Rational Number Project Home Page
Leavitt, Seth (2003). Creating the Web Pages for the Rational Number Project.
Unpublished M.Ed. paper.

Creating the Web Pages for

The Rational Number Project

http://cehd.umn.edu/rationalnumberproject/

Seth Leavitt

April, 2003
 
ACKNOWLEDGMENTS

I would like to express my appreciation to the following people:

Dr. Thomas Post, for giving me the opportunity and support to create something that I was learning how to create as I created it.

Dr. Kathleen Cramer, for helping turn that creation into this paper.

Table of Contents
ACKNOWLEDGMENTS
I. Rationale for this Project
II. A Brief History of the Internet and the World Wide Web
      Sharing Information on the World Wide Web
III. How the web site was created
IV. Reflections on the project
REFERENCES
APPENDIX A - Hobbes' Internet Timeline
APPENDIX B - Internet Hosts
APPENDIX C - Internet Networks

APPENDIX D - Complete Bibliography of the Rational Number Project
APPENDIX E - Project checklist
APPENDIX F - Web in progress folder screenshot
APPENDIX G - Root folder screenshot
 

Chapter 1 - Rationale for this Project

The purpose of creating the web site for the Rational Number Project <http://education.umn.edu/rationalnumberproject> was to make widely available the collected writings of a major research effort in mathematics education.

 

Brief History of the Rational Number Project
(return to Table of Contents)

In his introduction to the Rational Number Project web site, Dr. Thomas Post states:

The Rational Number Project (RNP) was the longest lasting cooperative multi-university research project in the history of mathematics education. NSF has, with the exception of 1983-84, funded it continuously since 1979.

The RNP’s most significant accomplishment is the collection of over 90 papers, book chapters, several books and other project publications. The vast majority of these are concerned with the learning and teaching of rational number concepts including fraction, decimal, ratio, indicated division, measure and operator. These studies led naturally to investigations of proportionality with specific attention to the components of proportional reasoning. We have examined the contributions of multiplication and division understandings to these earlier mentioned concepts and then proceeded to concern ourselves with the design of effective professional development programs for teachers and concurrently with appropriate assessment practices in our field. As project interests evolved, various project Co-PI’s cooperated in preparing material for publication. We have been quite successful in this regard and view these publications as a significant body of literature and contribution to what is known about these issues in our field.

These efforts also culminated in the development of three mathematics courses designed specifically for elementary teachers who traditionally do not have significant mathematical backgrounds, but who nevertheless are teaching mathematics to children each and every day. We have also produced two curriculum texts for teachers that reflect our suggestions as to how rational number concepts should be taught to children.

The collected body of work on the web site details much of the current thinking about teaching rational number concepts to elementary students. It is a tremendous resource for researchers, teacher educators, in-service teachers, and pre-service teachers. However, it is not readily available. Over 80 articles, books, and book chapters have been published. Some of the material is out of print. Much is not easily available, even at the libraries of major research universities.

 

Germination of the idea to create the Rational Number Project web site
(return to Table of Contents)

Dr. Thomas Post has been a key member of the Rational Number Project since its inception. He is also one of the principal investigators of the (MASP)^2 project (Minneapolis and St. Paul Merging to Achieve Standards Project). The (MASP)^2 project (1998 - ongoing) is a teacher enhancement project funded by the National Science Foundation (NSF). Its purpose is to provide professional development to in-service teachers as they implement standards-based mathematics curricula at the middle and high school level.

I worked with Dr. Post on the (MASP)^2 project from the summer of 1998 through the academic year 2000-2001. The work I did on (MASP)^2 became part of the germination for the Rational Number Project web site. I gained many insights into the creation of online resources and their effective dissemination.

(MASP)^2 was funded by the National Science Foundation to answer the call for professional development for in-service teachers implementing new, standards-based Mathematics curricula. These curricula, also developed with funding from NSF, were written with a different pedagogical perspective from traditional mathematics curricula. NSF saw the need for continued teacher support if the implementation of these curricula was to be successful.

(MASP)^2 developed a professional development model that consisted of

  • 80 hours of summer classes
  • 20 hours of academic year follow--up sessions
  • 30 hours of classroom mentoring

During the summers of 1998 and 1999, I participated in these professional development activities as an instructor. During the academic years 1998-1999 and 1999-2000, I was a classroom mentor.

As a classroom mentor, I visited over 30 middle-school classrooms for an extended time. The abundance of talent, ideas, teaching techniques, and teacher-developed resources was staggering. I did my best to bring the best of all I saw to all the teachers I worked with. This was a difficult task. I carried a heavy briefcase from classroom to classroom, sharing the products of other teacher's labor. I did my best to also share all the great ideas and techniques I'd observed. But it was physically impossible to share everything.

I am also an avid user of technology, for myself, for personal productivity in my classroom, and for continued learning. The World Wide Web is a great resource for me. I thought, "Why not use the power of electronic communication to disseminate all the ideas and resources I was finding?" So I proposed the establishment of the "CMP Online Resource Center." (CMP is the Connected Mathematics Project, an NSF-funded curricululm written at the Universiy of Michigan.) I would develop an online vehicle for teachers to actively share their thoughts, questions, ideas, and resources. My idea was accepted and the CMP Online Resource Center was born.

The CMP Online Resource Center
(return to Table of Contents)

For the academic year 2000-2001, I built and facilitated this online resource. The site was divided into the following sections:

    • Parent Resources
    • Grading
    • Portfolio
    • Management Issues
    • Reform Issues
    • Graduation Standards
    • ELL (English Language Learners)
    • Special Education
    • Mathematics Help
    • Sixth Grade
    • Seventh Grade
    • Eighth Grade

The online resource was very successful. Ninety-six teachers actively participated, logging over 1000 hours online. They participated in threaded conversations, downloaded and uploaded teacher-created supplemental resources, and shared their ideas for best classroom practice. Teachers found the site to be an extremely easy way to quickly get new ideas and have questions answered.

Dr. Post, as one of the Principal Investigators of the (MASP)^2 project, saw the success of this electronic communication tool. He saw how online communication was an effective means of sharing ideas and wondered, aloud, if it would be possible to use the World Wide Web to make the writings of the Rational Number Project accessible to the broader community of mathematics educators. I very glibly told him that yes, of course it was possible. He asked if I would work on the project. I accepted. At the time, I didn't know exactly what was involved in creating the resource he envisioned. Nor did I know the extent of the collected writings of the Rational Number Project. When I embarked on the project in the Spring of 2001, I learned what a major undertaking I had accepted. I will detail this undertaking in the third chapter of this paper.

The goal of this project is to describe in detail how this web site was constructed. This information will be helpful to other research groups interested in making their work available on the World Wide Web. This paper will be added to the Rational Number Project web site as a resource for others working to set up a web site.

In Chapter 2, I will present a brief history of the Internet and the World Wide Web to place my work creating the Rational Number Project web site into a historical perspective. Electronic communication is so ubiquitous now that users of the Internet are unaware of its origin. I believe that a general understanding of how the Internet grew and took on its present place in society will give the reader a better idea of the power of this medium for sharing information such as the work of the Rational Number Project.

Chapter 2 - A Brief History of the Internet and the World Wide Web

Sharing Information on the World Wide Web

Introduction
(return to Table of Contents)

In 2003, the Internet and the World Wide Web are an accepted and even an integral part of our culture and economy. It certainly wasn't always that way. The Internet, in various incarnations, has been around since 1969 when ARPANET(Advanced Research Projects Agency NET) first connected computers at UCLA, Stanford, UC-Santa Barbara, and the University of Utah (Rae-Dupree, 2002). The World Wide Web is much younger, only ten years old. The Web was born in 1993 at the European Particle Physics Laboratory (known as CERN) (Zimmerman, 1999). The reason the Internet, and more specifically the World Wide Web, became so important is that they fulfilled a deep need in modern society (Postrel, 1999).

The world's storehouse of knowledge was expanding, ever more quickly and widely. There was a need to disseminate all that was being learned. At the same time, computer technology was improving. Computers were able to store, catalog, and retrieve vast amounts of data quickly and almost effortlessly. The Internet grew as a means to communicate and to share information, first among the military and university researchers. As technology advanced and personal computers became more widely available, business and the general public were also able to take advantage of this new means of communication. A world wide library of information opened up to vast numbers of the world's citizens (World Almanac, 2003).

Definition of terms
(return to Table of Contents)

The terms "Internet" and "World Wide Web" are often used interchangeably. This is inaccurate. The Internet is simply a collection of computers and the cables and wireless devices that connect them. There are many different software applications that share information on the Internet - electronic mail (email), videoconferencing, and streaming audio for example. The World Wide Web is simply another application that uses the Internet to distribute information (Berners-Lee, T. 2003). It is by far the most widely used application. However, it is not the Internet. The Internet is the hardware that makes the World Wide Web possible.

The beginning of the Internet
(return to Table of Contents)

There are many people and many developments that have brought the Internet to the prominent place it is today. I will attempt to highlight these developments. For a more detailed history, I refer you to Appendix A - my abridged version of Hobbes' Internet Timeline (Zakon, 2003). The complete (and updated) timeline can be accessed at <http://www.zakon.org/robert/internet/timeline/>.

The event that is often credited for the impetus to create the Internet is the 1957 Soviet launch of Sputnik. President Eisenhower vowed that the United States would never be outdone by the Soviet Union. He established the Advanced Research Projects Agency (ARPA) (Gillies, 2001). ARPA sponsored many research projects.

Paul Baran, working on an ARPA-sponsored project for the RAND corporation, expressed his concern about the vulnerability of communications systems in the United States and advocated a more robust communication network. This Cold War motivation is often credited as the reason for the development of the Internet, but most Internet historians consider it to be a myth (Borden, 2000). The real impetus for the development of the internet came from physicists' desire to share information. In fact, in 1962, J.C.R. Licklider, Leonard Kleinrock, and Lawrence Roberts of MIT had designed the first network that allowed different kinds of computers to talk to each other, even before Mr. Baran's paper, "On Distributed Communications" was published (Baran, 1964).

