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:
- the mentor, who provides procedural instruction,
exercises and activities for skill building and concept development,
and connections to other topics based on working experience with
K12 students;
- the peer, who recognizes common difficulties/mistakes,
knows what might be exciting, gives sample solutions, and links
to other sources of assistance.
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:
Stephen Weimar, coordinating the Math Forum's involvement, recruiting advisory board members and project staff. and overseeing effective use of the Internet,
one or more writers developing the other voices, along with support from several Forum teachers and math doctors,
a Web developer, editing and designing the pages and integrating Internet resources,
a programmer producing the code for any interactive aspects of the text,
six members of the advisory committee,
and the Forum evaluation team.
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.