Strand 2:

Technologically presented learning material

ICTMT 5, Klagenfurt, 6-9 August 2001

(Schedule, tentative as of 08/06/01)

Chair: Bernard Winkelmann

Monday 15:15 - 16:00 Chair: B. Winkelmann

Creating and Teaching Online Mathematics Courses

Mary S. Hall (USA, mshall@mindspring.com)

Tuesday 8:30 - 9:15 Chair: Bernard Winkelmann

Animation, a Tool for Understanding Polar Coordinates

May Abboud (Lebanon, mabboud@lau.edu.lb)

Tuesday 9:30 - 10:15 Chair: Bernard Winkelmann

Computer Assisted Assessment of Mathematical Proof = Proof of Computer Assisted Assessment : An Integrated Approach to Higher Level Learning using Group Response Systems and On-Line Assessment

Michael McCabe*, Ann Heal, Alison White (UK, Michael.McCabe@port.ac.uk)

Tuesday 10:30 - 11:15 Chair: Bernard Winkelmann

Power Point computer support during mathematics lessons in secondary school

Peter Cooper, USA:

Design of Content Independent Instructional Systems

In designing and implementing instructional systems for remote use, the more sophisticated development environment allow for the use of multimedia content in a packaged environment. In such systems, the container/interface is bound to the content at compile time and prior to distribution. As part of a joint project with the United State Corps of Engineers Research Laboratory, the researchers investigated methods of separating the interface and data container from the content in ways that support a more dynamic approach to maintaining currency of content and distributed storage of instructional materials. The presentation session will include demonstrations of the training application, data entry applications and a look at existing training developed through the system.

Timo,Ehmke, Germany:

Geometria: A Tool for the Production of Interactive Worksheets on the Web

With this contribution I will introduce the Java-Applet Geometria, a tool for interactive worksheets to be presented on web-pages. Worksheets generally contain a dynamic figure together with some kind of geometric learning content. This content is described by means of a script-language (GeoScript) which provides the possibility to construct a euclidian figure and also supports the analytical definition of points, vectors and curves. A special feature is the feedback given to the student, while he/she is interacting with the figure. A tutoring component enables Geometria to evaluating and commenting on the student's answer.

Mary S. Hall, USA

Creating and Teaching Online Mathematics Courses

As distance learning has expanded, so also has the use of the Internet. More and more we are seeing the expansion of course material to the Internet. What are the issues for teaching course material on the Internet?

What students will benefit from such opportunities? These are some of the issues addressed in creating an online developmental mathematics course and other mathematics courses. This presentation will provide both resources and methods for teaching a course on the Internet as well as an emphasis on the new technologies becoming available. Several online mathematics courses will be used to demonstrate some basic forms of communication and evaluation that are necessary for a course to be successful.

Judith Hector, USA:

Teaching Probability and Statistics via the Internet

The author has taught a one-semester Probability and Statistics course via the Internet four times. The course is offered for university transfer credit at an American community college. The course is conducted totally online for students at a distance, but local students may meet for an orientation, midterm exam and final exam. From her experiences and research, the author discusses basic principles of teaching and learning mathematics on the Internet.

Duncan Lawson*, J. Reed, and S. Tyrrell, UK:

Extending a Mathematics Support Centre via the Web

The Mathematics Support Centre at Coventry University offers support to any student in the University who wants help with any area of mathematics, statistics or quantitative methods. The support offered by the Centre is in addition to that routinely received in lectures, tutorials, seminars, problems classes, etc. The primary mechanism of support is one-to-one contact with students offered on a 'drop-in' basis. This support is staff intensive and in order to optimise the use of staff time alternative methods of supporting students are continually under review. A recent development has been the introduction of a web-site for the Centre. This paper describes the background to the Mathematics Support Centre, the development to-date of the web-site and an evaluation of its use.

Stefan Priselac, Nancy Priselac, USA:

The Communiversity project delivers a restructured Pre-Calculus distant learning course

The presentation is multi-media in nature and can last from fifteen minutes to one hour depending on the allocation of time. The Communiversity at Garrett Community College provides diverse ways to deliver training, courses, programs and interaction across the globe as we redefine access from set time to anytime and from one place to many places as we create a new future in education.

Alfred Schreiber, Germany:

Project ZERO: Developing Online Material for Mathematics Teacher Education

This paper reports about a project dealing with the conception and production of supplementary learning material for mathematics teachers. It surveys the various types of courseware-modules presented herein online (e.g., dynamic geometry, computer-based-training-like frames, paper-and-pencil-exercises), and discusses their specific purpose and use. Emphasis is put on the problem of how to embody appropriate functions that provide the opportunity to evaluate user inputs - thus enabling an author to give "local" feedback to the student. Finally, some questions are raised concerning the form that should be used in the future to represent both data and logical structure of the underlying content.