Paul Baran's significant contribution to the development of the Internet was his idea of packet-switching, which was also developed independently and simultaneously in England by Donald Watts Davies. Packet-switching was a much more efficient way for computers to share information then had been previously developed (Gillies, 2001). In telephone communication, the connection is single use. That is, if two users are connected by telephone, the physical connection is occupied from the time the initial connection is made until the connection is broken (they hang up). With packet switching, every message is broken into small packets, sent out in bursts, and reassembled on the other end. The only time the hardware is occupied is for that instant that a packet passes through.

Conceptually, Baran's and Davies's approach seemed to borrow more from freight movers than from communications experts. Imagine that each message is a large house. How best to move that house from, say, Boston to Los Angeles? Theoretically, one could move the whole structure in a single piece. House movers do that over shorter distances all the time--slowly and carefully. It is more efficient, however, to disassemble the house if possible, load the pieces onto trucks and drive them over the nation's interstate highway system--another kind of distributed network. Not every truck will take the same route; some drivers might go through Chicago and some through Nashville. If the driver coming out of Nashville learns that the road is bad around Oklahoma City, he may go through Kansas City instead. But as long as each driver knows where to deliver his load, all the pieces should quickly arrive at the destination. Once there, they can be reassembled in their original order. (Lyon & Hafner, 1996)

In 1969, four mainframe computers were networked using packet-switching, forming ARPANET. The four computers were at UCLA, Stanford, UC-Santa Barbara, and the University of Utah. The first packets were sent from UCLA to Stanford. Charley Kline at UCLA tried to type the word "LOGIN". Interestingly, the Stanford computer crashed after to letter "G" was typed. This didn't deter the researchers and they were able to establish and maintain a connection and communicate between the four computers (Zakon, 2003).

ARPANET grew, adding more research institutions around the United States. In 1971, Ray Tomlinson invented an email program to send messages across the network. (In 1972, Tomlinson decides to use the "@" symbol for email addresses.) Email quickly became the dominant traffic on the Internet.

In 1973, the first international connections to the ARPANET were established with the University College of London (England) and NORSAR (Norway). In 1975, satellite links were established across the Atlantic and Pacific Oceans. Other networks were created on the Internet. In 1981, BITNET (Because It's Time NETwork) was established by the City University of New York.

Two events further propelled the development of the Internet. In 1982, the Transmission Control Protocol (TCP) and Internet Protocol (IP) were adopted by ARPANET.

This programming infrastructure was what let "the Internet" evolve to encompass a bunch of independent networks, both public and private. TCP/IP's creators wisely left those protocols very generic, enabling future innovators to build other structures, including those that made the World Wide Web possible, on top of them. (Postrel, 1999)

The second development occurred in 1985. The National Science Foundation (NSF) funded a "backbone" network among five supercomputing centers (JVNC@Princeton, PSC@Pittsburgh, SDSC@UCSD, NCSA@UIUC, Theory Center@Cornell). NSF also funded two-year grants for other universities to connect to NSFNet. This led to an explosion of connections, especially at universities. (See Appendices B and C) Researchers were able to tap into the work of their colleagues around the country and around the world. The Internet became well established as a tool of research. It would take the development of one more application to bring the power of the Internet to the general population.

The World Wide Web
(return to Table of Contents)

Work by Tim Berners-Lee at the European Particle Physics laboratory (CERN) in Switzerland is generally considered to have launched the World Wide Web. Berners-Lee's assignment at CERN was to develop a better method of communication between computers. He felt that the best model for communication was the human brain. He based his thinking about computers on the brain's ability to store, associate, and retrieve seemingly disparate things. In keeping with this idea, Berners-Lee published the specifications for universal document identifiers (now URLs- Universal Resource Locators), HyperText Markup Language (HTML), and HyperText Transfer Protocol (HTTP) in 1990. These breakthroughs opened the door to the World Wide Web (World Almanac, 2003).

In 1993, building on the protocols developed by Berners-Lee, Marc Andreessen at the University of Illinois developed the world's first graphical browser - Mosaic. Internet use exploded. The protocols developed by Berners-Lee coupled with the graphical browser developed by Andreessen made the Internet easy to use and accessible to millions of users world-wide.

It became relatively easy to put information on the Web and very easy to retrieve information. The Internet, and specifically the World Wide Web became a tool not only for researchers and the military, but for business and entertainment (Mueller, 2001).

Finally, a decision made by Tim Berners-Lee and CERN established the direction that the World Wide Web would follow:

The web finally took on its worldwide dimension in 1993 when CERN issued a statement relinquishing intellectual property rights and placing web software in the public domain, allowing anyone to download web software over the Internet and work on it. It was a controversial move, but it meant that anyone was free to contribute to (and benefit from) the web's development. (Gillies, 2001)

 

Sharing information on the World Wide Web
(return to Table of Contents)

The decision to make Web software public domain has set the tone for the subsequent development of the Web. The Web has become an utterly public and democratic institution. Practically anyone can make information available on the Web. Practically everyone can access information. This universal access makes the Web the perfect vehicle for sharing. University researchers have known this for a long time and have made use of the Internet for that purpose. With the advent of the World Wide Web, this tool for sharing ideas and knowledge has opened up to more and more people every day.

The World Wide Web is easy to use. Web browsers have become more powerful with each succeeding generation. Information on almost every conceivable subject is available with the click of a mouse. And it's not just text - multimedia brings in text, graphics, sound, and motion.

Multimedia, technophiles say, has three advantages. First, the sheer amount of information available: whole libraries can be called up on a computer screen. Second, the information can be searched with ease: instead of quixotic indexing, the computer can hunt for any word or combination of letters. Third -- and this is why the technology is called multimedia -- the information can be presented with sounds and images as well as text. (Rundle, 1998)

How does this effect education? On his FAQ (frequently asked questions) page on the Web, Tim Berners-Lee states:

I hope that educators will pool their resources and create a huge supply of online materials.  I hope much of this will be available freely to those especially in developing countries who may not have access to it any other way.  Then I think we will see two things.  One will be that keeping that web of material up to date will take a lot of time and effort - it will seem like more effort than creating it in the first place.  The other is that we will see how essential people, and their wisdom, and their personal interactions, are to the educational process.  A university is a lot more than its library. (Berners-Lee, T. 2003)

 
Chapter 3 - How the web site was created

Overview
(return to Table of Contents)

With the establishment of the Rational Number Project web site, a major body of research is now easily available to the entire community of mathematics educators.

The creation of the Rational Number Project web site <http://education.umn.edu/rationalnumberproject> proved to be a major effort. From the sheer volume of the writings to all the details that went into creating the final web site, the project was a challenging undertaking. This section will detail the process I followed to create the web site.

From start to finish, the task included the following parts:

  • obtaining an IP address for the site
  • purchasing and configuring a web server
  • locating all the articles in the bibliography
  • obtaining copyright permission to publish the articles online
  • converting paper copies of the articles to electronic files
  • recreating the tables, graphs and figures found in the articles
  • creating workable web pages that faithfully reproduced the original articles but included some of the features available in electronic publication that are not available in print (such as hyperlinks).

Like the World Wide Web, the project didn't proceed in a linear fashion. After obtaining an IP address and configuring the web server, the project proceeded in all directions. While waiting for copyright permission, I began to assemble all the articles in the bibliography. As I continued finding the articles, I began the process of converting paper text to electronic text. Once that process was mastered (though not completed), I began learning how to create web pages. I also began to learn how to recreate charts, graphs, and figures. Finally, as each article was completed, I posted it to an ever-expanding web site.

For the purpose of detailing the project, I'll describe each part as if they took place in sequential order. The following is the "how to" of setting up a web site of scholarly material.

Obtaining an IP address for the site and purchasing and configuring a web server
(return to Table of Contents)

The Rational Number Project web site was created after I had already created the CMP Online Resource Center. I had obtained an IP address and set up a server for that project so I simply had to reconfigure the server to host the Rational Number Project site. However, it is informative to understand the details of that part of the project so I will include them here.

The CMP Online Resource Center (and, following that, the Rational Number Project web site) were created as projects under the auspices of the University of Minnesota. Working with IT (Information Technology) services from the University, I was given a static IP (Internet Protocol) address for my server. It is necessary for a web server to have a static (as opposed to dynamic, or changing) address because the IP address is how the user of the World Wide Web locates a site. When a user types a web address (or URL - Universal Resource Locator) such as <http://education.umn.edu/rationalnumberproject> into his/her web browser, a DNS server (Domain Name Server) converts that user-friendly, English-language web address into a numeric IP address, unique to the web server on which the site is housed, in this case, the Rational Number Project server.

Later on in the project, I was contacted by the Web manager for the College of Education, University of Minnesota. She felt that the site would be better housed on servers maintained by the college as opposed to our own server. I have made that transition. Since the University of Minnesota is the Internet Service Provider (ISP) in either case, the transition from our own server to the college server will not be noticed by the users of the web site. The college will simply take over the IP address that I was assigned and automatically point all requests for that address to the college server.

Before I started the Rational Number Project web site, I had purchased a web server to host the CMP Online Resource Center. (I have a Macintosh G4 server, with 256 mb of RAM and a 40 gb hard drive, running AppleShare version 6.1. This server has been working extremely well, with no problems in the two-and-one-half years that it has been running.) At the time, I thought that the CMP Online Resource Center was going to be the sole user of the server and that when that project was over, I would take the server off the web. If I had known that I was going to create a permanent site for the Rational Number Project, I wouldn't have purchased my own server. I would have contacted the college and arranged for a permanent home for the Rational Number Project web site on the college server right from the start. However, no harm was done since the college has been very accommodating in making the transition to their server.

Locating all the articles in the bibliography
(return to Table of Contents)

Dr. Post provided a detailed bibliography of the articles produced by the five principal investigators involved with the Rational Number Project. (See Appendix D for the complete bibliography.) He had copies of about 75% of the articles in the bibliography. That was a good start. Most of the rest of the articles were obtained through inter-library loan through the University of Minnesota library system. However, some articles were not available through inter-library loan. For those articles, I contacted the authors directly. In all but one case, the original authors were able to provide me with a photocopy of the published article. In one case, I had to rely on the manuscript that the author had in her files.

Obtaining copyright permission to publish the articles online
(return to Table of Contents)

Obtaining copyright permission was easy for the first seventy-five or so articles. The last dozen proved to be more difficult. A few were really difficult to obtain and I never did get permission to publish three.

