Mathematics Learning Materials on the Web

(a Topic-by-Topic guide to professionally reviewed web-based resources suitable for use at senior secondary and junior post-secondary levels)

The Problem

There are several large websites devoted to cataloging mathematical material, but although the
items are listed by subject, they tend not to be broken down by detailed topic, and their search
engines typically respond to a query for a particular topic with listings that include all mentions of the topic (eg even just as an item in a course syllabus).  There are also several sets of topic-by-topic on-line course materials, but these tend to each represent only the work of one
author or team. Searching these resources for material on any particular topic is still much like
going to the library and taking out several books and looking up the topic in each of them.

A further problem is that even academically hosted catalogues include links to material that may be misleading or inaccurate and some sites which do claim to review material appear to do so on the basis of criteria of dubious relevance and often without attribution.

What still appears to be missing therefore, is a site where one can follow a heirarichal outline or index of topics to reach a listing of reviewed and classified "learning object" resources on whatever particular topic is of current interest. This is particularly needed at the secondary/post-secondary transition level where students are becoming more independent but lack the research skills needed to effectively navigate and evaluate the material on their own.
 
 

A Proposed Solution

The concept has also been endorsed by a Focus Group on "Mathematics Education and the Web at the Tertiary Level" at a conference on "Technology in Mathematics Education at the Secondary and Tertiary Levels" held at Brock University in St.Catharines Ont in June of '99.

As mentioned above, Mathematics is in fact reasonably well-served by several large databases of material at the "course-by-course" level of subject breakdown. What appears to be missing is a service which identifies only all relevant links at a more refined "topic-by-topic" level of detail, and it is on this aspect that we expect to focus our attention (with initial emphasis primarily on faculty and students at the secondary/post-secondary transition and junior undergraduate level).

A rough layout of a possible model for the proposed service has been set up at Langara College.
(Although incomplete, and not very polished, this test site has been favourably reviewed by the Science and Engineering section of the Internet Scout Project)
 

Target Audience (principal beneficiaries) and Primary Product

Additional Benefits

Giving access to global resources while maintaining awareness of Canadian material: A major reason for using the web is to provide quick distribution of the best ideas no matter where in the world they originate, but one reason for having a Canadian based site (even at the risk of duplicating efforts undertaken elsewhere) might be to save our students from the perception that everything interesting happens in the US and to save local products from being swamped by the sheer volume of available material (at least when that material offers no significant advantage).

Service to the international community: If well done, this project will be of use to learners and teachers of mathematics all over the world. Its emphasis is at the college level where there is more likely to be at least some internet access. Also one of its primary goals is to minimize the amount of time spent by users in searching for material, and increasing user efficiency is of course particularly important where access is limited.
 

Questions to Address

1.     first see what's already available and identify what, if anything, is needed,
2.     then seek partnerships and/or funding,
3.     review and compare the available tools,
4.     and proceed to develop as much of the needed resource as we can.

Comparison to Other Related Projects

What Exists Already?

Math Forum

Math Archives

Calculus@Internet

CoolMath

Chinese International School

MathCentral

Some of the technical issues associated with this project may have been addressed in the context of similar projects in other subject areas.
 
 

What is Still Needed?

• More detailed breakdown (at least at the Precalculus/Calculus level where students are just beginning to explore on their own and may not yet have the capacity for locating what they need from out of a large pool of options)
• More guidance for students as to quality of material and how it relates to our curriculum.
• Clearer identification of authorship, both of resources and of reviews.
• More emphasis on exploration & discovery as opposed to explanation & demonstration (or at least a clear separation of these two resource types). This may be a personal predjudice on my part, but it seems to me that too many sites are just rewrites of textbook material - (and that these are also the ones most likely to include misleading or erroneous material!)

