Pages of Math

A proposal submitted to Instructional Materials Development
by C. Kenneth Fan, Institute for Advanced Studies, and
Stephen Weimar, Math Forum, Swarthmore College

Summary

"Pages of Math" will be a coherent, on-line mathematics curriculum covering essential mathematics taught in grades K through 12 (not including Calculus). This text grows out of and extends projects of the Math Forum such as Ask Dr. Math in which users interact with mathematicians and these interactions are archived as a resource for other users. These projects exploit features of the World Wide Web to enable independent exploration for remedial and advanced work. Our curriculum project will take advantage of the opportunities for non-linear learning, easy access to multiple approaches for problem-solving, and user involvement in a continuing development process. The text will be available free of charge to anyone with access to the Internet. Funding is requested for a one-year, proof-of-concept phase.

Need

If the Internet is going to make a significant contribution to education, there must be quality sources of instruction and information available on-line. A number of such resources are beginning to emerge, including many housed at the Math Forum. Unfortunately, most Internet resources are too fragmented and uneven in quality to be of use for extended study of a topic, much less for an entire subject. While the Math Forum and others are working with curriculum providers to establish on-line support and enhancements for their materials, there is a clear need, as demonstrated by the use of services such as the Forum's Ask Dr. Math (http://mathforum.org/dr.math/), for direct instruction on-line.

Additionally, from cognitive science research and from experience in Math Forum projects, we are increasingly aware that it is important to have different styles of explanation and assistance available to learners. This is illustrated well by the thousands of questions and answers archived on the Forum. One can see some learners thriving on the logic and systematic approach of the mathematician, while others simply need procedural support, and still others need the perspective of someone who has been confused in just the way that they are.

Dr. Ken Fan has stood out from the beginning of his volunteer participation in Ask Dr. Math for the high level of his mathematics, the clarity of his communication, and his ability to adjust instruction to the needs and situation of the user. Our proposal grow out of his realization that the different voices of the "math doctors" and the many different questions of the users provided essential elements for building a coherent on-line resource for learning mathematics in the K12 curriculum. Such a resource will present in one location the clear explanations and interactive examples that reinforce and extend classroom teaching beyond current limitations of scope, training, and resources.

Projects such as MegaMath (http://www.cs.uidaho.edu/~casey931/mega-math/index.html) have demonstrated the potential of the Internet to introduce important mathematical ideas to students of all ages. The proposed "Pages of Math" will enable the on-line user to connect these powerful ideas to the development of fundamental skills and to a broader context spanning many years of the K12 curriculum.

Description of the Materials

The goal is to create and provide free of charge a coherent instructional mathematics resource of the highest quality, covering core mathematics topics in grades K-12, to anyone with access to the Internet. During the proof-of-concept phase we will develop specific topics with a high level of interest and need in each area of K-2, 3-5, 6-8, and 9-12 as determined by project staff and the advisory committee through study of the Ask Dr. Math archives, a survey of the Forum user community, and a review of the evolving national standards developed by NTCM and others.

There are two major strategies which will be adopted to make this project uniquely effective.

First, in recognition of the many different approaches to mathematics, the text will not be written in a single voice. We anticipate using three voices, although during the first year we will research the literature and our own archives of interactions in order to define the most effective "personalities" and experiment with the process of fitting them together so that each voice has a distinct and worthwhile purpose. The user will be able to choose the personality from which to learn a topic, though the other two personalities will be only a click of the mouse away. Examples of personalities include:

Second, interactive features of the World Wide Web will be exploited both to pioneer a new curriculum development process as well to enhance the educational value of the product. The ease of interaction with users afforded by the Internet offers an unprecedented opportunity to publicly build curricular resources. Continuous feedback and usage by the wider community, as well as the easy integration of submitted and existing materials, opens new horizons for curriculum development and potentially redefines the timeframe and structure of this process. The curriculum emerges out of and directly responds to developing Internet communities that can then support its growth and implementation.

