Download Developing Web Based Courses on a Shoe-String

James W. Wilson
Mathematics Education Web
Course Development on a Shoestring
Developing Web Based Courses on a Shoestring:
Courses for Inservice and Preservice
Mathematics Teachers
By
James W. Wilson
University of Georgia
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 7050 Teaching Secondary School Mathematics
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.
EMAT 4950 Professional Seminar in Mathematics Teaching,
Making available papers I have written
Making available material from my students
Implementing projects
Mathematics Education Multicultural Web Site
Project InterMath
Making available personal information
Resume
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James W. Wilson
Mathematics Education Web
Course Development on a Shoestring
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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
James W. Wilson
Mathematics Education Web
Course Development on a Shoestring
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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, openended 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.
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Mathematics Education Web
Course Development on a Shoestring
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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
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Mathematics Education Web
Course Development on a Shoestring
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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, XFunction, 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 access 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
James W. Wilson
Mathematics Education Web
Course Development on a Shoestring
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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 writeups 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.
James W. Wilson
Mathematics Education Web
Course Development on a Shoestring
7
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
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Mathematics Education Web
Course Development on a Shoestring
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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
[email protected]
http://jwilson.coe.uga.edu