The University of Minnesota has a copyright service for professors and instructors. Professors and instructors often use copy written material in their classes. If students were to buy a textbook, this, of course, is not an issue. Sometimes, just one chapter of a book or an article from a journal is all that the teacher wants. He or she contacts the Copyright Center in advance of using the article (or chapter). The Copyright Center contacts the publisher. They explain what the teacher is using the work for and ask for permission. The publisher writes back with permission granted (no fee), permission granted (with a fee), or permission denied. If permission for this use is granted, the teacher is free to use the material in his/her course. Most times, it is a fairly straightforward process and the publisher grants permission (with or with a fee). Sometimes, there needs to be some negotiation. Sometimes it's an outright denial.

I contacted the Copyright Center to see if they could help me obtain copyright permission to publish articles on the World Wide Web, available to any user world-wide. This was an unusual request. Sometimes teachers put articles on the Web in a password protected environment, which is virtually the same thing as making photocopies for students (from the publisher's standpoint). A limited number of users have access to the material. When an article or book chapter is published on the World Wide Web, without password protection, the material becomes universally available. This is a different situation for publishers.

After some discussion, the Copyright Center understood the scope of my project. I provided them with a complete bibliography and they proceeded to contact publishers.

Many publishers replied quickly with full permission and charged no fee. ERIC/CSMEE (ERIC Clearinghouse for Science, Mathematics, & Environmental Education) replied immediately and gave full permission with no fees. Book publishers (from which chapters were used) were also quick in responding, mostly all granting permission, some with fees, some without. If a fee was charged, it was nominal. No fees were greater then $25. Journals were also fairly accommodating, responding relatively quickly, and usually granting permission.

The Copyright Center keeps a copy of all permissions it receives. I did not request copies for our files. If necessary, we can get copies from the Center.

Some publishers never responded and permission was denied in some cases. In those cases, I followed up personally rather than ask the Copyright Center to follow up. In some cases, the journal no longer existed or had been absorbed by another journal. When I tracked down that information and contacted the right person, permission was generally granted. Tracking this information down usually involved sending out emails to various people involved, and then following their suggestions. Email made this process a great deal easier than pencil-and-paper mail. (This is an example of how electronic communication can enhance learning. Today, almost everyone has an email address. Responding to an email is quick and usually painless, so people readily reply to reasonable requests.)

An example of this process follows. I did not receive immediate permission to use the following article:

Post, T., Behr, M., & Lesh, R. (1986). Research-Based Observations About Children's Learning of Rational Number Concepts. Focus on Learning Problems in Mathematics, 8(1), 39-48.

The request from the copyright center had received no reply. On July 9, 2002, I searched the Web for a name associated with the journal. I emailed this contact, explaining my project and asking for his help. He forwarded my message to two people on the Board of Directors and also referred me to the organization that presently holds the copyrights for the journal. I wrote to the members of the board and was informed to contact _____ at Center for Teaching/Learning of Mathematics in Framingham, Massachusetts. I contacted him and he indeed was the person who could give me permission to use the article. On July 13, I received an email that simply stated, "This email serves official note to use these articles on the web site."

The National Council of Teachers of Mathematics (NCTM) gave permission for older material, such as articles and book chapters. However, NCTM is making more and more of their published work available online. Much of it is only available to members. If the material was available online through NCTM, we were only granted permission to publish a summary of the article, its conclusions, and a bibliography. An example of this is the article:

Cramer, K. A, Post, T. R., del Mas, R. C. (2002) Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula With the Effects of Using the Rational Number Project Curriculum. Journal for Research in Mathematics Education. 33 (2) 111-144.

One publisher, SUNY Press, has a policy of only granting permission for electronic publication to libraries. I was not able to convince them to allow us to use their material. However, they did allow a summary, conclusions, and bibliography, as with NCTM. Rational Number Project authors had two chapters in the book The development of multiplicative reasoning in the learning of mathematics. G. Harel & J. Confrey (Eds.) published by SUNY Press.

I have kept copies of all the copyright permissions that I personally obtained. They are in the files of the Rational Number Project in Dr. Post's office.

In summary, obtaining copyright permission is an important part of a project like this. The effort needed to accomplish this depends on the number of references, their age, and the policies of each publisher.

Converting paper hard copies of the articles to electronic files
(return to Table of Contents)

At present, there are 83 entries in the bibliography of the Rational Number Project. Dr. Post has a xeroxed copy of most of these articles and book chapters on file in his office. He also has copies of many of the journals and books from which the copies were made.

The process of converting printed text to electronic text depended on the quality of the printed copy. Sometimes, the copies were fairly hard to read. In that case, I would look for the original journal or book and make new, cleaner copies. (Copiers are better today then they were in 1979.) If I could not find the original, the easiest solution was to simply retype the article.

If the xerox copy was good, the work went much more easily. This was the case for about 90% of the material. With a good copy, I could use Optical Character Reading software (OCR software) to convert the printed word to electronic text. OCR software takes the image of a page of text (an electronic photograph), looks at each bit of the image and converts the bits into alphanumeric characters, producing a text version of the image. The OCR software I used was OmniPagePro (version 8) with a Hewlett-Packard ScanJet 530c scanner. I scanned each page individually, creating one file in OmniPagePro for each article. After scanning the entire article, OmniPagePro would convert the image files into one electronic text file.

OCR software is not perfect. Stray marks and imperfect print cause the software to mis-recognize some text. After the software has converted an image into text, the user needs to proofread the results to catch the errors. OmniPagePro has a dictionary feature. At first, I used this feature of the software but it was a bit cumbersome. It was clumsier then using the spell check feature in a word processor. I looked for another solution. Since I had electronic text, I realized that I could save the text into word processing software and then use the spell check feature of that software. I saved the text created by OmniPagePro directly into Microsoft Word, without ever looking at it for errors.

Once the text was in Microsoft Word, it was just a tedious process of proofreading. There were well over one thousand pages of text to proofread for this project. I was fortunate to have the help of two graduate students in this task. I converted the paper text to Microsoft Word documents, and then the three of us worked on proofreading those documents. After the electronic texts were proofread, they were handed back to me (actually, emailed to me) to insert the tables, graphs, and figures and to convert to the whole business into workable web pages.

Recreating the tables, graphs and figures found in the articles
(return to Table of Contents)

Recreating the tables, graphs, and figures found in the articles was the most difficult part of the process of turning this body of work into a usable web site. Every article contained tables, graphs, and/or figures. My task was to reproduce these graphics faithfully so that the reader on the World Wide Web would see exactly what a reader of a journal or book saw.

At first, I thought I could just scan each image and insert it into the web page. This didn't work. I scanned images and viewed them in a web browser. (I previewed all the material in Netscape Communicator and Internet Explorer.) The untouched scans did not look that good. They tended to have telltale marks, off color backgrounds, and other problems that made them inadequate to put directly on the Web. I needed to learn how to retouch the scans.

I took a crash course in Adobe PhotoShop at the Digital Media Center, which is a group at the University of Minnesota that helps faculty use electronic media for teaching and learning. Adobe PhotoShop is an extremely complex piece of software, used by graphics professionals to create and manipulate images. I only needed to manipulate the images of the figures found in the articles. I learned how to use a small part of PhotoShop to accomplish this task.

PhotoShop did a good job cleaning us scans of images. However, it was not the best took for recreating every graphic. The process of creating every table, graph, and figure proved to be highly individualized. I examined each graphic individually and decided on the most efficient way to reproducing it electronically.

Tables are used extensively in web page building. As I learned how to use page-building software, I realized that the best way to reproduce all the tables was to create them directly with the software. Web page building software turns the process of building web pages into a combination of word processing and graphic design rather then a process of writing computer code. One feature of the software is the creation of tables. The user defines the size of the table (width, and height) and its attributes (number of rows and columns, borders, backgrounds, etc.)

As I worked on each article in the bibliography, I would recreate each table using page building software (I used Dreamweaver 3 and later Dreamweaver 4). I saved these tables for the final step when I would put together all the text and graphics and create the finished web pages.

I used two different strategies to recreate the graphs. For some graphs, scanning the graph and treating it like an image was the best approach. But if the data was evident in the graph (or contained in text in the article), I could usually recreate the graph using spreadsheet software. (I used the spreadsheet function in AppleWorks 5 and Microsoft Excel.) This method was far superior to scanning and touching up. It created a perfect reproduction of the graph from the article. In addition, the file size was much smaller. This is a consideration when it comes to building web pages. The larger the file size, the longer it takes for the page to load on a user's computer. A file that loads quickly is more useful then one that takes too much time to load.

I also used a blend of these two strategies for the figures. If I could easily recreate the figure (such as a set of fraction circles), I would. I used the draw function in AppleWorks and another piece of graphics software called Fireworks. This had the same advantage as recreating the graphs. The graphic was very clean and tended to be smaller in size.

Sometimes, I could scan parts of the figure and incorporate the scanned image into a new image. Lastly, if the figure was complex, I usually just scanned it and cleaned it up with PhotoShop.

Each graphic had to be handled individually. This was an extremely time consuming process but in the end, it produced web pages that were highly readable with accurate tables, graphs, and figures.

Creating workable web pages that faithfully reproduced the original articles but included some of the features available in electronic publication that are not available in print (such as hyperlinks)
(return to Table of Contents)

The Rational Number Project web site is a collection of over seven hundred files. It is important to have an organizational scheme when creating any web site but it is especially important for a site of this size. First, I developed a checklist (see appendix E) to keep track of progress. This was important since the articles were not developed one at time in a linear fashion. Three people were working on creating electronic text. Later in the project, as the deadline approached, another student joined the project. She was skillful at building web pages and shared that task with me. Copyright permissions came in fits and starts and had to be recorded. Keeping track of each article's status was essential. As each article was completed, I posted it to the ever expanding web site.

Another organizational tool was to create two folders at the root level on the hard drive of my computer. The first I titled "web in progress" and the second was simply called "root." I created a folder for each article within "web in progress". Then I developed a naming scheme for all the folders, files, and images (See Appendix F for a screenshot of the Web in progress folder).

Each article had a folder within "web in progress." I named each article for the year it was published. For example, 3 articles were published in 1990. So I had folders titled 1990_1, 1990_2, and 1990_3. I used the underscore in the title just to get into the habit of naming items for the web. (Web page names can not contain any spaces.) Folders were named with the full year (for example, 1990_1). Within the folder 1990_1, I would place all related files. The Microsoft Word file that contained the text of the article was titled 90_1.doc (the .doc suffix indicates the file is a Microsoft Word document).

