Announcement and Call for Contributions
The CD/Internet Central Resource for Calculus Curricula

- by -

Robert R. Curtis, Ph.D., C•I•R•L Project Director
San Joaquin Delta College, Stockton, CA 95207
curtis@ms.sjdccd.cc.ca.us

Draft Date: August 14, 1996

I. Introduction

C•I•R•L will bring to the academic community a vast collection of the best instructional materials for calculus offering different approaches, philosophies, and technologies, presented with the power of hypertext, the World-Wide-Web, and an expanding host of client applications which will bring a new and exciting dynamic to teaching calculus.

Materials in C•I•R•L will range from multi-authored written expositories, to multi-platform laboratory projects, to dynamic and interactive homework problem answer-checking, to student group projects, to interdisciplinary materials from all disciplines where the calculus is applied.

C•I•R•L will exist on the World-Wide-Web with a coupled CD-ROM, combining the power of local and global information access.

C•I•R•L will be a collection of a variety of authors' works. A CALL FOR CONTRIBUTIONS is in effect. Authors of accepted works will be fiscally compensated for their contributions in one of several compensation schemes, with copyright retained by the author.

Special services for hearing-impaired and sight-impaired students will be an integral part of this project.

II. Goals

The goals of the C•I•R•L project are the following:
  1. To provide users with an easy to use, well-organized, searchable database of the highest quality content to allow them to explore, experiment, and tailor materials to their individual teaching and learning needs.
  2. To provide a variety of excellent course materials from a wide spectrum of authors whose works have been heretofore unpublished because the materials only covered a small range of topics or areas.
  3. To provide a cutting-edge, visionary product which expands the use of the electronic medium for calculus education.
  4. To provide an interdisciplinary approach to calculus, that will allow readers to start from their discipline of interest and explore the concepts of calculus which apply to problems in their discipline.

III. Audience

The audience for this project will consist of students and instructors involved in the following courses: Due to the variety of levels, approaches, and textual support existing in the project, this project will have wide appeal among student, instructors and institutions. Expected uses of C•I•R•L include: For the student, C•I•R•L will present an invaluable source of reference and interactive materials, regardless of the textbook used for their course, potentially being the textbook/reference for their course. Dynamic and interactive examples will provide the student with feedback and response to their academic work that at many institutions used to be the role of the homework grader.

For the professor, C•I•R•L offers an easy-to-use course development and design resource. With a few clicks of a mouse, the professor can select a desired approach and academic level to a particular topic in calculus, and provide students with electronic guidance (via the internet) to support this approach (or printed materials concerning this approach). Additionally, professors can customize assignments using a variety of media and materials, ranging from reading assignments, problem sets, investigations, research projects, technologically-based problems, group projects, portfolio problems, all with an individually-defined mixture of traditional, classical, and reform-type problems and explanations.

For Math, Science, and Engineering departments, C•I•R•L will provide two types of connections between the disciplines: (1) links from mathematical topics to applications problems in a variety of disciplines; (2) links from discipline-specific and industrial-based problems branch-linked to the host of mathematical topics required for analysis of the complex applied problem. The latter aspect of this presentation is uniquely accomplished in a hypertext environment.

IV. Brief Content Description

The content in C•I•R•L will be of wide breadth and scope. Our goal is to create an entirely new presentation method for calculus curricula, and with it, an entirely new student study model for investigating and researching the topics in calculus, using the power of the electronic medium in a way not seen before.

Written Expository

As a base for explanation of calculus topics, the written expositories will be short blocks, explaining specific and dedicated approaches to topics. Design of these written expository areas will require a new textual design for acquiring information from screen-based text, in contrast to previous attempts that simply put print texts onto the computer screen. All written expositories will additionally feature high-quality printable output protocols to allow paper-based compilation of written materials.

