of the map to take home or think about later. In the end, Group A decides it would be too much work to try combining the maps and they don’t mention the similarities to their other classmates.

Dr. Elliot Soloway is currently the Arthur F. Thurnau Professor in the Electrical Engineering and Computer Science department in the College of Engineering, School of Information, & School of Education at the University of Michigan in Ann Arbor.

Katy Luchini is a doctoral student in computer science at the University of Michigan in Ann Arbor.

Dr. Christopher Quintana is a research scientist in the School of Education & College of Engineering at the University of Michigan in Ann Arbor.

Dr. Cathleen Norris is a professor in the Department of Cognition and Technology, University of North Texas, Denton, and president of the National Educational Computing Association.

Vignette 3: A Fistful of Stars
By Randy L. Bell

Tequa and Celeste were still working on their assignment when the bell rang at 3:05 p.m., simultaneously signaling the completion of Mr. Under-hill’s ninth-grade Earth science class and the end of the school day. As they logged off from their wireless Web connection on their hand-held devices, Mr. Underhill reminded students that they were to continue their research on open star clusters at home and added that he expected them to use their handheld device skills to locate and observe at least one open cluster in the sky that night. This last set of directions was met with a chorus of good- natured groans as students ribbed Mr. Underhill for once again “forcing” them out under the stars on a chilly November night. Undaunted by their dramatics, Mr. Underhill shouted “Carpe noctum!” to his students as they left the room.

Later, on the bus ride home, Tequa and Celeste shared what they had learned about open star clusters from their Web searches earlier in class. Each had recorded facts about open clusters on their handheld devices, along with several images taken by telescopes. Among the bits of information Tequa had gleaned was that open star clusters are also called galactic clusters, because they occur within our galaxy. Open clusters may contain as few as 10 stars, or as many as several hundred of them. More than 1,000 open clusters have been located within our galaxy, but of these, only a handful of the nearest ones are visible without the aid of a telescope. Chief among these are the Pleiades cluster in the constellation Taurus the Bull.

Celeste had collected some of this same information but had also spent time researching which cluster would make a good candidate for their observations that night. With the pocket planetarium program on her handheld device, she easily constructed a customized star map for the evening’s observation by entering the location, time, and date. The program also showed her that the Pleiades would be high above the eastern horizon at 8:30 p.m.

Later that evening in Tequa’s backyard, the two girls located the Pleiades for the first time. Their handheld devices provided a map of the stars in the eastern sky and even indicated when they were facing in the right direction. Tequa had brought a pair of binoculars to look at the Pleiades (as suggested by one of the Web sites), and she and Celeste took turns marveling at the dozens of blazing blue-white stars making up the cluster. It occurred to Tequa that the shape of the brightest stars in the cluster was vaguely familiar to her. Celeste said she remembered reading something about it in her research that day, so she retraced the history of her Web searches on her handheld device and found that the Japanese name for the Pleiades is Subaru. Of course! Tequa sees the Subaru emblem on her parents’ vehicle practically every day.

Later, as the girls explored the rest of the night sky using the “sky tour” feature of their handheld devices, Celeste quipped that perhaps Mr. Underhill wasn’t so cruel after all for encouraging them to look at the night sky so often. At that moment, her handheld device buzzed and displayed a message from her mother that it was time to head home. Taking a shortcut across a neighbor’s yard, Celeste heard Tequa’s triumphant shout of “Carpe noctum!” as she rounded the corner to her own house.

(Editor's Note: the following is the online supplemental content.)

The Next Day
The next day, Mr. Underhill taught his Earth science students to use the planetarium software on their handheld devices to control the robotic telescope he'd recently purchased for the class. Tequa and Celeste were thrilled to learn that Mr. Underhill had selected them as the first students to take the telescope home for a weekend of celestial observations and picture-taking. The two young women spent much of Saturday night in Tequa's backyard observing the wonders of their solar system and galaxy. The telescope and handheld device made it so easy as they communicated effortlessly through a wireless connection. Once connected, the handheld device spoke out loud, asking if they would like to take a tour of the night's best objects.

When the telescope failed to respond to Tequa's response of "Absolutely," Celeste piped in "Yes." The handheld device's voice recognition software began slewing the telescope to a series of celestial objects. That night, the telescope introduced Tequa and Celeste to Jupiter and its moons, the rings of Saturn, the Andromeda galaxy, the Orion nebula, and a host of star clusters. For each object they "visited," the handheld device described what they were seeing, as well as its size, distance, and many other interesting details. The software even suggested the best magnification to use for each object, as well as the settings necessary to to record the best image with the telescope's built-in CCD camera. On their first try, the two budding astronomers captured a clear image of the Pleiades open cluster, which they saved on each of their handheld devices.