Image files were named in a manner that would make it easy to place them within the html document (more about that below). Most often, the file was simply a figure from the article. I named those files fig1, fig 2, fig3, etc. Sometimes, the image files were only part of a figure. In that case, I used names like 231a, 231b, 231c. The 231 was the page in the article and the a, b, c were the subparts of the final image. I would use these parts to create the final image, which would then be named fig5 (for example).

I was careful to include any suffixes with the images. Some software programs need the suffix in order to open the file. If the image was created in PhotoShop, I used .psd. AppleWorks images had the suffixes .cwk or .pict, depending on which format I saved the image. Fireworks produced images with the suffixes .gif and .jpg. Once all the necessary files for an article were created, I was ready to create the web page.

Again, it is important to have a carefully planned file structure for the web pages. Hyperlinks are defined by the path the web browser (Netscape or Internet Explorer, for example) travels to find the appropriate file. If the file structure on the web server (the computer that holds the actual files that the user's web browser accesses) is different from the file structure used to create the pages, the browser will be unable to find the file and the user will receive an error message. See Appendix G for a screenshot of the root folder. This folder is the one that is imported onto the web server.

As mentioned above, I used the web building software Dreamweaver. I created a new document and titled it appropriately. For example, the web document would be named 90_1.html (html stands for HyperText Markup Language - the language read by web browsers).

The first page I created was the draft home page for the web site. I needed a home page so that I would have a file to link to all of the documents. A home page is the first page that viewers will see when they enter a URL (Universal Resource Locator - a web address) such as <http://education.umn.edu/rationalnumberproject> into their web browser. This page contains photographs of the five Principal Investigators, links to their personal pages on the web and their email links, a search engine for the site (more about that below), and an introduction to the Rational Number Project written by Dr. Post. There are also links to two versions of the bibliography- one in alphabetical order and the other in chronological order.

Each bibliography page contains complete citations of the works of the Rational Number Project. The title of each article is a hyperlink that brings up the article itself.

I would then turn to the raw material for the web page - the Microsoft Word document and the related images. Microsoft Word has a feature that lets you save a word processing document as a web page. I'd open the Word document and "save as html". I'd save this document with the convention 1990_1.html so that I wouldn't confuse it with the finished document (which would be 90_1.html).

There are sometimes problems with the html code that Microsoft Word writes. I'd open 1990_1.html in Dreamweaver (web page building software). Dreamweaver has a feature that cleans up Word html. I would run that feature and save the document. I'd highlight the entire text and copy it to the clipboard.

I'd then create a new document with Dreamweaver and give it a name (such as 90_1.html). I would insert a table that was 600 pixels wide with no border. This table is invisible to the viewer but it dictates how the page is displayed in the viewers web browser (more about that below). I started each table with ten rows. I'd paste the text created by Microsoft Word into the second row of the table. (The first row of the table was reserved for the article citation and a link back to the Rational Number Project home page.)

Every page on the Rational Number Project web site is basically a table with all the text and graphics inside the table. If fact, there are tables within tables, and tables within tables, within tables. The reason for this is that it controls what the viewer sees on their screen when they view any of the pages. Almost every computer has a screen big enough for a table 600 pixels wide. Therefore, the entire width of the article will be on the screen and the viewer won't have to scroll left to right. (Some viewers increase the font size on their own browser. In that case, the page might not be completely visible.) Another reason that each page is in a table 600 pixels wide is that this is a comfortable size for the eye to scan left to right. It's not too long nor too short.

Each block of text was contained in its own row in the table. When I came to a figure in the article, I would insert three table rows. The middle row would be for the figure and the rows above and below the figure were used to control how much white space there was between the figure and the text above and below. I could now insert the figures I created for the document into the middle row.

Images are not actually contained in web pages. The web page has a reference to the image actual image file. When the page loads in a browser window, the browser looks to the image and loads it in the appropriate place.

This is where the importance of the "root" folder comes to play. The "root" folder contains all the html documents and all the images that make up the site. The html documents are at the root level of the "root" folder. I created a folder within the "root" folder called "images." This isn't necessary but it is helpful for keeping track of the work, especially with a site this big. Inside the "images" folder are a set of folders, each named for the article associated with it. All the images are inside these folders.

I proceeded in this fashion until the entire web page was created. That is, all the text and images were in place. Now it was time to take advantage the ability to use hyperlinks within a document. Every footnote has a hyperlink that brings the viewer to the bottom of the document (where the footnotes reside). There is a link to return to the location in the text that has the footnote. In other words, as a reader comes to a footnote, he or she can click on it, read the footnote, and then click on a link to bring them back up to the text they were reading.

Similarly, if a table, graph, or figure is not close to the text that refers to it, or if the text refers back to it, those references are hyperlinked. For example, if the author refers back to figure 3, the reader can click on the words "figure 3". The browser brings figure 3 into the window. Again, there is a hyperlink to bring the reader back to the location in the article where he or she was reading.

Another feature of the World Wide Web is the search engine. Search engines enable users to rapidly find web pages based on key words or subjects. One powerful search engine is "Google." Google provides a search service to universities. After registering with Google, you are provided with code to insert into your own web site. This code makes use of Google search technology and enables a user to search the particular web site, and not the entire World Wide Web.

Some of the articles have a large number of figures, graphs, or tables. In those cases, file size was a consideration. It would take a long time for the article to load if all the figures were contained in the document. In those cases, the hyperlinks open a new document that contains all the figures, graphs, and tables.

I registered with Google and inserted the code into the home page and the two bibliography pages. If a user is interested in a particular subject, such as pedagogical approaches to teaching rational numbers, they can use Google search feature on the pages. This search will be confined to the Rational Number Project web site and return results found in the writings of the Rational Number Project.

The final step in this long process is to post the material on the World Wide Web. This can be done in a variety of ways, depending on the Internet Service Provider (ISP) that is hosting the site. The Rational Number Project was originally on a server I controlled. I used server software called FirstClass. Putting the files on this server was simply a matter of dragging and dropping them in place. When the project was completed, I was contacted by the University of Minnesota College of Education webmaster. She thought we should put the site on the College of Education servers. This proved to be a good idea. The college servers are maintained and backed up by university IT (Information Technology) personnel. I still have control over the content of the site but I don't have to maintain the hardware. In the long term, this will guarantee that the writings of the Rational Number Project will continue to be available to interested readers on the World Wide Web.

(return to Table of Contents)

Chapter 4 - Reflections on the project

Creating the web pages for the Rational Number Project was a new experience for me. I've been using computers since 1988 and I have a pretty good grasp on how to accomplish many tasks with the help of a computer. I've also used the Internet for many years. I am fairly skillful and finding information. I can also couple Internet resources with other computer applications to create products for personal use or for use in my classroom.

But I had never created a web page before I began this project.

I had a very basic idea about how web pages were constructed. I had seen some simple examples of HTML , the language of the web. I had also seen how a graphic could be incorporated into a web page. I knew some people who were writing web pages. I figured I could too.

With that background, I agreed to create what proved to be a pretty massive web site. As I worked, I learned. As I learned, I was able to understand better how the World Wide Web was put together. As I understood, I was able to incorporate more ideas into the web pages I was creating. The process was very cyclical. Each new skill led to better understanding which led to more skills, etc.

This was an extremely positive learning experience. There was always more to learn, more challenges to meet. I enjoy intellectual challenges and look forward to learning more about potential uses of the Internet and the World Wide Web. I look forward to incorporating these resources more and more into my own teaching and my own learning. I think there is vast potential and we've only scratched the surface.

Since I completed the pages for the Rational Number Project, I've created a web site for my school, Lyndale Community School. <http://www.mpls.k12.mn.us/schools/elementary/lyndale/index.html> I've included more of the multimedia aspects of the web on Lyndale's site, including rollover images, Quicktime movies, and PowerPoint slide shows. The site showcases the school and the students and informs the school community of upcoming events.

I have also created a small intranet that is only accessible within the school. I've gathered resources (web sites) that are useful and interesting to students. As I learn more, I plan to incorporate more tools for students on our intranet, such as interactive activities created by the students themselves.

The Rational Number Project web site poses an ongoing challenge. Four of the five Principal Investigators of the project are still writing and publishing. I intend to keep the web site current, adding new material as it is published. When the site migrated from the server that I maintained to the server maintained by the College of Education, I had to learn a new piece of software - Microsoft FrontPage. This is the software the college uses to both run its server, edit existing pages, and add new pages. FrontPage is new to me and I'll have to spend some time learning its nuances as I continue to maintain the Rational Number Project web pages.

I also had to learn how to manage a very large project. I worked on this project for a year and a half. Over the course of the project, I had worked with four different graduate students, and the copyright center (at the University of Minnesota). I had to keep track of all the different aspects of the project and proceed in a timely manner. I've learned a great deal about time management as well as how to best effectively incorporate the work of other people into my own work.

Creating the Rational Number Project web site was a rewarding undertaking. I'll continue to look for challenges of this nature. I know the work I do will contribute to my own learning. My hope is that it will contribute to the learning of others as well.

(return to Table of Contents)

REFERENCES

Baran, P. (1964) On distributed communications: Introduction to distributed communications network. RAND Corporation internal memorandum RM-3420-PR. http://www.rand.org/publications/RM/RM3420/

Berners-Lee, T. (2003). Tim Berners-Lee FAQ. http://www.w3.org/People/Berners-Lee/FAQ.html

Borden, M. (2000). A Brief History of the Net. Fortune, Oct 9, 2000 v142 i8 p34+.

Gillies, J. (2001). Whence the web? Was the World Wide Web an invention of the US military, or did it come out of Microsoft? The answer, perhaps surprisingly, is more scientific than that, although both defence and business had their parts to play. OECD Observer, Jan 2001 p67(4).

Lyon, M., & Hafner, K. (1996). Casting the Net. The Sciences, Sept-Oct 1996 v36 n5 p32(5).

Mueller, M. (2002). The World Wide Web and the Transformation of Internet Domain Names. Antenna, April 2001, Volume 13, No. 2

This essay is an excerpt from Ruling the Root: Internet Governance and the Taming of Cyberspace, MIT Press.

