mathematics learning and teaching

USA

bitter@asu.edu

http://www.tblr.ed.asu.edu

*Mathedology*™
is a professional development program designed to help elementary
teachers improve their mathematics instruction and align their
teaching with the National Council of Teachers of Mathematics
(NCTM) Professional Standards for Teaching Mathematics. *Mathedology*™
employs Progressive Networks' G2 RealPlayer technology, which
provides simultaneous streaming video to the users via the Internet.
Teachers across the country can now access any or all of the 25
lessons in the *Mathedology*™ program, using any type
of Web browser or on CD-ROM. The interactive multimedia (IMM)
program *Mathedology*™ provides video of 25 K-5 elementary
mathematics lessons exemplifying the NCTM discourse standards.
The program uses a uniform, Web-based, graphic user interface
for each of the 25 lessons. A search engine allows searching the
database for specific lessons or by (a) grade level, (b) language
environment, or (c) content of lesson.

Netherlands

The goal of the *Rekennet* project, is
to support primary school teachers in their task to teach realistic
mathematics. The *Rekennet* consists of two components: a
social rekennetwork and an internet website. In the social rekennetwork
primary schoolteachers meet each other and talk about mathematics
in their daily profession. We call this horizontal professionalization:
teachers learning from teachers. At the other hand, didactical
experts of the Freudenthal Institute join the meetings and hear
what the problems are in order to reflect efficiently. The internet
website (http://www.fi.uu.nl/rekenweb)
gives the ultimate opportunity to communicate with colleagues.
The rekenweb also contains a lot of computergames for children,
workingsheets that teachers can print and use in their lesson,
practical suggestions etc. The content of the rekennet is based
on the suggestions of the primary school teachers. Thus the *Rekennet*
has a lot of opportunities to reach the teachers and to provide
them with useful ideas and materials for their daily lesson.

USA

This paper presents an innovative approach
to teaching an introductory numerical analysis course interactively
using the Computer Algebra System *Mathematica*. This approach
promotes learning by experimenting through allowing the students
to interact with the text. The powerful interactive programming
capabilities, high-speed calculations, and the versatile graphics
and animations available in *Mathematica* are utilized in
developing interactive text modules in topics such as approximation,
Riemann sums, numerical integration, interpolation, modeling with
exponential functions and others. Students are asked what-if questions
and to supply interpretations and comments on various results.
This approach also enables the students to examine examples of
practical complexity and to discover the capabilities and limitations
of the various numerical techniques. Examples of the modules developed
will be presented in this paper. These examples discuss Newton's
method for solving equations, polynomial interpolation, numerical
integration and adaptive quadrature.

http://www.anglia.co.uk/education/mathsnet/

The development of interactive online resources
for school use by teachers and pupils and at home by individual
learners should be focussed on providing one single means (which
I will call the *viewer*) of accessing many varied types
of interactivity. Currently this viewer is the web browser and
the varied types of interactivity available to mathematics include
dynamic geometry, algebra, graphing, spreadsheeting and others
created using technologies such as JavaScript, Java and various
browser *plugins*. In the future the viewer is likely to
be some form of digital TV interface. These developments, viewed
optimistically, could open up ICT to students and reduce the technological
barriers existing so far. My contribution will include consideration
of the experience and benefits of using the Internet in school
and at home, how these two means of access should differ, and
a review of what is currently available, including particularly
examples of current best practice.

P.O.Box 7181, Kampala

Uganda

In many countries in Sub-Saharan Africa (SSA), the number of applicants for tertiary education is far greater than the facilities available in the existing institutions to handle them. Access to science -based courses including mathematics is even more difficult since the facilities available can only allow for a small percentage of all those who qualify. The African Virtual University (AVU) is a World Bank ( WB) project started in 1997 ,initially in six SSA countries, to try and respond to the growing demand for tertiary education, especially in the sciences and mathematics. The mission of AVU is to use the power of modern information technology to increase access to educational resources throughout SSA. At its inception the countries which acquired the AVU sites were Ethiopia, Ghana, Kenya, Tanzania, Uganda and Zimbabwe. At the end of 1999, more countries in SSA had acquired AVU sites where satellites facilities are installed .In Uganda there are three AVU sites located at different University campuses. In this paper, the learning activities at the AVU sites are described using Uganda as a reference point. The AVU is presently moving from the pilot phase to the operational phase. As this happens a lot of issues will have to be addressed by the SSA countries, among which are the funding of AVU, curriculum design, accreditation of AVU certificates, location of AVU headquarters in SSA, improvement of facilities at AVU sites and more. The perspectives of SSA Universities with regard to these issues are also highlighted here as a response to the World Bank policy position. Finally the paper also draws attention to ICMI to study the operations of AVU, with a view to helping to improve the Instruction of Mathematics in SSA.

Japan

The new Japanese curriculum ,which will be enforced from April 2002, has aims related to developing autonomous and creative students. In order to build an educational environment consistent with this new curriculum, we think we should make hypermedia sub-textbooks instead of printed paper textbooks. Our hypertext materials have the following characteristics: (i) They are offered via CD-ROM; (ii) Some subject materials are mutually linked to much more relevant materials through hypertext; each hypertext screen should provide detailed explanations when students encounter unfamiliar concepts or theorems; (iii) Our hypertext materials are collected from 4th grade to 9th grade levels materials as the fundamental parts. (iv) College students and teachers will be able to make their lesson plans with links of their frames to our hypermedia materials.