Dynamic and Interactive Expository

All written expositories will provide readers with dynamic and interactive levels where examples become live, interaction with the explanation drives the information acquisition, and the power of electronic presentation is realized. Beyond the written expository will be the living expository, where the reader become engaged with active learning process. Virtual experiments, animations, classroom presentations, virtual manipulatives, and interactive answer-checking will provide the backbone of the living expository in C•I•R•L.

Problem Sets and Examples

Paper texts must edit their problem selections, and provide only those problems that appear to follow their textual explanations. Yet professors routinely provide their own individual explanations in lecture, and, subsequently, find their paper texts' problem sets inadequate to their emphasis. C•I•R•L will provide the instructor with a customizable bank of problem sets, in a variety of formats from static, pencil and paper-based sets, to dynamic and interactive problem sets in all of the following areas:
  • Algebraic Skill Problems
  • Graphical Problems
  • Numerical Problems
  • Combined Approach Problems
  • Reform Problems
  • Theoretically and Conceptual Problems
  • Application (short) Problems
  • Application (complex, industrial) Problems
  • Related Discipline-Specific Problems
  • Group Problems
  • Student Research Projects
  • Open-Ended Problems
  • Portfolio Projects
  • Laboratory Projects
  • Non-Technical Laboratory Projects
  • Computer Algebra Projects
  • Modeling
  • Term Paper Projects
Interactive Problems of Various Models
Computer-Graded Problems
On-Line Graded Practice Examinations
On-Line Virtual Examinations

Figure 1: The C•I•R•L Homebase, one of many different navigational front-ends

Laboratory Projects

C•I•R•L will host an expansive collection of laboratory projects, ranging from short, one-hour assignments, to week-long and multi-week student projects. A variety of different teaching philosophies will be highlighted, ranging from traditional to applied to reform approaches in laboratory exercises.

Unlike other sets of laboratory exercises and projects that are tied to a particular computer algebra or graphing calculator platform, laboratory projects and exercise sets in C•I•R•L will be multi-platform, allowing the curriculum to be separated from the technology whenever possible. This will allow different instructors to follow the same laboratory curriculum, but use the technological tool of their choice.
Supported Technologies:
Computer Platforms
  • Windows OS
  • Mac OS
  • Unix
Graphing Calculators
  • Texas Instruments: 80, 81, 82, 83, 85, 92
  • Casio/Sharp 7700's
  • Hewlett-Packards 48's
Computer Algebra Systems
  • Mathematica
  • Maple
  • Theorist
  • Derive
  • MathCad
  • Joy of Mathematica
  • Various ODE solvers
  • MatLab

Virtual Experimentations

Following the physical sciences educational model, an expanding set of topics lend themselves to the virtual experimentation model whereby students investigate a topic through a series of experiments using a variety of computer algebra, graphing calculus, multimedia and other data collection and analysis tools, leading towards an understanding of the topic via an active learning scientific model.

Collaborative Learning Projects and Innovative Classroom Activities

Many instructors across the nation have been writing and experimenting with the collaborative learning model, and C•I•R•L will present a wide selection of these problem sets, classroom activities, and student projects. These materials will come from classroom developed and tested sources, providing practical implementation of this teaching model.

Animated and Multimedia Presentations

Sometimes a short movie, animation, or dynamic presentation makes the classroom lecture exciting and productive. C•I•R•L will present a collection of animations specifically intended for the classroom demonstration, in addition to use as a learning resource. Unlike multimedia flash and glitz, these presentations will be directed by pedogogy rather than hype.

On-Line Homework Grading

A common myth of electronic and interactive resources is that of replacement of the instructor in the calculus classroom. While not supporting this myth in C•I•R•L, it is possible to replace the homework grader. As budgets dwindle for support services to calculus courses, instructors are feeling increasing strain to provide better feedback services to their students.

The current internet technologies provide an opportunity to move completely out of the answer-key feedback model towards a truly interactive and recording system the plays the role of the homework grader, with instantaneous interaction, grading, and feedback to the student on their work. We recognize that many problems in calculus will not lend themselves to this kind of service, but a vast spectrum of problems can be presented with these feedback mechanisms, and progressive improvements will occur as technological advances for the internet are made.

