**Http://jwilson.coe.uga.edu**
contains several examples of web development I have implemented
in the area of mathematics education, in particular for courses
for inservice and preservice mathematics teachers. These include
use of the Web Page for

Implementing courses that I teach at the University of Georgia:

**EMAT 4680/6680**
Technology and Secondary School Mathematics,

**EMAT 4690/6690** Technology
Enhanced Instruction in Secondary School Mathematics,

**EMAT 4700/6700**
Advanced Explorations with Technology in Mathematics Instruction,

**EMAT 6990** Masters
Seminar in Mathematics Education

**EMAT 6000** Special
Problems in Mathematics Education

**EMAT 8990** Doctoral
Seminars in Mathematics Education.

**EMAT 4600/6600**
Problem Solving in Mathematics.

**MATH 7200** Fundamentals of Geometry I

**MATH 7210** Fundamentals of Geometry II

Making available papers I have written(e.g. seePapers),

Making available material from my students(e.g.Samples),

Implementing projects

Making available personal informationResume

Post-Tenure Review File

Graduate Faculty Application File

Photo Albums

I have developed the EMAT 4680/6680, EMAT 4690/6690, and EMAT 4700/6700 around extensive use of technology tools for mathematics exploration, learning, and teaching. Thus technology in these courses is an integral part of the discipline of mathematics learning and teaching. The technology impacts on what mathematics is learned, how it is learned, and helps the mathematics teachers in these courses adapt to mathematics education reform.

On the other hand, technology changes the delivery of mathematics education instruction. It has transformed the ways I interact with students about their explorations. It has made resources readily available on the Internet. For example, students quickly learn to bookmark the MacTutor Web Site at St. Andrews (Scotland) for ready access to mathematics history by topic or person.

Most important, in my view, when the students create web presentations of their write-ups, essays, instructional units, or papers and implement these with HTML editors, there is a qualitatively different nature to what they learn and understand. Creating web documents and maintaining files is a challenge. I have implemented these with a minimal use of templates because I find that templates often get in the way of learning the ropes. My web site emphasizes simplicity and functionality and that carries over to the web productions of the students. We want graphics when they serve a purpose. Glitz and frames can be saved to the next level of sophistication.

I have also incorporated technology tools into the EMAT 4600/6600 Mathematics Problem Solving course. The collections of problems in EMAT 6600 are presented on the Web Site to always be available to students and to take advantage of the hypertext format to link to hints, solutions, other problems, or applications.

The Web Site has extended my impact to mathematics education beyond my classes. The site receives extensive contact from throughout the world. My site is linked by other major sites such as the Math Forum, which adds to the number of contacts received.

**EMAT 4680/6680, EMAT 4690/6690, EMAT
4700/6700, and Project InterMath**

The underlying psychological theme in
these courses is the use of **visual** **reasoning** in
mathematical discourse. The technology tools are essential to
enabling students to construct visual and symbolic representation
of ideas and to incorporate these into their approaches and thinking
about problems. The visualizations produced with the aid of technology
are not the end product but rather a means to facilitate student's
mental images that help them form, relate, and organize mathematical
concepts.

There are several pedagogical and curricular features to these courses that are worth noting. First, the courses are an implementation of the NCTM Standards in teaching field and teacher education courses. Second, they implement cooperative learning. Third, they implement portfolio assessment. The student productions (write-ups, essays, instructional units, and problem solutions) represent the students' choice of "best work" in these courses. Fourth, they underscore the contrast of demonstration and proof and an understanding of the need for both in mathematics instruction. Fifth, they capitalize on the use of animation. Sixth, they respond to the use of technology.

The course, EMAT 4680/6680 Technology in Secondary School Mathematics is required of all mathematics education undergraduate students (4680) and is available as a teaching field elective for graduate students (6680). The course serves dual roles of presenting technology as an integral part of the substance of mathematics and of demonstrating to preservice and inservice mathematics teachers ways that technology can be used in instruction. Courses on instructional computing are required for mathematics certification grade 7-12 in Georgia.

EMAT 4680/6680 presents students with mathematics problems, open-ended mathematics investigations, challenges to organize and communicate information from these investigations, and some technology tools to accomplish such tasks. The mathematics content is at the level of the secondary school curriculum -- but not necessarily from present secondary school mathematics curriculum. These include relations and their graphs, functions and their graphs, demonstration and proof, measurement, geometry of the plane, locus problems, conics, sequences, limits, polar equations, parametric equations, and three dimensional surfaces.

