**Introduction**

Technology tools have been become integral to mathematics and mathematics learning. This course is built on the vision of making such tools available to every mathematics teacher in Georgia. A course on instructional computing is required for Georgia certification.

The course, **EMAT4680/6680 Technology and
Secondary School Mathematics**, is required of all mathematics
education undergraduate students (4680) and 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.

The underlying psychological theme in the course
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 this course that are worth noting. First, the course is an implementation of the NCTM Standards in a teaching field and teacher education course. Second, it implements cooperative learning. Third, it implements portfolio assessment. Fourth, it underscores the contrast of demonstration and proof and develops an understanding of the need for both in mathematics instruction. Fifth, it capitalizes on the use of animation. Sixth, it responds to the use of technology.

**Alternative Assessment/Portfolio Assessment.
**The NCTM Assessment Standards emphasize
important mathematics, learning, equity, openness, valid inference,
and coherence. Essentially, the Student Folders in this course,
accumulated on a Web Page constructed by the student, becomes
a collection of each student's **best work**. This is the notion
of developing a portfolio. The write-ups call for summary, synthesis,
explanation, presentation, and communication. The process attends
to the NCTM assessment standards.

**The Technology**

As this class is currently taught, we meet in a MacIntosh computer enhanced classroom with student workstations and a teacher workstation with a Chisholm projector. All of these computers are on the Mathematics Education zone of the campus Ethernet and thus have access to the Internet. The software tools include graphing programs (such as Graphing Calculator 2.2.1, Algebra Xpresser, 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 Graphing Calculator 2.2.1), word-processing tools (prefer Microsoft Word), paint and draw programs (such as MacPaint or Superpaint), utility programs such as Simpletext, and information access tools (such as Netscape or Internet Explorer).

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
page, **The EMT 4680/6680 Home Page**, at

The students can access the course page via
a browser from **any** site with Internet access -- in the
classroom, at home, elsewhere on campus, or totally away from
Athens. EMAT 4680/6680 was developed on the vision that access
by teachers from their school workspace will be available in the
future. Few teachers have Internet access in their classrooms
today. More have the access somewhere in their school but seldom
is it functional for anything related to classroom instruction.
Almost all have access to the Internet at home.

Each student has an e-mail account. An Internet server is maintained and 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 on campus or by FTP transfer from home. 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 twelve 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.

The instructor presents demonstrations and explanations, clarifies 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. Provision is made to accept material from the students using alternative software or Windows platform applications.