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Step 1: Creating the Repository
Collecting and Reviewing Tools

Collecting Tools: Our goal is to collect and review all the important high quality technology tools used in mathematics education, K - Calculus: software for graphing calculators, PDAs such as Palm Pilots, and other handhelds; small computer programs ("mathlets"); medium sized packages (Geometer's Sketchpad, etc.); and very large "computer algebra systems" (Maple, Mathematica, etc.). (Some of the medium and large programs now make it possible to construct easier to use project-oriented "sketches" or "notebooks," further enriching the situation.) Our strategy is to first incorporate large collections where quality tools exist, collaborate with manufacturers for "emerging technologies" to learn of new developments, and work with a publisher to make sure we cover the major commercial products. In this fashion we will rapidly build up a sufficiently large collection of reviewed tools to draw teachers to the site (see Step 2: Driving Use for a discussion of how we will attract users). We will also engage the developer community (ibid) by addressing technical barriers. Then, as teachers nominate their favorite tools, and developers learn from each other and become aware of the opportunities for ideas and teacher collaboration furnished by the community, their interactions will help expand and enrich the collection.

Texas Instrument has by far the largest collection of material available for programmable calculators. As mentioned earlier, Palm Pilot, Visor and WIN CE products are bursting onto the scene. One of our partners, SRI, will help us track these newer platforms as tools develop for them (further discussed in the Sustainability section).

If you know where to look, there are many mathlets on the Web. Two of our partners are highly regarded for the quality of their applet production, the Shodor Foundation and Utah State's National Library of Virtual Manipulatives. Each has a collection of around 100 tools. The Math Forum also has at least 500 other appropriate tools that students have collected, tested, and screened as part of the JOMA project.

The Shodor Foundation in making their collection available to us will develop resources to help existing high-quality collections expose their metadata and become accessible to the many users of NSDL. More particularly, they will develop a community object toolset that will enable collections to expose their existing materials to the digital libraries while facilitating the building of new tools. This is going beyond merely tagging existing applets but would be tested by accomplishing this. See their subcontract for more information.

We will collect and review regular commercial computer programs larger than mathlets, and will work with Key Curriculum Press to assure that we develop a solution appropriate for software publishers and that we include all the major programs.

It should be noted that by "collecting" we will in general have only a link to the actual tool. When possible we will house the actual tool itself (even the source code) since this avoids unexpected changes in the tool or link.

ReviewingAssuring quality in the collection: We will find tools that hold pedagogical promise, function well on at least some common platforms, and provide correct results. We will work early on with teachers, students, online library staff, and developers to refine that informal definition of quality as usage, feedback, and review instruct us (see our descriptions of the JOMA and ESCOT projects, above). Existing quality standards by digital libraries such as Eisenhower National Clearinghouse, Merlot, iLumina, and JOMA will be carefully considered.

As we have done with the Internet Mathematics Library and are formalizing in the Online Mentoring Project, we will train and oversee knowledgeable persons to review the math tools. This approach appears to be much faster than the review process currently in use by other digital libraries, and has resulted in our large and trusted collection. We will invite applications from contacts we already have - Math Forum visitors and associates, Texas Instrument's T^3 instructors, and College Board workshops for 400 AP teachers. We will also look for interested reviewers through NCTM and other journals and through websites. Reviewers will comment on expected pedagogical value, usability and technical issues, accuracy and insight for chosen math content, and platforms for which the tool works. Reviewers will also give tools an overall rating. Users will be able to rate tools in the style of book reviews.

Public review and discussion will also include: implementation experience and advice, effectiveness for given purpose and context, pointers to related resources and research, etc. Each tool will have its own discussion area and bug report list. When users report that a tool doesn't run on their platform, we will corroborate the report and supplement the review accordingly. Discussions will give teachers and developers a place to converse about pedagogical uses and potential improvements.

Literature Reviews: George Reese of University of Illinois Urbana-Champagne (see attached CV) will coordinate reviewing the literature of research on the use of technology in math education. He (and others as the project evolves) will give articles brief capsule reviews and ratings, paying particular attention to their relevance to teachers and developers. They will also nominate articles to feature in the public discussions, advertise them on the site in the style of, and facilitate the ensuing conversation, with a special eye toward helping teachers participate profitably in the discourse.

Building a Web Site to Get People to the Right Tools

Design Principles: The web site will be designed so that users can rapidly and conveniently get to the math tools that interest them. For example, users will be able to restrict their viewing to appropriate platforms.

Based on our previous digital library activities (see Result of Previous Work, above) and on what we have learned from the work of others, we will

Special Pages: The site's home page will highlight a few items of general interest, such as our monthly education article discussion, discussions of general interest taking place elsewhere on the site, and occasions for groups to work together (e.g. teachers and developers or teachers developing lesson plans on a particular topic). There will also be links to more specialized entry points for browsing.

The main entry points to the Math Tools digital library for teachers will be via pages corresponding to typical K-Calculus courses, and by content strand for the earlier years:

Elementary Math (content strand portal) Number and Operations, Geometry, Data and Probability, Patterns and Relationships (Algebra), Measurement.