Postrel, V. (1999). Source code. Reason, May 1999 v31 i1 p4(2).

Rae-Dupree, J. (2002). Piecing together the Internet. U.S. News & World Report, April 22, 2002 p68.

Rundle, D. (1998). Internet history. History Today, Nov 1998 p14.

World Almanac and Book Of Facts. (2003). About the Internet. World Almanac and Book Of Facts. PRIMEDIA Reference Inc.

Zakon, R. (2003). Hobbes' Internet Timeline v6.0. http://www.zakon.org/robert/internet/timeline/

Zimmerman, C. (1999). The Internet Decade.(top ten events in history of internet). InternetWeek, Dec 20, 1999 p12.

(return to Table of Contents)

Appendix A

Hobbes' Internet Timeline v6.0 by Robert H'obbes' Zakon

http://www.zakon.org/robert/internet/timeline/

Hobbes' Internet Timeline Copyright (c)1993-2003 by Robert H Zakon. Permission is granted for use of this document in whole or in part for non-commercial purposes as long as this Copyright notice and a link to this document, is included. As the Timeline is frequently updated, copies to other locations on the Internet are not permitted.

1957

  • USSR launches Sputnik, first artificial earth satellite. In response, US forms the Advanced Research Projects Agency (ARPA), the following year, within the Department of Defense (DoD) to establish US lead in science and technology applicable to the military (:amk:) 1961
  • First paper on packet-switching (PS) theory

1966
  • First ARPANET plan

1967

  • First design paper on ARPANET published by Larry Roberts: "Multiple Computer Networks and Intercomputer Communication
  • National Physical Laboratory (NPL) in Middlesex, England develops NPL Data Network under Donald Watts Davies who coins the term packet. The NPL network, an experiment in packet-switching, used 768kbps lines

1968

  • Bolt Beranek and Newman, Inc. (BBN) awarded Packet Switch contract to build Interface Message Processors (IMPs)
  • Network Working Group (NWG), headed by Steve Crocker, loosely organized to develop host level protocols for communication over the ARPANET.

1969

  • ARPANET commissioned by DoD for research into networking
  • Nodes are stood up as BBN builds each IMP [Honeywell DDP-516 mini computer with 12K of memory]; AT&T provides 50kbps lines
    • Node 1: UCLA (30 August, hooked up 2 September)
    • Node 2: Stanford Research Institute (SRI) (1 October)
    • Node 3: University of California Santa Barbara (UCSB) (1 November)
    • Node 4: University of Utah (December)
  • "Host Software" by Steve Crocker (7 April)
  • First packets sent by Charley Kline at UCLA as he tried logging into SRI. The first attempt resulted in the system crashing as the letter G of LOGIN was entered. (October 29) [ Log entry ]

1970
  • ARPANET hosts start using Network Control Protocol (NCP), first host-to-host protocol
  • First cross-country link installed by AT&T between UCLA and BBN at 56kbps. This line is later replaced by another between BBN and RAND. A second line is added between MIT and Utah

1971

  • 15 nodes (23 hosts): UCLA, SRI, UCSB, Univ of Utah, BBN, MIT, RAND, SDC, Harvard, Lincoln Lab, Stanford, UIU(C), CWRU, CMU, NASA/Ames

  • Ray Tomlinson of BBN invents email program to send messages across a distributed network
  • Project Gutenberg is started by Michael Hart with the purpose of making copyright-free works, including books, electronically available. The first text is the US Declaration of Independence

1972
  • Ray Tomlinson (BBN) modifies email program for ARPANET where it becomes a quick hit. The @ sign was chosen from the punctuation keys on Tomlinson's Model 33 Teletype for its "at" meaning (March)

1973
  • First international connections to the ARPANET: University College of London (England) via NORSAR (Norway)
  • Vint Cerf and Bob Kahn publish "A Protocol for Packet Network Interconnection" which specified in detail the design of a Transmission Control Program (TCP)

1975

  • Satellite links cross two oceans (to Hawaii and UK) as the first TCP tests are run over them by Stanford, BBN, and UCLA

1978

  • TCP split into TCP and IP (March)

1981

  • BITNET, the "Because It's Time NETwork" started as a cooperative network at the City University of New York, with the first connection to Yale
    • Original acronym stood for 'There' instead of 'Time' in reference to the free NJE protocols provided with the IBM systems
    • Provides electronic mail and listserv servers to distribute information, as well as file transfers

1982

  • DCA and ARPA establish the Transmission Control Protocol (TCP) and Internet Protocol (IP), as the protocol suite, commonly known as TCP/IP, for ARPANET
    • This leads to one of the first definitions of an "internet" as a connected set of networks, specifically those using TCP/IP, and "Internet" as connected TCP/IP internets.
  • DoD declares TCP/IP suite to be standard for DoD

1983

  • Name server developed at Univ of Wisconsin, no longer requiring users to know the exact path to other systems
  • ARPANET split into ARPANET and MILNET; the latter became integrated with the Defense Data Network created the previous year. 68 of the 113 existing nodes went to MILNET
  • Desktop workstations come into being, many with Berkeley UNIX (4.2 BSD) which includes IP networking software

1984

  • Domain Name System (DNS) introduced
  • Number of hosts breaks 1,000
  • Kremvax message announcing USSR connectivity to USENET

1985

  • 100 years to the day of the last spike being driven on the cross-Canada railroad, the last Canadian university is connected to NetNorth in a one year effort to have coast-to-coast connectivity

1986

  • NSFNET created (backbone speed of 56Kbps)
  • New England gets cut off from the Net as AT&T suffers a fiber optics cable break between Newark/NJ and White Plains/NY. Yes, all seven New England ARPANET trunk lines were in the one severed cable. Outage took place between 1:11 and 12:11 EST on 12 December

1987

  • NSF signs a cooperative agreement to manage the NSFNET backbone with Merit Network, Inc. (IBM and MCI involvement was through an agreement with Merit). Merit, IBM, and MCI later founded ANS.
  • The concept and plan for a national US research and education network is proposed by Gordon Bell et al in a report to the Office of Science and Technology, written in response to a congressional request by Al Gore. (Nov) It would take four years until the establishment of this network by Congress

1988

  • 2 November - Internet worm burrows through the Net, affecting ~6,000 of the 60,000 hosts on the Internet
  • NSFNET backbone upgraded to T1 (1.544Mbps)
  • Countries connecting to NSFNET: Canada (CA), Denmark (DK), Finland (FI), France (FR), Iceland (IS), Norway (NO), Sweden (SE)

1989

  • Countries connecting to NSFNET: Australia (AU), Germany (DE), Israel (IL), Italy (IT), Japan (JP), Mexico (MX), Netherlands (NL), New Zealand (NZ), Puerto Rico (PR), United Kingdom (UK)

1990

  • ARPANET ceases to exist
  • The World comes on-line (world.std.com), becoming the first commercial provider of Internet dial-up access
  • Countries connecting to NSFNET: Argentina (AR), Austria (AT), Belgium (BE), Brazil (BR), Chile (CL), Greece (GR), India (IN), Ireland (IE), Korea (KR), Spain (ES), Switzerland (CH)

1991

  • Gopher released by Paul Lindner and Mark P. McCahill from the Univ of Minnesota
  • World-Wide Web (WWW) released by CERN; Tim Berners-Lee developer
  • NSFNET backbone upgraded to T3 (44.736Mbps)
  • Countries connecting to NSFNET: Croatia (HR), Czech Republic (CZ), Hong Kong (HK), Hungary (HU), Poland (PL), Portugal (PT), Singapore (SG), South Africa (ZA), Taiwan (TW), Tunisia (TN)

1992

  • Countries connecting to NSFNET: Antarctica (AQ), Cameroon (CM), Cyprus (CY), Ecuador (EC), Estonia (EE), Kuwait (KW), Latvia (LV), Luxembourg (LU), Malaysia (MY), Slovakia (SK), Slovenia (SI), Thailand (TH), Venezuela (VE)

1993

  • US White House comes on-line (http://www.whitehouse.gov/):
  • Worms of a new kind find their way around the Net - WWW Worms (W4), joined by Spiders, Wanderers, Crawlers, and Snakes ...
  • Businesses and media begin taking notice of the Internet
  • Mosaic takes the Internet by storm; WWW proliferates at a 341,634% annual growth rate of service traffic. Gopher's growth is 997%.
  • Countries connecting to NSFNET: Bulgaria (BG), Costa Rica (CR), Egypt (EG), Fiji (FJ), Ghana (GH), Guam (GU), Indonesia (ID), Kazakhstan (KZ), Kenya (KE), Liechtenstein (LI), Peru (PE), Romania (RO), Russian Federation (RU), Turkey (TR), Ukraine (UA), UAE (AE), US Virgin Islands (VI)

1994

  • ARPANET/Internet celebrates 25th anniversary
  • Shopping malls arrive on the Internet
  • Countries connecting to NSFNET: Algeria (DZ), Armenia (AM), Bermuda (BM), Burkina Faso (BF), China (CN), Colombia (CO), Jamaica (JM), Jordan (JO), Lebanon (LB), Lithuania (LT), Macao (MO), Morocco (MA), New Caledonia (NC), Nicaragua (NI), Niger (NE), Panama (PA), Philippines (PH), Senegal (SN), Sri Lanka (LK), Swaziland (SZ), Uruguay (UY), Uzbekistan (UZ)

1995

  • NSFNET reverts back to a research network. Main US backbone traffic now routed through interconnected network providers
  • The new NSFNET is born as NSF establishes the very high speed Backbone Network Service (vBNS) linking super-computing centers: NCAR, NCSA, SDSC, CTC, PSC
  • WWW surpasses ftp-data in March as the service with greatest traffic on NSFNet based on packet count, and in April based on byte count
  • Traditional online dial-up systems (CompuServe, America Online, Prodigy) begin to provide Internet access
  • Thousands in Minneapolis-St. Paul (USA) lose Net access after transients start a bonfire under a bridge at the Univ of MN causing fiber-optic cables to melt (30 July)
  • A number of Net related companies go public, with Netscape leading the pack with the 3rd largest ever NASDAQ IPO share value (9 August)
  • Country domains registered: Ethiopia (ET), Cote d'Ivoire (CI), Cook Islands (CK) Cayman Islands (KY), Anguilla (AI), Gibraltar (GI), Vatican (VA), Kiribati (KI), Kyrgyzstan (KG), Madagascar (MG), Mauritius (MU), Micronesia (FM), Monaco (MC), Mongolia (MN), Nepal (NP), Nigeria (NG), Western Samoa (WS), San Marino (SM), Tanzania (TZ), Tonga (TO), Uganda (UG), Vanuatu (VU)