These services will be pushed towards the offering of on-line examinations, which may be used by instructors either for practice and preparation purposes, or used for actual evaluation purposes.

Textbook Linking and Instructor-Defined Paths

C•I•R•L will provide linking from any current calculus textbook's table of contents to the resources in C•I•R•L. E.g., a student using Anton's Calculus will have a hyperlinked page from Anton directly to relevant resources on C•I•R•L.

Signature Course Paths will provide instructors will pre-designed courses through the materials in C•I•R•L by selected and respected educators throughout the world.

Instructors will also be able to customize paths through the C•I•R•L project for their students. This will allow individual professors and schools to focus the students as they see fit, without needing to conform to a given text or set of materials.

Figure 2: The popup menus from the first navigational front end, demonstrating the features and scope of the project.

Interdisciplinary Applications

The interdisciplinary theme in calculus education will have firm foundations in C•I•R•L, with materials ranging from short, light-application problems, to real-world, industrial problems, to scientific problems requiring multi-discipline concepts.

This bank of applications will be drawn from contributing authors, and from excerpts of textbooks and source materials in related fields such as biology, physics, astronomy, chemistry, engineering, etc.

By linking to other sites on the Web and by including real data from industry, it is possible to expose students to many different types of applications in a large variety of fields. It will be important to seek out the best source material for applications from a variety of authors.

Internet Aspect of C•I•R•L

The power of the internet/CD interconnection aspect of C•I•R•L will be to provide a truly-living text/resource bank. Materials will be continually updated, expanded, and enhanced with new technologies and delivery methods. The CD/WWW interaction will be seamless, providing to the user the instantly up-to-date materials and access to the very latest materials from our WWW sites, as well as all internet sites world-wide.

Many of the interactive aspects of C•I•R•L will be delivered via the WWW, allowing a secure way of providing course management, answer-checking, and exam grading and recording for the students and instructors.

The WWW connection also provides the platform by which instructors can post assignments, example, exercises, class notes, practice examinations, etc. to their students from C•I•R•L, interacting directly with students in a variety of media supported via the WWW connection.

V. How To Contribute Your Work

A CALL FOR CONTRIBUTIONS is in effect. Contributions can be of any size, ranging from a single problem set to an entire text or innovative project.

Authors interested in contributing their work should prepare a 100 word or less abstract describing the work. You may also submit with your abstract a short (less than 5 pages) sample of your work. An extended Guidelines for Contributors is available.

This abstract and sample may be submitted in a number of ways:

On submission, an author's abstract will be sent to the project director, and/or an appropriate associate editor (or designate) for review.

From this review, it will be determined whether the materials are acceptable, potentially acceptable, or unacceptable. If the materials are potentially acceptable, the author will be notified of required changes/improvements as determined by the reviewer and/or the Core Development Team.

Contributing authors will not be responsible for hypertext enhancements, interactive exercises, etc. These kinds of additions will be the responsibility of the Project Director. High-quality graphics, multi-platform computer algebra notebooks, additional resources, and other enhancements of a contributed work, although welcome, will likewise not be the responsibility of the author.

All contributed works must be original works of the author(s) for which the author(s) holds copyright. Should the contributed works be under copyright of another body, copyright and/or licensing permission must be obtained, and it is the responsibility of the author(s) to obtain such permission.

Contributed works by an author(s) will be under exclusive license for a defined period of time. It is our goal to allow flexibility to those authors wishing to contribute a work to C•I•R•L and potentially create and evolve their work into a larger, self-standing title. Further details are available from the Project Editor.

Contributing authors will receive full recognition of their contribution in the main body of the project, accompanying their work. Contributions will be financially compensated under individual agreement.

Those wishing to obtain password access to the development stages of C•I•R•L are encouraged to apply via a non-disclosure agreement and short survey. These can be obtained from the Project Director: curtis@ms.sjdccd.cc.ca.us

Road Map

Information Curriculum Contacts

http://www.calculus.net
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