EMAT 4690/6690 extends the work with technology in mathematics instruction in two directions. The students produce instructional units incorporating the use of technology in their present or future mathematics classes (some have an opportunity to use the units in their classes). Second, the students develop depth of inquiry in mathematics explorations of their own choice and communicate these via the essays in HTML format on my server.

EMAT 4700/6700 is organized around the development of a single major problem defined by the student, carried forward, and developed in an HTML presentation.

Project InterMath is a five-year project funded by the National Science Foundation to developed the model from the EMAT 6680 and EMAT 6690 to materials for middle school mathematics teachers. It is a Web Based program to introduce middle school mathematics teachers to using technology tools in their mathematics classes (such as calculators, graphing programs, spreadsheets, and Geometer's SketchPad), and, to provide the teachers generative tools that will allow them to improve their own knowledge of mathematics.

**I am a Hybrid!!**

I am not hip to the language of distance education but I was told that I was a hybrid (or was it my courses?). Anyway, there is a combination of classroom instruction, use of e-mail, web access, and independent study. In the EMAT 6680 (the first course for most of these students), meeting in the laboratory is essential. Working through all of the pitfalls of learning to use the software, learning to manage files, and learning to create HTML documents with the mathematics symbols and graphics is best done in the laboratory with an instructor immediately there to help. As students become more technology literate before taking this course, we are moving toward delivery of the instruction via electronic media to the school work site and concentrating more on the mathematical explorations with teachers and students.

In the EMAT 6690, however, student situations can vary but a high percentage of the work can be done reasonably in the student's home site.

Project InterMath is designed around 45 hours of instruction in a laboratory and 55 hours of inquiry by the student from their home site. The laboratory instructions will be done around the state at InTech centers and the Web Site will be managed by our collaborators at Georgia Institute of Technology. The Web site will house the course materials for the 45 hour segment, the student productions (write-ups and instructional units) and resource materials.

**EMAT 4600/6600 Mathematics Problem Solving**

The course on mathematical problem solving has been taught in our department since 1969. Some wags might accuse me of using the same problems now that I did in 1969!!! The technology and the web site make even those old problems have new life, and, there are many new problems. Topics like iteration to solve equations such as

Rø = 2641 and R sin ø = 2640

are now appropriate and readily available to the secondary school. (These equations arise in finding the distance from a chord of a circle to its corresponding arc when the chord is 5280 feet and the arc is 5282 feet).

There is an extensive set of problems on this Web Site and I add more on a regular basis. This course has been offered to well prepared students via the web access and e-mail communication.

The course syllabus places the development of a teaching resource as the structure for student work. Preparing this teaching resource in HTML format is an option for students who have those skills.

**The Technology**

As this class is currently taught, we meet in a computer enhanced classroom with student workstations arranged around the rim of the room and tables in the center. There is a teacher workstation with a Chisholm through the lens projector. This laboratory is in the Mathematics Education zone of the campus Ethernet and thus all computers have T1 access to the Internet. The software tools include graphing programs (such as Graphing Calculator 2.3, X-Function, Maple, or MatLab) dynamic geometry programs (such as Geometer's Sketchpad, Cabri, or Geometric Supposer), Spreadsheets (such as Excel or ClarisWorks), three dimensional surface graphers (such as Graphing Calculator 2.3), word-processing tools (Microsoft Word), paint and draw programs (such as MacPaint or Superpaint), utility programs such as Simpletext, Information Access tools (such as Netscape, Internet Explorer, Eudora, and CU-SeeMe), and HTML editors (such as Adobe PageMill 3.0, word or ClarisWorks).

The EMAT 4680/6680 is organized with sets of open-ended problems
grouped into 13 **Assignments. **Perhaps a better phrase would
be "Study Guides." The course information, syllabus,
and assignments are implemented on a Web Site, **The EMT 468/668
Home Page**, at **http://jwilson.coe.uga.edu/EMT668.html**.
The students can access the Web site from where ever they have
Internet access -- in the classroom, at home, elsewhere on campus,
or totally away from Athens. I began this course with the vision
of a time when in-service mathematics teachers would have access
to the Internet from their classrooms. We are closer now than
in 1995 but still have a ways to go. I have found my inservice
teachers have Internet accesss at home before they have it at
their school or in their classroom.