Some 'Philosophical' Issues

Technical Issues

• Networked Database - I/O via HTML using forms for input
• Output Format (HTML constructed "on the fly". Needs to respond to a heirarichal tree of topic refinements and/or to a restricted vocab keyword search, with an up to date list of recommended resources including a url or link for each resource, along with (optional) further descriptions and reviews as well as the usual(?) metadata.)
• Input Format for adding new items (should be by HTML form) - Ideally, reviewers, on finding a site of interest should be able to jump to a Resource Report Form page into which they can copy the resource's url and position in the topic tree as well as other information (metadata) such as author, date, etc., and a brief review/explanation.
• Metadata content (Dublin Core, IMS,...?)
• Database Structure
• Project Scale and Scalability (Yes there's a lot of stuff, but there are not yet hundreds of items on each topic. "We" don't have to review everything at once, and the work can be distributed.  It should eventually be possible for different topic areas to be hosted on different servers or at least managed by different people, but for now at least, one server should suffice)
• Mirroring of Resources? (Not Now - but later might want to get permission to archive and repost if sites removed)
• Mirroring of Service? (We may need a plan in case the load becomes high, but don't expect to need it right away)
• Software(Oracle?Access?MySQL? fronted by ColdFusion?PHP?ASP?)
• Reviewing Team (how to organize, resolve differences of opinion, etc)
• We need a permanent domain name and url (eg mathweb.net, .org, .com, .ca?)

Budget and Funding

Initial Setup (1st year)
1/2 year release (possibly shared) for  project coordinator(s) ($35000)
liaison (meetings with international Math Metadata committees, etc)($5000)
student assistants (500hrs @$10/hr = $5000)
(to help with site identification and review and with page-by-page topic classification of complex sites - possibly supported in part by work-study programs)
web server hardware and connection ($2500+$100?/mo = $3500)
technical support ($7500)
software ($2500)
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Total                      $58500

Promotion (2nd year) (subject to "international" funding)
1/4 year release for project coordinator ($17500)
international Math Education meetings and orientation sessions ($10000)
internet service connection ($1200?)
equipment and software replacement/amortization($1000)
student aides (to help with ongoing site identification) ($1250)
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Total                       $31000
 

Ongoing (per year)
1/8 release for project coordinator($8525)
internet service connection ($1200?)
equipment and software replacement/amortization($1000)
student aides (to help with ongoing site identification) ($1250)
ongoing liaison ($1000)
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Total                     $13000

Note : These costs for "doing it properly" are many times less than what has been provided to related projects in the U.S., but of course something could indeed be done with a lot less - basically, we can adjust our activity to match any level of funding with an appropriate corresponding level of product.

Partnership Contributions

- partial release/ pd time
- web server and internet connection

business partnerships
 

Facilities

Statement of Work

  1.Design and implement a topic-by-topic guide to web-based resources in support of the learning and teaching of mathematics.

  2.Design and implement a process for dynamically updating the resource guide by addition of suitably evaluated materials, and by automatically checking for and removing broken links.

  3.Create and maintain a website and mailing lists to foster a community focused on the identification and evaluation of web-based math resources (particularly with regard to their suitability in support of the BC secondary and post-secondary curricula).

  5.Evaluate and report on the feedback gathered from the community pertaining to the above
    resource guide. Make recommendations for follow-up research.

In order to maximize access to the materials produced, all software, teaching materials, and
reports produced for this project will be made freely available on the World-Wide Web as open
source material.
 

Schedule

1. First half-year period

Set up website and mailing lists to begin community building and connect with other groups interested in similar research. Work out initial design for the service. Select software tools and implement a prototype to gauge the implementability of the design and suitability of tools. Start using the input mechanism to add resources from a small group of initial reviewers and collect feedback on the process and on the utility of its results.

2. Second half-year period

Use feedback to refine design of the service. Continue adding resource links and open the addition and review process to a broader community of site reviewers. Promote the service more widely and initiate a process of ongoing evaluation.
 
 
 

List of Key Personnel

Advisory Committee

Ethel Thayer - Canada's SchoolNet
Keith Taylor - University of Saskatchewan (originator of the 'Exercises in Math Readiness', and VicePresident-West of the Canadian Mathematics Society)
Malgorzata Dubiel - Simon Fraser University (President of the Canadian Math Education Study Group and Co-chair of the Education Panel at the Pacific Institute of Mathematical Sciences)
Bruce McAskill - British Columbia Ministry of Education
Klaus Hoechsmann - University of British Columbia  (Education Officer of Pacific Institute of Mathematical Sciences)
Jonathan Borwein - Simon Fraser University (Shrum Professor of Science, Director of the Centre for Experimental and Constructive Mathematics, and President-elect of the Canadian Math Society)
Gene Klotz - Swarthmore University, Director of the Math Forum (perhaps the preeminent center worldwide for mathematics education on the Internet)

(additional names and info may be added to this list)
 

References