Computer - Human Interaction in Symbolic Computation

The well attended March 1994 HIse workshop in Amsterdam was a very lively con­ ference which stimulated much discussion and human-human interaction. As the editor of this volume points out, the Amsterdam meeting was just part of a year-long project that brought many people together from many parts of the world. The value of the effort was not only in generating new ideas, but in making people aware of work that has gone on on many fronts in using computers to make mathematics more understandable. The author was very glad he attended the workshop. * In thinking back over the conference and in reading the papers in this collection, the author feels there are perhaps four major conclusions to be drawn from the current state of work: 1. graphics is very important, but such features should be made as easy to use as possible; 2. symbolic mathematical computation is very powerful, but the user must be able to see "intermediate steps"; 3. system design has made much progress, but for semester-long coursework and book-length productions we need more tools to help composition and navigation; 4. monolithic systems are perhaps not the best direction for the future, as different users have different needs and may have to link together many kinds of tools. The editor of this volume and the authors of the papers presented here have also reached and documented similar conclusions.

Contenu

The ACELA project: aims and plans.- 1 Introduction.- 2 Interactive books.- 3 Interactive mathematical books.- 4 Architecture.- 5 The content of the book.- 6 Related work.- 7 Conclusion.- References.- Active structured documents as user interfaces.- 1 Introduction.- 2 Limitations of graphical user interface toolkits.- 3 Active and structured documents.- 4 The Grif editing toolkit.- 5 Applications based on active structured documents.- 6 Related work.- 7 Conclusion.- References.- Direct manipulation in a mathematics user interface.- 1 Introduction.- 2 Previous work.- 3 Design overview.- 4 Overview of static interface elements.- 5 Direct manipulation.- 6 Usability.- 7 Interval arithmetic.- 8 Implementation details.- 9 Directions for future work.- 10 Conclusion.- References.- Successful pedagogical applications of symbolic computation.- 1 Introduction.- 2 Symbolic computation and pedagogy.- 3 The EPGY course software.- 4 User interface and design issues.- 5 Logical structure of a derivation.- 6 Two examples.- 7 What is gained.- 8 Limitations and desiderata.- 9 Final remarks.- References.- Design principles of Mathpert: software to support education in algebra and calculus.- 1 Introduction.- 2 Purposes of software for mathematics education.- 3 Design principles.- 4 Cognitive fidelity and glass box in Mathpert: operations and pedagogy.- 5 Customizing the solution in Mathpert.- 6 The correctness principle in Mathpert.- 7 Using the computer's power when the user is stuck.- 8 Traditional interface issues: ease of use.- 9 Interfaces and pedagogy.- 10 Use and availability of Mathpert.- References.- Hypermedia learning environment for mathematical sciences.- 1 Introduction.- 2 Related work in the field.- 3 Components of mathematical hypermedia.- 4 Designing mathematical hypermedia.- 5 Structure of the hypermedia database.- 6 Learning interface.- 7 Conclusion and research topics.- References.- Chains of recurrences for functions of two variables and their application to surface plotting.- 1 Introduction.- 2 Chains of recurrences for functions of one variable.- 3 Chains of recurrences for functions of two variables.- 4 A Maxima/IZIC implementation.- 5 Conclusions and future work.- 6 Availability.- References.- Algorithm animation with Agat.- 1 Introduction.- 2 Overview of Agat.- 3 Using Agat.- 4 The Agat language.- 5 The graphical features of Agat.- 6 Some applications of Agat.- 7 Implementation.- 8 Conclusion.- References.- Computation Computation and images in combinatorics.- 1 Introduction.- 2 Overview of CalICo.- 3 The use of CalICO as illustrated by examples.- 4 The tutor.- 5 Formal coding and symbolic computation.- 6 Graphical workshops and graphical interfaces.- 7 Communication manager.- 8 Availability and implementation.- 9 Conclusion.- References.