The resources of the Math Forum will be used to establish connections with other highly rated Internet resources and support contexts so that the user has the option of going beyond the boundaries of this text, both in terms of knowledge and assistance. Hypertext also offers an opportunity to not only connect to other resources but to reinforce prior concepts and direct the users to important relationships and themes that span topics. One of the most important benefits may be the capacity to present a coherent association of NCTM Standards within this Internet-based curriculum, thus facilitating the integration of these evolving standards and new technologies into the classroom. The Forum has begun to do this with some of its individual units. Additionally, every mathematical term will be highlighted so that if the user is ignorant of a term, the user simply has to point and click for an explanation and opportunities for exploration.

Ultimately, it will be desirable to have evaluative test questions generated in this environment. In this way, the student will be given different problems to solve each time that emerge from the path followed through the material and respond to his/her interests and capacities, in contrast to the set list of problems found in a traditional mathematics textbook.

Impact

It is expected that children who feel stymied in the classroom (both talented and challenged) will be supported in their desire to pursue the mathematics on which they want/need to focus, at a pace that suits them best. Testimony reveals that this is already the case with current Forum projects. In this instance it is facilitated by having the entire K-12 mathematics curriculum (excluding Calculus) available "at one's fingertips". This project also leverages the efforts of the Math Forum and others to support parent and wider community involvement in the education of our young people.

One of the benefits of this project is that one doesn't have to wait for completion in order to have others make use of what has been produced. The integration of this text with heavily used services such as Ask Dr. Math and the Problem of the Week will provide access to many users seeking this kind of resource. It also extends the value of the investment already made in the Math Forum's efforts by building on existing material and projects. Thousands of users make use of Ask Dr. Math each week, hundreds of thousands visit the Math Forum each month, and through the Forum's collaborations with others projects including several Urban Systemic Initiatives, many more will be introduced to the use of this resource. As a freely available resource, we will encourage use and incorporation of the text or individual elements such as the glossary into other mathematics pages.

Plan

The goal is to complete the full project in five years. A working version should be available in three years which covers the most essential and basic mathematics encountered in grade school. In the first six months of the proof-of-concept phase we will develop an outline and structure for the curriculum, write units on several key topics, research possible "personalities" and recruit other project personnel and an advisory review committee. This committee shall consist of teachers, mathematics educators, and mathematicians drawn from the communities with which the Math Forum is currently working such as the Presidential Awardees, AMA, and NCTM. It will critique and offer resources to the development of the text.

During the summer a project team will come together to begin developing the other voices of the text, program sample interactive elements, and produce units on additional topics. As these draft materials are made available and some production continues in the fall, project staff will respond to user feedback, questions, and contributions, experimenting with user involvement in the curriculum's development.

Initially the project staff will involve:

We will seek funding for the additional years of this project from the NSF if the proof-of-concept is successful.

Evaluation

The Math Forum evaluation team consists of Norman Webb, as external evaluator, and local evaluators, K. Ann Renninger (quantitative aspects of formative and summative evaluation of Forum projects) and Wesley Shumar (qualitative aspects of the processes involved in on-line community development, project oversight and Math Forum organizational development).

In the proof-of-concept phase this project will be integrated into the evaluation of Forum projects. This process involves initial user questionnaires, followed by focus groups used to establish rubrics for project development, on-site visits, and follow-up questionnaires in a six-month cycle. Initially the emphasis will be on gathering information about how the resource is used, suitability of the topics and structure, improvements desired by users, and the impact of user input on the development process.

Additionally, we will study the factors affecting the productivity of the project team, their responsiveness to rubrics, and the quality of the contributions of the contributing writers and user involvement. This study makes use of staff interviews, regular project reports, and email correspondence of the staff with each other, users, and collaborators.

In subsequent years, when enough of the text is done to permit use as a standalone resource for extended study, we will recruit teachers and students new to this resource to pilot this use of the resource. This study will parallel the continuing evaluation outlined above.