1996

  • Internet phones catch the attention of US telecommunication companies who ask the US Congress to ban the technology (which has been around for years)
  • Various ISPs suffer extended service outages, bringing into question whether they will be able to handle the growing number of users. AOL (19 hours), Netcom (13 hours), AT&T WorldNet (28 hours - email only)
  • Restrictions on Internet use around the world:
    • China: requires users and ISPs to register with the police
    • Germany: cuts off access to some newsgroups carried on CompuServe
    • Saudi Arabia: confines Internet access to universities and hospitals
    • Singapore: requires political and religious content providers to register with the state
    • New Zealand: classifies computer disks as "publications" that can be censored and seized
    • source: Human Rights Watch
  • Country domains registered: Qatar (QA), Central frican Republic (CF), Oman (OM), Norfolk Island (NF), Tuvalu (TV), French Polynesia (PF), Syria (SY), Aruba (AW), Cambodia (KH), French Guiana (GF), Eritrea (ER), Cape Verde (CV), Burundi (BI), Benin (BJ) Bosnia-Herzegovina (BA), Andorra (AD), Guadeloupe (GP), Guernsey (GG), Isle of Man (IM), Jersey (JE), Lao (LA), Maldives (MV), Marshall Islands (MH), Mauritania (MR), Northern Mariana Islands (MP), Rwanda (RW), Togo (TG), Yemen (YE), Zaire (ZR)

1997

  • early in the morning of 17 July, human error at Network Solutions causes the DNS table for .com and .net domains to become corrupted, making millions of systems unreachable.
  • Country domains registered: Falkland Islands (FK), East Timor (TP), R of Congo (CG), Christmas Island (CX), Gambia (GM), Guinea-Bissau (GW), Haiti (HT), Iraq (IQ), Libya (LY), Malawi (MW), Martinique (MQ), Montserrat (MS), Myanmar (MM), French Reunion Island (RE), Seychelles (SC), Sierra Leone (SL), Somalia (SO), Sudan (SD), Tajikistan (TJ), Turkmenistan (TM), Turks and Caicos Islands (TC), British Virgin Islands (VG), Heard and McDonald Islands (HM), French Southern Territories (TF), British Indian Ocean Territory (IO), Svalbard and Jan Mayen Islands (SJ), St Pierre and Miquelon (PM), St Helena (SH), South Georgia/Sandwich Islands (GS), Sao Tome and Principe (ST), Ascension Island (AC), US Minor Outlying Islands (UM), Mayotte (YT), Wallis and Futuna Islands (WF), Tokelau Islands (TK), Chad Republic (TD), Afghanistan (AF), Cocos Island (CC), Bouvet Island (BV), Liberia (LR), American Samoa (AS), Niue (NU), Equatorial New Guinea (GQ), Bhutan (BT), Pitcairn Island (PN), Palau (PW), DR of Congo (CD)

1998

  • Hobbes' Internet Timeline is released
  • Country domains registered: Nauru (NR), Comoros (KM)

1999

  • Internet access becomes available to the Saudi Arabian (.sa) public in January
  • DoD issues a memo requiring all US military systems to connect via NIPRNET, and not directly to the Internet by 15 Dec 1999 (22 Aug)
  • Somalia gets its first ISP - Olympic Computer (Sep)
  • .ps is registered to Palestine (11 Oct)

2000

  • The US timekeeper (USNO) and a few other time services around the world report the new year as 19100 on 1 Jan
  • A massive denial of service attack is launched against major web sites, including Yahoo, Amazon, and eBay in early February

2001

  • High schools in five states (Michigan, Missouri, Oregon, Virginia, and Washington) become the first to gain Internet2 access

2002

  • A distributed denial of service (DDoS) attack struck the 13 DNS root servers knocking out all but 5 (21-23 Oct). Amidst national security concerns, VeriSign hastens a planned relocation of one of its two DNS root servers

2003

  • The first official Swiss online election takes place in Anières (7 Jan)
  • The SQL Slammer worm causes one of the largest and fastest spreading DDoS attacks ever. Taking roughly 10 minutes to spread worldwide, the worm took down 5 of the 13 DNS root servers along with tens of thousands of other servers, and impacted a multitude of systems ranging from (bank) ATM systems to air traffic control to emergency (911) systems (25 Jan)

     

Hobbes' Internet Timeline FAQ

1. How do I get Hobbes' Internet Timeline?

The Timeline is archived at http://www.zakon.org/robert/internet/timeline/. Should you only have email access, you can learn how to request this document and access the rest of the Internet by sending an email to one of the following addresses. mail-server@rtfm.mit.edu (Americas) with the following line in the body of the message: send usenet/news.answers/internet-services/access-via-email mailbase@mailbase.ac.uk (elsewhere) with the following line in the body of the message: send lis-iis e-access-inet.txt

2. Is the Timeline available in other languages or editions?

Chinese (Big5) by Tony Mao
Chinese (GB) by Guo Li
French by Didier Mainguy
German by Michael Kaul
Italian by Ivo Aceto
Japanese by Katsunori Tanaka (RFC/FYI translation)
Persian (PDF) by Rahi Moosavi
Portuguese by Simone Villas Boas
Spanish by Pablo Ibarrolaza & Monica Piazza

If you are interested in translating to another language or format, email me first

3. Can I re-print the Timeline or use parts of it for ... ?

Drop me an email. The answer is most likely (though don't assume) 'yes' for non-profit use, and 'maybe' for for-profit; but to be sure you are not going to break any copyright laws, drop me an email and wait for a reply. Also, please note that I get a bunch of requests with improperly formatted return email addresses. If you don't hear from me in a week (typical turn around is < 1 hour), check your header and email again. BTW, don't forget to tell me who you are and your affiliation; anonymous requests will not be answered.

(return to Table of Contents)

Appendix B

Internet Hosts
(return to Table of Contents)

Appendix C

Internet Networks

(return to Table of Contents)
Appendix D
Complete Bibliography of the Rational Number Project (as of November 3, 2003)

2003

Cramer, K. (2003) Using a translation model for curriculum development and classroom instruction. In Lesh, R., Doerr, H. (Eds.) Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching. Lawrence Erlbaum Associates, Mahwah, New Jersey.

Lesh, R., Cramer, K., Doerr, H., Post, T., Zawojewski, J., (2003) Model Development Sequences. In Lesh, R., Doerr, H. (Eds.) Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching. Lawrence Erlbaum Associates, Mahwah, New Jersey.

Cramer, Kathleen (2003). Mathematics for Elementary and Middle School Teachers: Functions and Proportionality Course. Unpublished curriculum.
 

2002

Cramer, K. A, Post, T. R., del Mas, R. C. (2002) Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula With the Effects of Using the Rational Number Project Curriculum. Journal for Research in Mathematics Education. 33 (2) 111-144.

Cramer, K., Henry, A., (2002) Using Manipulative Models to Build Number Sense for Addition of Fractions. National Council of Teachers of Mathematics 2002 Yearbook: Making Sense of Fractions, Ratios, and Proportions (pp. 41-48). Reston, VA: National Council of Teachers of Mathematics.
 

2001

Cramer, K., (2001) Using Models to Build Middle-Grade Students' Understanding of Functions. Mathematics Teaching in the Middle School. 6 (5), 310-318.
 

2000

Lesh, R., Kelly, A., (2000) Multitiered Teaching Experiments. In A. Kelly, R. Lesh (Eds.), Research Design in Mathematics and Science Education. (pp. 197-230). Lawrence Erlbaum Associates, Mahwah, New Jersey.

Lesh, R., Hoover, M., Hole, B., Kelly, A., Post, T., (2000) Principles for Developing Thought-Revealing Activities for Students and Teachers. In A. Kelly, R. Lesh (Eds.), Research Design in Mathematics and Science Education. (pp. 591-646). Lawrence Erlbaum Associates, Mahwah, New Jersey.
 

1998

Post, T., Cramer, K., Harel, G., Kiernen, T., & Lesh, R. (1998) Research on rational number, ratio and proportionality. Proceedings of the Twentieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, PME-NA XX Volume I (pp. 89-93). Raleigh, North Carolina.
 

1997

Behr, M., Khoury, H., Harel, G., Post, T., Lesh, R., (1997) Conceptual Units Analysis of Preservice Elementary School Teachers' Strategies on a Rational-Number-as-Operator Task. Journal of Mathematics Education, 28(1), 48-69.

Cramer, K., Behr, M., Post T., Lesh, R., ( 1997) Rational Number Project: Fraction Lessons for the Middle Grades - Level 1, Kendall/Hunt Publishing Co., Dubuque Iowa.

Cramer, K., Behr, M., Post T., Lesh, R., ( 1997) Rational Number Project: Fraction Lessons for the Middle Grades - Level 2, Kendall/Hunt Publishing Co., Dubuque Iowa.
 

1995

Cramer, K., & Post, T. (1995). Facilitating children's development of rational number knowledge. In D. Owens, M. Reed, and G. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of PME-NA. (pp. 377-382). Columbus, OH: PME.

Harel, G., & Behr, M. (1995). Teachers' solutions for multiplicative problems. Hiroshima Journal of Mathematics Education, 3, 31-51.

Orton, R., Post, T., Behr, M., Cramer, K., Harel, G., & Lesh, R. (1995). Logical and psychological aspects of rational number pedagogical reasoning. Hiroshima Journal of Mathematics Education, 3, 63-75.

Titus, J. (1995). The concept of fractional number among deaf and hard of hearing students. American Annals of the Deaf, 140(3), 255-263.
 

1994

Bart, W., Post, T., Behr, M., Lesh, R. (1994). A diagnostic analysis of a proportional reasoning test item: An introduction to the properties of a semi-dense item. Focus on Learning Problems in Mathematics, 16(3), 1-11.

Behr, M., Harel, G., Post, T., & Lesh, R. (1994). Units of quantity: A conceptual basis common to additive and multiplicative structures. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 123-180). Albany, NY: SUNY Press.