Edgar Smith* and A. Waterson, Australia:

Online mathematics teaching:the development of student-instructor interaction

We discuss differences between teaching styles in online mathematics teaching and other less technical subjects. We discuss how to "lean over a student's shoulder" online. Techniques are both automatic and software mediated discussions with students. Discussions are extremely expensive in terms of staff time, so we consider automated responses. These are illustrated with sample problems in elementary fluid mechanics in a subject delivered via WebCT. We discuss how to evaluate and improve automated responses.

Hans Stam, Peter van Wijk, Netherlands:

Mathematics and Internet

The Internet is primarily used as a source of information, as reference work and as a medium in which to look things up. There is, it is true, a lot to be found on the Internet, but for (arithmetic) education the Internet can be more than an encyclopaedia or library.

In order to organise the various ways in which the Internet can be used in education, we take the classification based on the idea that there are various sorts of places on the Internet.

Cluster 2

Mary Abboud, Lebanon:

Animation, a Tool for Understanding Polar Coordinates

Students in undergraduate classes have a great deal of difficulty in plotting graphs of functions given in polar co-ordinates. In previous work done, animation was used as a tool to understand how a linear transformation affects the graph of a function, and here I am extending this work to enable students to better understand polar Coordinates and the relationship to Cartesian Coordinates. In our experience, the use of a Computer Algebra System such as Mathematica does not by itself guarantee that students will improve their visualisation skills or their understanding of mathematical concepts. It is necessary to design projects where students are encouraged to observe phenomena, make conjectures and then test whether these conjectures are really true. We present in this paper the work that we have done and which can be used with students of Calculus.

Douglas Butler, UK:

Adding a sparkle to classroom teaching - Using Word, Excel and the Internet

A live large-screen demonstration of the creative use of generic software tools both in the classroom and in the creation of worksheets. Surprisingly complex single line mathematical expressions can be created in Word as text using the Unicode font set and user-defined ALT-keys (in preference to the equation editor, though that is still required for multi-layer expressions). These expressions can be pasted into single-font environments such as an Excel cell or an email. Also the drawing toolbar can be used to create a wide variety of diagrams, though there are disappointing limitations.

The finding and categorising of useful web resources will be discussed; and the associate pasting of text, graphics and data (often with difficulties to overcome) off the internet will also be covered, including a trawl through the amazing web resources linked from the Oundle School (UK) site

http://www.argonet.co.uk/oundlesch

There will also be a look at some of the pitfalls when using Excel, and an introduction to the concept of using dynamically linked objects to visualise mathematics.

Tatyana Byelyavtseva, Ukraine:

Power Point computer support during mathematics lessons in secondary school

The article includes the analyses of computer support during mathematics lessons in secondary school. One of the main purposes of this is to analyse lessons dedicated to developing basic geometric concepts. The influence of new computer technologies on the process of stimulation the scientific research among pupils of secondary schools is also shown.

Michael McCabe, Ann Heal, Alison White, UK

Computer Assisted Assessment of Mathematical Proof = Proof of Computer Assisted Assessment : An Integrated Approach to Higher Level Learning using Group Response Systems and On-Line Assessment

In the School of Computer Science and Mathematics at the University of Portsmouth, computer assisted assessment (CAA) has been used successfully in support of maths teaching for almost 10 years. CAA is most commonly used for first year university modules, where the numbers of students are greatest and the topics covered are basic. This leads to the common conception that CAA is only appropriate for low-level learning.

Mathematical proof is a topic which students find difficult to grasp and involves a higher level of learning. Traditional exam questions on proof are time-consuming to mark, but CAA can provide an efficient and effective alternative. The speed and accuracy of marking objective questions and the ability to give immediate feedback are among its obvious benefits. It remains to demonstrate that CAA can generate results equivalent to those of a written, hand-marked examination. We will explain how this has been achieved:

• by carefully designing test questions and considering learning objectives
• by exploiting both on-line assessment and group response systems (also referred to as an audience (or class or personal response) system
• by integrating both public and private practice of CAA into learning
• by analysing the results of computer marked exams

Pavel Leischner, Czech Republic:

The collection of interactive solids figures and spatial situations in the Cabri - geometry

The article gives information on the collection of interactive solid figures and spatial situations in the program Cabri-geometry. These aids would facilitate the teaching of stereometry at high and elementary schools. It is intended for the spatial imagery evolving. It should make students pass from experimental manipulations with the spatial situation to mental ones.

Key Words: High school stereometry, spatial imagery, teaching with software, Cabri-geometry.

Vladimir Nodelman, Israel:

Parametric nature of mathematics' objects and computer environment

Although the simplest mathematics' objects may be considered as based on parameters. Most of parameters are numeric. In computer software it is a regular task to implement numeric input. The problem is in:

• visually discrete nature of an "input box" entry opposite to continuity of most mathematics notions' parameters,
• not friendly interface with static changes in correspondence to entered values.

We present an approach which let the student DYNAMICALLY enter and change parameters in not pure numeric way, even prepare such input by himself in order to analyse parameters' rule and mathematics' objects "behaviour"