Dourouti 45110

Greece

In learning situations, technology is often used by learners as a medium to find information provided by the teacher or by other people. Educators and technologists are interested in finding the appropriate way in which to use information technology in the teaching and in the learning process. Some researchers believe that shifting from the traditional delivery of lectures to a class into a technology rich environment requires an enormous amount of effort on the part of the lecturer and student. In WWW exploration and distant learning situations technology is always present. In our work we used technology to replicate the traditional way of lecturing statistics to an undergraduate class of over 20 students in the Department of Education. The course covered descriptive statistics and the course material included an extensive number of examples, exercise work and homework. This material was on our Department's Internet site written in our language and was available for students to take it in at their own time. Participating students did not all have the same amount of knowledge of use of technology. So, firstly we explained to them how to use it. Then, each student in the course was given a unique ID and password to access the course material any time. The terminals in the Computer Center in our University had an Internet access and the students used them any time during the week. Once a week a meeting/lecture between the lecturer and students was held to go over difficult material and to work through statistical examples. Paper copies of descriptive statistics were copied and distributed to students. Information was also given about other statistical online course notes on the world wide web. During the week the lecturer/student communication was established via email. At the end of the course students had a 3-hour written examination based on course content. Our analysis of the use of these 'www statistical lectures' suggested that: (a) fewer lecturing hours were needed, compared with face to face teaching; (b) the student's technical bias at the beginning of the course had no impact on their overall performance; and (c) students mastered the subject well.

Japan

http://mathmuse.sci.ibaraki.ac.jp/urabe/

I am organizing an enterprise for mathematics
education on the Internet, called *Mathematics Museum, Japan*.
The URL is the following: http://mathmuse.sci.ibaraki.ac.jp/
(Japanese version) http://mathmuse.sci.ibaraki.ac.jp/indexE.html (English
version).You can actually enjoy mathematics there. This site has
several significant features. First, the purpose is to rouse naive
intellectual curiosity of younger people. Second, it is a cooperative
enterprise of Japanese mathematics researchers and educators.
Third, it is a site connecting various sites spread across the
whole of Japan. Fourth, we employ multimedia and interactive properties
of the web and try to reduce the number of sentences used. Fifth,
it is a world-wide enterprise on the Internet. The most important
aspect of education is to give human beings motivation for study
by themselves. Several years ago I hoped to do some work on this
aspect, and made the plan. It has already been introduced in various
books on Internet, and has a high reputation.

UK

The NRICH Online Maths Club (http://nrich.maths.org.uk) is a grant-funded internet service that provides a range of mathematics enrichment resources for primary and secondary teachers and students. The main aim of the project is to support young able mathematicians and their teachers and provide opportunities for mathematical enrichment beyond the limitations of set curricula. Collectively, the fifteen or so website sections encompass: News, articles, resource reviews, links to other sites, problems, investigations, puzzles, challenges, games, activities, communication facilities - publication of students solutions, email talk-lists, web-board conferencing, on-line mentoring. New material is presented each month, with past material archived into an accessible and searchable library. As of 1st February 2000, there were 4334 registered members, across 73 countries, though a conservative estimate puts the number of distinct users at 30 thousand. Evaluation studies suggest that there are some specific characteristics of the website that significantly impact on both learners and teachers.

Germany

Communication is an essential part of mathematics
education and mathematics teacher education. Communications through
technology can support the goals of mathematics education courses
and programs, and can promote the professional development of
participating teachers and educators. This presentation is about
a semester-long course of 150 teacher students. Every student
had to have an email-address and had to have access to the Internet.
Via the Internet we provided web-based lecture notes, exercises,
a listserve, and a webboard for electronic discussions of special
topics about mathematics education. We were especially interested
in the meanings that new types of communication, namely technology-assisted
communication, make possible. *Announcements *initiated by
teachers or students, *discussions* in the whole Group or
in small groups, *dialogues* between Instructors or between
instructors and students, *explorations *or *reflections*.
The presentation will provide an overview of the Internet-based
class room activities and of some results of the empirical investigation.

Michigan State University, East Lansing, MI 48824

USA

The qualitative college algebra course at Michigan
State University is offered both as a traditional course by the
Mathematics Department and as an internet course by the Virtual
University. On-campus students may enroll in either version. This
presentation will discuss the development, by members of the Mathematics
Department, of the parallel online course as well as the results
of its first implementation. Also discussed will be the succeeding
course, *Applications of Algebra*, which is currently taught
in lecture/lab format but uses the internet for resources from
online lectures to an asynchronous help room. Both these courses
have very large enrollments. The author hopes that the description
of the situation at her institution will contribute to the discussion
of successful and less-successful approaches tried at other institutions.

Radford University

USA

http://www.runet.edu/~wyang/

*Mathematics and technology in the East and the West*

An overview is given of the impact of mathematics computational tools on mathematics education. The author shows how technology is used as an exploratory tool in the U.S. One question that many U.S. educators debate about is how much algebraic manipulation techniques are required when technology is introduced in a classroom. Implementing technology into mathematics curriculum may be difficult in many Asian Pacific regions. One reason may be because many education systems in the Asian Pacific regions still adopt the "college entrance examination". Thus, many students and even parents usually ask how technology can help students do better in the examinations? In the process of adopting new technology into classrooms and examinations, the author suggests that requiring basic manipulation skills from students is desirable and we ought to be careful when we design a problem which requires the use of technology. We may not have comprehensive solutions for both educators in the U.S. and in the Asian Pacific regions, but we will provide some partial solutions.