Harel, G., Behr, M., Post, T., & Lesh, R. (1994). The impact of number type on the solution of multiplication and division problems: Further considerations. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 365-388). Albany, NY: SUNY Press.

Harel, G., Behr, M., Post, T. & Lesh, R. (1994). Invariance of ratio: The case of children's anticipatory scheme of constancy of taste. Journal for Research in Mathematics Education, 25(4), 324-345.

Heller, P., Post, T., Behr, M., & Lesh, R. (unpublished). The effect of two context variables on qualitative and numerical reasoning about rates.

 

1993

Behr, M., Harel, G., Post, T., & Lesh, R. (1993). Rational Numbers: Toward a Semantic Analysis - Emphasis on the Operator Construct. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational Numbers: An Integration of Research (pp. 13-47). Hillsdale, NJ: Lawrence Erlbaum Associates.

Cramer, K. & Post, T. (1993, May). Connecting Research To Teaching Proportional Reasoning. Mathematics Teacher, 86(5), 404-407.

Cramer, K. & Post, T. (1993, February). Making connections: A Case for Proportionality. Arithmetic Teacher, 60(6), 342-346.

Cramer, K., Post, T., & Currier, S. (1993). Learning and Teaching Ratio and Proportion: Research Implications. In D. Owens (Ed.), Research Ideas For the Classroom (pp. 159-178). NY: Macmillan Publishing Company.

Post, T., Cramer, K., Behr, M., Lesh, R., & Harel, G. (1993). Curriculum implications of Research on the Learning, Teaching, and Assessing of Rational Number Concepts. In T. Carpenter, E. F& Harel, G. (In press). Designing instructionally relevant assessment reports. In T. Carpenter & E. Fennema (Eds.), Research on the Learning, Teaching, and Assessing of Rational Number Concepts. Lawrence Erlbaum and Associates.

 

1992

Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296-333). NY: Macmillan Publishing.

Behr, M. & Post, T. (1992). Teaching rational number and decimal concepts. In T. Post (Ed.), Teaching mathematics in grades K-8: Research-based methods (2nd ed.) (pp. 201-248). Boston: Allyn and Bacon.

Harel, G., Behr, M., Post, T., & Lesh, R. (1992). The Blocks Task: Comparative Analyses of the Task With Other Proportion Tasks and Qualitative Reasoning Skills of Seventh Grade Children in Solving the Task. Cognition and Instruction, 9(1), 45-96.

Lesh, R. & Lamon, S. (1992). Introduction: Trends, Goals, and Priorities in Mathematics Assessment. In R. Lesh & S. Lamon (Eds.), Assessments of Authentic Performance in School Mathematics (pp. 3-16). Washington, DC: American Association for the Advancement of Sciences Press.

Lesh, R. & Lamon, S. (1992) Assessing Authentic Mathematical Performance. In R. Lesh & S. Lamon (Eds.), Assessments of Authentic Performance in School Mathematics (pp. 17-62). Washington, DC: American Association for the Advancement of Sciences Press.

Lesh, R., Lamon, S., Gong, B. & Post, T. (1992) Using Learning Progress Maps to Improve Educational Decision Making. In R. Lesh & S. Lamon (Eds.), Assessments of Authentic Performance in School Mathematics (pp. 343-375 ). Washington, DC: American Association for the Advancement of Sciences Press.

Lesh, R., Lamon, S., Lester, F. & Behr, M. (1992) Future Directions for Mathematics Assessment. In R. Lesh & S. Lamon (Eds.), Assessments of Authentic Performance in School Mathematics (pp. 379-425). Washington, DC: American Association for the Advancement of Sciences Press.

Lesh, R., Hoover, M. & Kelly, A. (1992). Equity, Technology, and Teacher Development. In I. Wirszup & R. Streit (Eds.), Developments in School Mathematics Education Around the World: Volume 3 (pp. ). Reston, VA: National Council of Teachers of Mathematics.

 

1991

Behr, M., Harel, G., Post, T. & Lesh, R. (1991). The Operator Construct of Rational Number. In F. Furinghetti (Ed.) Proceedings of PME XV Conference (pp. 120-127). Assisi, Italy: PME.

Harel, G., Behr, M., Post, T. & Lesh, R. (1991). Variables Affecting Proportionality: Understanding of Physical Principles, Formation of Quantitative Relations, and Multiplicative Invariance. In F. Furinghetti (Ed.) Proceedings of PME XV Conference (pp. 125-133). Assisi, Italy: PME.

Post, T., Harel, G., Behr, M. & Lesh, R. (1991). Intermediate Teachers' Knowledge of Rational Number Concepts. In E. Fennema, T. Carpenter, S. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 177-198). NY: State University of NY Press.

 

1990

Behr, M. & Harel, G. (1990). Understanding the Multiplicative Structure. In G. Booker, P. Cobb, & T.N. de Merldicutti (Eds.) Proceedings of the PME XIV Conference Volume III (pp. 27-34). Mexico: Consejo Nacional de Ciencia y Technologia, Gobierno del Estado de Morelos.

Harel, G. & Behr, M. (1990). The Construct Theory of Rational Numbers: Toward a Semantic Analysis. In G. Booker, P. Cobb, & T.N. de Merldicutti (Eds.) Proceedings of the PME XIV Conference (pp. 3-10). Mexico: Consejo Nacional de Ciencia y Technologia, Gobierno del Estado de Morelos.

Heller, P., Post, T., Behr, M., & Lesh, R. (1990). Qualitative and Numerical Reasoning About Fractions and Rates by Seventh and Eighth Grade Students. Journal for Research in Mathematics Education, 21(5), 388-402.

 

1989

Bezuk, N., & Cramer, K. (1989). Teaching About Fractions: What, When, and How? In P. Trafton (Ed.), National Council of Teachers of Mathematics 1989 Yearbook: New Directions For Elementary School Mathematics (pp. 156-167). Reston, VA: National Council of Teachers of Mathematics.

Cramer, K., Post, T., & Behr, M. (1989, January). Cognitive Restructuring Ability, Teacher Guidance and Perceptual Distracter Tasks: An Aptitude Treatment Interaction Study. Journal for Research in Mathematics Education, 20(1), 103-110.

Cramer, K., Post, T., & Behr, M. (1989, September). Interpreting Proportional Relationships. Mathematics Teacher, 82 (6), 445-452.

Cramer, K., Behr, M., & Bezuk, N. (1989, October). Proportional Relationships and Unit Rates. Mathematics Teacher, 82 (7), 537-544.

Harel, G., & Behr, M. (1989). Structure and Hierarchy of Missing Value Proportion Problems and Their Representations. Journal of Mathematical Behavior, 8(1), 77-119.

Heller, P., Ahlgren, A., Post, T., Behr, M., & Lesh, R. (1989, March). Proportional Reasoning: The Effect of Two Context Variables, Rate Type and Problem Setting. Journal for Research in Science Teaching, 26(1), 205-220.

Post, T. (1989, September). One Point of View - Fractions and Other Rational Numbers. Arithmetic Teacher, 37(1), 3-28.

Post, T., & Cramer, K. (1989, March). Knowledge, Representation and Quantitative Thinking. In M. Reynolds (Ed.) Knowledge Base for the Beginning Teacher - Special publication of the AACTE (pp. 221-231). Oxford: Pergamon Press.

 

1988

Behr, M., & Post, T. (1988). Teaching Rational Number and Decimal Concepts. In T. Post, (Ed.), Teaching Mathematics in Grades K-8: Research Based Methods (pp. 190-231). Newton, MA: Allyn & Bacon, Inc.

Behr, M., Wachsmuth, I., & Post, T. (1988). Rational Number Learning Aids: Transfer From Continuous Models To Discrete Models. Focus on Learning Problems in Mathematics, 10(4), 1-17.

Bright, G., Behr, M., Post, T., & Wachsmuth, I. (1988, May). Identifying fractions on number lines. Journal for Research in Mathematics Education., 19(3), 215-232.

Conner, G., Harel, G., & Behr, M. (1988). The effect of structural variables on the level of difficulty of missing value proportion problems. In M. Behr, C. Lacampagne, & M. Wheeler (Eds.), Proceedings of the Ninth Annual Conference of PME-NA (pp. 65-71). DeKalb, IL: PME.

Harel, G., Post, T., & Behr, M. (1988). An assessment instrument to examine knowledge of multiplication and division concepts and its implementation with in-service teachers. In M. Behr, C. Lacampagne, & M. Wheeler (Eds.), Proceedings of the Ninth Annual Conference of PME-NA (pp. 411-417). DeKalb, IL: PME.

Harel, G., Post, T., & Behr, M. (1988, July). On the textual and semantic structures of mapping rule and multiplicative compare problems. In A. Borbas (Ed.) Proceedings of the XII International Congress, Psychology of Mathematics Education (PME) Volume II (pp. 372-379). Budapest: PME.

Lacampagne, C., Post, T., Harel, G., Behr, M. (1988, November). A model for the development of leadership and the assessment of mathematical and pedagogical knowledge of middle school teachers. In M. Behr, C. Lacampagne, & M. Wheeler (Eds.), Proceedings of the Ninth Annual conference of PME-NA (pp. 418-425). DeKalb, IL: PME.

Lesh, R., Post, T., & Behr, M. (1988). Proportional Reasoning. In J. Hiebert & M. Behr (Eds.) Number Concepts and Operations in the Middle Grades (pp. 93-118). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics.

Post, T. (1988). Some notes on the nature of mathematics learning. In T. Post (Ed.), Teaching Mathematics in Grades K-8: Research Based Methods (pp. 1-19). Boston: Allyn & Bacon.

Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of pre-algebra understandings. In A. Coxford & A. Shulte (Eds.) The Idea of Algebra K-12: Yearbook National Council of Teachers of Mathematics (pp. 78-90). Reston, VA: NCTM.

Post, T., Harel, G., Behr, M., & Lesh, R. (1988). Intermediate teachers knowledge of rational number concepts. In Fennema, et al. (Eds.), Papers from First Wisconsin Symposium for Research on Teaching and Learning Mathematics (pp. 194-219). Madison, WI: Wisconsin Center for Education Research.