High School Math (typical course names) Algebra 1, Geometry, Algebra 2, Trig/Pre-Calculus, Calculus, Prob and Stat, Discrete Math, AP Calculus, AP Prob and Stat

Developers will have an entry point to take them directly to information about programming for various platforms, sharable software development tools, and review comments from teachers about the effectiveness of the tools.

The entry point for students will provide links to resources such as Ask Dr. Math, tools related to material they are studying, and discussions. The parent's entry point will also contain discussion groups concerned with the meaning of technology changes in mathematics education, and one about special problems of homeschoolers.

Math Forum Services: The proposed software library will integrate with activities elsewhere on the Math Forum site, resulting in a rapid influx of users.

tPOWs: Simply having wonderful tools available will not be enough to help many teachers who are unfamiliar with their pedagogic use. We will embed them in a context where their use is natural, valuable, and effortless: into our own suite of Problems of the Week, as Technology Problems of the Week (tPOWs), where technology plays a useful role. This proved to be a successful approach with the ESCOT project (see above). We will recruit a group of "t-problemists" as we search for facilitators, reviewers, and other ways for users to be involved with the project. The problemists will be trained, supervised, and directed by our Problem of the Week personnel.

The Shodor Foundation will participate in the proposed problem of the week activities (see subcontract). They have a good start on these with a number of open-ended problems and they develop problems that don't simply have "an answer" but require the students to make and defend observations about the nature of patterns and phenomena.

Our summer workshops (see below) will begin with teachers finding good candidates for tPOWs and continue as the teachers collaborate with developers to produce or modify tools to fit the needs of the problem. Their collaboration will drive adaptation and innovation: once we have a tPOW for one platform, if a similar tool exists on another platform, the problem can be simply reused with the new platform (we will identify for programmer attention those platforms lacking an appropriate tool). Not only will our tPOWs be reusable across platforms, some of the more general purpose and powerful programs will be reusable as well, and be suitable in many tPOWS. (Reusability is considered a very powerful idea in the CS world and we expect its application here to help make the tPOW concept viable).

We will build up a database of good problems for which a technology tool would be a valuable or even necessary asset, thereby putting the horse before the cart. The database will be constructed from t-problemist ideas, summer workshops, and general submissions. This database will show developers pedagogically important areas in need of new tools, and thereby stimulate their creation. Our developer areas will contain relevant lists of specifications for these tools.

Search Engine: The Math Forum will build on the experience we have had configuring and refining our site search which identifies common searches and starting points, as well as common spelling errors (it is especially good at spelling Pythagoris). We expect to participate in the NSDL drive toward federated searching, so that our materials will be visible from other sites.

This project will also benefit from our other research on enhancing user navigation, and we are studying user ability to learn from archived resources with strategies that combine functions such as user tracking and registration, case-based reasoning, ontology development, etc. See Step 2, below. User Services User Support: For each course and content strand, we will provide a facilitator who helps users learn how to use the technology and the resources. Questions may be addressed by the facilitator, other users, and, when appropriate, by the manufacturers of handheld devices (with whom we are developing special arrangements; see the letter of support from Texas Instruments). We will look to the pedagogical needs of users, providing and facilitating discussion groups in line with the Math Forum's Teacher2Teacher project.

For further information on user involvement, using profiling for user support, and user discussion support see Step 2.

Developer Support: In the burgeoning area of small tool development, we pointed out above that one of the keys to building quality material is to connect software developers to teachers. We have observed that at the college level, mathlet developers are quite interested in working together and sharing information (browse through the Developer's Area of JOMA). For handheld programmers, we will work closely with the manufacturers, who have an interest in seeing good material for their products. A Test Area will host beta versions of tools for constructive comments on the technology and pedagogy.

Two key software notions for efficiently and effectively developing software are reusability and interoperability (see above). These should play an important role for our tool developers, but since many have a background in teaching mathematics rather than in computer science, they may lack an appreciation of these ideas. Jeremy Roschelle, whose ESCOT project was in part devoted to these ideas, will work with developers on these crucial concepts. In particular, he will customize the evaluation framework for reuse and interoperability that he developed for the JOMA collection to the Math Tools Digital Library. He will also interview key contributors and users about these issues, perform independent technical analysis, develop recommendations, and report to our developer community. Exemplary tools will be highlighted for developers. See the SRI subcontract.

We will work with the National Library of Virtual Manipulatives (hereafter NLVM) at Utah State who have developed techniques to allow teachers to save applet states and associate them with activities. These features utilize a cross-browser XML-based approach for which they will share source code, examples, and documentation. We will develop standards and provide general software tools so that other developers will be able to include these features as part of their applets. Another goal is to provide teachers with the ability to configure an applet in exactly the state desired for use in a lesson plan or activity. See the subcontract for further information.

AP Courses: We will work with the College Board to make Advanced Placement course areas particularly appropriate to the needs of the AP community. For, the method of instruction and use of technology may be different in these courses than in other courses. Moreover, graphing calculators are now heavily tied into AP work, so our AP consultant will also advise us on graphing calculators. AP Stat students are expected to be familiar with computer output from software.

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