Each student has an e-mail account. I maintain my own file server using WebStar 4.2. Each student has a folder on the server. Any work they want to submit, formally or informally, is transferred to that folder via the Ethernet. If they are off campus they can have FTP access to the server. Alternatively, if they are off campus and have only e-mail access, they can submit work via e-mail with an attached file. Work for this folder, depending on the assignment and the circumstances, may be submitted with nearly any of the applications used in the course.

Students may work in groups of two or three. They decide. Write-ups
that are jointly prepared are so labeled and placed in the folder
of each student. **Write-ups** are presentations of student
explorations, synthesis, and communication that are submitted
for grade in the course. There are five write-ups required. **Final
Projects **are submitted and discussed on the scheduled date
of the final examination but the projects are worked on for up
to three weeks prior to the due date.

As the instructor, I present demonstrations and explanations, clarify problems, and answer inquiries using the teacher workstation. A typical class session might have about one-third of the time in this whole-group mode. The balance of the time is with students working on the computers, either individually or in groups. The students are alerted that they will need computer time beyond what we have in class and most of them are resourceful in locating such access -- after hours, in other labs, or at home.

**The Frayed Shoestring**

The topic for this panel is the development of the web-based courses on a shoestring. I will make a few points about my journey.

First, I have been a mathematics teacher and mathematics educator for since 1958. I worked as a computer programmer in the 1960s and I have the followed the ebb and flow of various technologies and mathematics teaching over the years. Through it all my interest remains first and foremost in the mathematics and mathematics teaching. (45 minute lecture suppressed here).

Second, there was a time when writing computer programs code to solve some mathematics problems was an interest. There is little of that now. We have end-user programs such as graphing programs, dynamic geometry, or spreadsheets that can accomplish the problem solving tasks in much more powerful and efficient ways.

Third, I took major responsibility for the technology in secondary mathematics courses (EMAT 4680/6680, EMAT 4690/6690, and EMAT 4700/6700 in 1992. It was at that time we moved from a writing computer programs (BASIC, PASCAL, or LOGO) to end user programs such as spreadsheets, graphing packages, and geometry packages.

Fourth, I put the course syllabi and problems on a web server in 1994. During 1994-95 I taught 8 sections of these courses and developed the first implementation of the Web Pages using a text editor and direct HTML code. My vision was that students' productions -- write-ups to investigations or instructional units -- would also go on the web. Discussions with our college technology tzars told me that student productions would never me possible on the college web server and that influenced my decision to maintain my own server on an office computer. There was a web site on "creating your own web site in 15 minutes" that I picked up from Minnesota with a server software called MacHttp. Eventually this was replaced with WebStar.

Workload accountability by administrators at my university is an art form. Officially we have teaching load of 4 classes per academic year. I have never had less that 6 per year. Obviously I had no workload release in 1994-95 for developing the Web site.

At this time I was also working with the development of the Learning and Performance Support Laboratory (as its acting director) -- an R & D center funded by the Georgia Research Alliance and affiliated with the Georgia Center for Advanced Telecommunications Technology. GRA funding helped pay for the infrastructure costs of computers and fiber optic cable and Ethernet system. It did not fund personnel costs.

Each year since 1994-95 I have had workload for 6 of these classes and a have continued to refine the web site. There have never been graduate assistants or released load for me. In other words, the web pages have grown totally as a part of what I wanted to do with instruction I was responsible for in these classes.

The InterMath project was funded in 1999. Much of the material developed there has been supported by the project and reflects the work of advanced graduate students -- all with extensive teaching experience. Most had been students in my EMAT 6680 classes. Our co-workers at Georgia Tech are funded to develop a web site for InterMath and the instructional material now on my web site will be migrated there sometime later this year.

I have continued to use a MacIntosh computer for the server. I started with a Quadra 880, then went to a PowerPC 8100 and switched to a PowerPC 8500. I used LaCie external hard drives for back up -- powerful lessons are to be learned on the need for multiple backups when there are 40000 + files involved. Difficult lessons about server management have been learned under fire. In 1999, we brought in a G3 with an 8 gig hard drive, mostly for the larger hard drive storage space. We have upgraded WebStar with each version of the software. We are current using WebStar Suite 4.2 with the HTML and the FTP servers activated.

**Jim Wilson**