Reiss, M., Behr, M., Lesh, R., & Post, T. (1988, July) The assessment of cognitive structures in proportional reasoning. In J. Bergeron, et al. (Eds.), Proceedings of the Eleventh International Conference, Psychology of Mathematics Education PMR - XI Volume II (pp. 310-316). Montreal, Canada: PME.

Cramer, K. & Lesh, R. (1988). Rational number knowledge of preservice elementary education teachers. In M. Behr (Ed.), Proceedings of the 10th Annual Meeting of the North American Chapter of the International Group for Psychology of Mathematics Education (pp. 425-431). DeKalb, Il.: PME.
 

1987

Behr, M., Harel, G., Post, T., & Lesh, R. (1987). Theoretical analysis: Structure and hierarchy, missing value proportion problems. In J. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the Eleventh International Conference, Psychology of Mathematics Education PMR - XI Volume II (pp. 269-274). Montreal, Canada: PME.

Harel, G., Behr, M., Post, T., & Lesh, R. (1987). Qualitative differences among seventh grade children in solving a non numerical proportional reasoning blocks task. In J. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the Eleventh International Conference, Psychology of Mathematics Education PMR - XI Volume II (pp. 282-288). Montreal, Canada: PME.

Lesh, R., Behr, M., & Post, T. (1987). Rational Number Relations and Proportions. In C. Janiver (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 41-58). Hillsdale, NJ: Lawrence Erlbaum.

Lesh, R., Post, T., & Behr, M. (1987). Dienes revisited: Multiple embodiments in computer environments. In I. Wirsup & R. Streit (Eds.), Development in School Mathematics Education Around the World (pp. 647-680). Reston, VA: National Council of Teachers of Mathematics.

Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving. In C. Janvier, (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum.

Post, T., & Cramer, K. (1987, October). Children's strategies when ordering rational numbers. Arithmetic Teacher, 35(2), 33-35.

 

1986

Behr, M., & Post, T. (1986). Estimation and Children's Concept of Rational Number Size. In H. Schoen & M. Zweng (Eds.) Estimation and Mental Computation: 1986 NCTM Yearbook (pp. 103-111). Reston, VA: National Council of Teachers of Mathematics.

Behr, M., Reiss, M., Harel, G., Post, T., & Lesh, R. (1986, July). Qualitative Proportional Reasoning: Description of Tasks and Development of Cognitive Structures. In Proceedings of the Tenth International Conference for the Psychology of Mathematics Education (PME-10) (pp. 235-240). London, England.

Post, T., Behr, M., & Lesh, R. (1986). Research-Based Observations About Children's Learning of Rational Number Concepts. Focus on Learning Problems in Mathematics, 8(1), 39-48.

Post, T., Behr, M., Lesh, R., Wachsmuth, I. (1986, Spring). Selected Results from the Rational Number Project. In Proceedings of Ninth Psychology of Mathematics Education Conference the Netherlands (pp. 342-351). International Group for the Psychology of Mathematics Education, ANTWERP The Netherlands. This paper was reprinted in The Math Times Journal-Official Journal of the Minnesota Council of Teachers of Mathematics, Vol. 1, No. 1.

Wachsmuth, I., Bright, G., Behr, M., & Post, T. (1986). Assessing fifth grade children's rational number knowledge in a non verbal application context: The darts game. Recherches en Didactique des Mathematiques., 7(3), 51-74.

 

1985

Behr, M., Wachsmuth, I., & Post, T. (1985, March). Construct a Sum: A Measure of Children's Understanding of Fraction Size. Journal for Research in Mathematics Education, 16(2), 120-131. A condensed earlier version appeared as On Children's Quantitative Concept of Rational Number: Construct and Estimate the Sum. In J. Bergeron & N. Herscovics (Eds.), Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education Volume II (pp. 272-79). Montreal, Canada: September 1983.

Heller , P., Post, T., & Behr, M. (1985, October). The Effect of Rate Type, Problem Setting and Rational Number Achievement on Seventh Grade Students Performance on Qualitative and Numerical Proportional Reasoning problems. In S. Damarin & M. Shelton (Eds.), Proceedings of the seventh General Meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 113-122). Columbus, Ohio: PME.

Post T., Wachsmuth I., Lesh R., & Behr M. (1985, January). Order and Equivalence of Rational Number: A Cognitive Analysis. Journal for Research in Mathematics Education, 16(1), 18-36.

Reiss, M., Behr, M., Lesh, R., & Post, T. (1985, July). Cognitive Processes And Products in Proportional Reasoning. In L. Streefland (Ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education (pp. 352-356). Noordwijkerhout (Utrecht), Holland: PME.
 

1984

Behr, M., Wachsmuth, I., & Post, T. (1984, August). Tasks to Assess Children's Perception of the Size of a Fraction. In A. Bell, B. Low & J. Kilpatrick (Eds.), Theory, Research and Practice in Mathematical Education (pp. 179-18). Fifth International Congress on Mathematical Education, South Australia: Shell Centre for Mathematics Education.

Behr, M., Wachsmuth, I., Post T., & Lesh R. (1984, November). Order and Equivalence of Rational Numbers: A Clinical Teaching Experiment. Journal for Research in Mathematics Education, 15(5), 323-341.

 

1983

Behr, M., Lesh, R., Post, T., & Silver E. (1983). Rational Number Concepts. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91-125). New York: Academic Press.

Lesh, R., Landau, M. & Hamilton, E. (1983). Conceptual models in applied mathematical problem solving research. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts & Processes (pp. 263-343). NY: Academic Press.

Wachsmuth I., Behr M., & Post T. (1983, July). Children's perception of fractions and ratios in grade 5. In R. Hershkowitz (Ed.), Proceedings of the International Group for the Psychology of Mathematics Education VII (pp. 164-169). Rehovot, Israel: Department of Science Teaching, The Weizmann Institute of Science.

 

1982

Post, T., Behr, M., & Lesh, R. (1982, April). Interpretations of Rational Number Concepts. In L. Silvey & J. Smart (Eds.), Mathematics for Grades 5-9, 1982 NCTM Yearbook (pp. 59-72). Reston, Virginia: NCTM.

 

1981

Behr, M., & Post, T. (1981). The Effect of Visual Perceptual Distractors on Children's Logical-Mathematical Thinking in Rational Number Situations. In T. Post & M. Roberts (Eds.), Proceedings of the Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 8-16). Minneapolis: University of Minnesota.

Behr, M., Post, T., & Lesh R. (1981, July). Construct Analyses, Manipulative Aids, Representational Systems and the Learning of Rational Numbers. In Proceedings of the Fifth Conference of the International Group for the Psychology of Mathematics Education. (pp. 203-209). Grenoble, France: PME.

Post, T. (1981, May). Fractions: Results and Implications from National Assessment. The Arithmetic Teacher, 28(9), 26-31.

Post, T. (1981). The Role of Manipulative Materials in the Learning of Mathematical Concepts. In Selected Issues in Mathematics Education (pp. 109-131). Berkeley, CA: National Society for the Study of Education and National Council of Teachers of Mathematics, McCutchan Publishing Corporation.

 

1980

Behr, M., Post, T., Silver, E., & Mierkiewicz, D. (1980, August). Theoretical Foundations for Instructional Research on Rational Numbers. In R. Karplus (Ed.) Proceedings of Fourth Annual Conference of International Group for Psychology of Mathematics Education (pp. 60-67). Berkeley, CA: Lawrence Hall of Science.

 

1979

Post, T. (1979). Making Time for the Basics: Some Thoughts on Viable Alternatives Within a Balanced Mathematics Program. In S. Sharron & R. Reys (Eds.), Applications in School Mathematics, 1979 Yearbook (pp. 352-356). Reston, VA: National Council of Teachers of Mathematics.

Post, T., & Reys, R. E. (1979). Abstraction Generalization and Design of Mathematical Experiences for Children. In K. Fuson & W. Geeslin (Eds.), Models for mathematics learning. (pp. 117-139). Columbus, OH: ERIC/SMEAC.

 

 
(return to Table of Contents)
Appendix E
 
Progress checklist
Status
Copyright
status
Web
name
  

Ready
For
Web

OK

92_7
book
chapter
w/3 above

Lesh, R., Lamon, S., Gong, B. & Post, T. (1992) Using Learning Progress Maps to Improve Educational Decision Making. In R. Lesh & S. Lamon (Eds.), Assessments of Authentic Performance in School Mathematics (pp. 343-375 ). Washington, DC: American Association for the Advancement of Sciences Press.

Ready
For
Web

OK

92_8
book
chapter

Lesh, R., Lamon, S., Lester, F. & Behr, M. (1992) Future Directions for Mathematics Assessment. In R. Lesh & S. Lamon (Eds.), Assessments of Authentic Performance in School Mathematics (pp. 379-425). Washington, DC: American Association for the Advancement of Sciences Press.

Word
File

OK

92_9
book
chapter

Lesh, R., Hoover, M. & Kelly, A. (1992). Equity, Technology, and Teacher Development. In I. Wirszup & R. Streit (Eds.), Developments in School Mathematics Education Around the World: Volume 3 (pp. ). Reston, VA: National Council of Teachers of Mathematics.

Word
File

DENIED

91_4
book
chapter
same as
88_11

Post, T., Harel, G., Behr, M. & Lesh, R. (1991). Intermediate Teachers’ Knowledge of Rational Number Concepts. In E. Fennema, T. Carpenter, S. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 177-198). NY: State University of NY Press.

Paper
File

OK

89_5

Harel, G., & Behr, M. (1989). Structure and Hierarchy of Missing Value Proportion Problems and Their Representations. Journal of Mathematical Behavior, 8(1), 77-119.

Word
file

DENIED

88_11
book
chapter
same as 91_4

Post, T., Harel, G., Behr, M., & Lesh, R. (1988). Intermediate teachers knowledge of rational number concepts in integrating research on teaching and learning mathematics. In Fennema, et al. (Eds.), Papers from First Wisconsin Symposium for Research on Teaching and Learning Mathematics (pp. 194-219). Madison, WI: Wisconsin Center for Education Research.

Word
File

OK

87_3
book
chapter
w/87_5

Lesh, R., Behr, M., & Post, T. (1987). Rational Number Relations and Proportions. In C. Janiver (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 41-58). Hillsdale, NJ: Lawrence Erlbaum.
(return to Table of Contents)
Appendix F
Web in progress folder
 
Appendix G
Root folder
(return to Table of Contents)
 
 
(top)