The next afternoon Celeste uploaded the image file to a the class virtual locker. This automatically inserted the picture into a special Web page Mr. Underhill had constructed. As the semester progressed, every student in class added a picture to the online bulletin board, which bacame an impressive showcase of the students' experiences under the stars.

Randy L. Bell (RandyBell@virginia.edu) is an assistant professor of science education in the Curry School, specializing in applications of technology in science education.

Moore’s Law and Exponential Change
Moore’s Law observes that the growth curve of integrated circuitry is exponential rather than linear. For example, the following table displays the increase in the number of transistors on Intel microprocessors over the past quarter-century.

The human mind can better comprehend linear change than exponential change. If a class of students is asked to estimate how thick a sheet of paper would be if it were folded 50 times, the average estimate is generally less than a foot. The thickness of a sheet of paper varies by weight and manufacturer, but #24 bond paper is approximately 0.1 millimeters thick. It is only possible to double a sheet of paper seven times by hand; if this is done, a doubling each time yields the following result.

First fold - 0.1 millimeters
Second fold - 0.2 millimeters
Third fold - 0.4 millimeters
Fourth fold - 0.8 millimeters
Fifth fold - 1.6 millimeters
Sixth fold - 3.2 millimeters
Seventh fold - 6.4 millimeters

Because there are 25.4 millimeters per inch, the first seven folds yield a result that is less than a quarter inch thick. However, if this doubling were to continue until a total of 50 folds were achieved, the resulting stack of paper would be 56,294,995 kilometers thick. Because there are .62 miles per kilometer, the total thickness if it were possible to achieve this would be 34,981,710 miles. At its farthest approach, the moon is 252,700 miles from Earth. In other words, a piece of paper folded 50 times (if it were possible to do so) would extend far beyond the orbit of the moon. However, because we encounter few examples of exponential change of this type in life, most people generally estimate that the thickness of the paper folded just 50 times will be a foot or less.

The cost of computing and transistor density are closely related. Since the appearance of electronic computers, the upward curve of growth measured in millions of instructions per second (MIPS) per dollar has been even faster than exponential.

Hans Moravec (1998b), principal research scientist in the School of Computer Science at Carnegie Mellon University describes this trend as “an accelerating rate of innovation.”

The science fiction of one generation is a commonplace phenomenon for the next. In 1949 a skilled person with a desk calculator could compute a 60-second missile trajectory in about 20 hours. ENIAC required only 30 seconds to perform the same analysis. Based on this trend, the editors of Popular Mechanics made a now-famous prediction in the same year, "Where a calculator on the ENIAC is equipped with 19,000 vacuum tubes and weighs 30 tons, computers in the future may have only 1,000 vacuum tubes and perhaps only weigh 1.5 tons."

Today a $5 musical greeting card that plays a tune when opened contains a microchip that has computing capacity and memory comparable to the ENIAC. The editors of Popular Mechanics became famous not because they overestimated the effects of exponential growth, but because they underestimated it.

Experts tend to underestimate both the rate of growth and the social implications of technological innovations. In 1943 Thomas Watson, the chairman of IBM, concluded, “I think there is a world market for maybe five computers.” Similarly, in 1977 Ken Olsen, president and founder of Digital Equipment Corporation, stated, “There is no reason for any individual to have a computer in their home.” Thomas Watson guided IBM and the world into the age of mainframe computers, while Ken Olsen led the transition to mini-computers. The fact that these intelligent and capable individuals were unable to foresee the implications of the next phases of computing illustrates the difficulty of grappling with the implications of exponential technological change.

However, exponential technological change is not the entire explanation. Technology of any sort, not just computer technology, changes social expectations and culture. Business executives who can word process don’t need the same type of secretary. Universal access to cars means that it is no longer necessary to shop on or live near Main Street. Changed expectations and culture lead to new demands for the expansion and/or tailoring of technology. For example, a word processor with a spell checker and HTML editor or a car with cruise control and power steering. Watson, Olsen, and many others not only did not recognize the technological future, they did not foresee the flattening of organizational charts and distribution of responsibility and authority (Watson), and the use of the computer as a communication device and entertainment center (Olsen).

References
Moravec, H. (1998a). Robot: Mere machine to transcendent mind. New York: Oxford University Press.
Moravec, H. (1998b). When will computer hardware match the human brain? Journal of Evolution and Technology [Online], vol. 1. Available: www.transhumanist.com/volume1/moravec.htm.