The Math Forum conducts projects that seek to find effective uses of the Internet for mathematics education: Problems of the Week, Ask Dr. Math, Teacher2Teacher, online discussion groups, Web Units, an Internet Resource Collection, and workshops for teachers. We research the use of these services and the participation of teachers, students, parents, and others. The following observations are drawn from these experiences and related studies.
I. KEY ELEMENTS OF THE INTERNET FOR THESE PURPOSES:
Access to and interaction with persons and resources at a distance
Archiving and retrieval
The opportunity for anyone to publish
Hypertext, links between resources, and different types of resources
Up-to-date, responsive to the new, rapidly changing materials
Information and data focused
Academic and scientific origins
New, not-yet-settled or packaged
II. WHAT ARE SOME OF THE IMPORTANT USES OF THE INTERNET
FOR MATHEMATICS EDUCATION?
- Conversations about mathematics and education:
- Teachers and students connecting to mathematicians, hobbyists, professionals in the field, peers
Multiple perspectives; mathematics linked to history, culture, situations, tools available; enriched by different approaches.
- Individualization and personal support:
- easy access to a wide range of material
variety of constructed learning environments
a place to ask unanswered or withheld questions, to have someone's attention
the potential to teach people rather than the text
breaking past the limitations of the persons and resources in the classroom
- Choices offered by the Internet enable students to focus on interesting problems with, in addition, opportunities to practice. Contact with the richness of mathematics. Students are more likely to treat mathematics as mathematics rather than as a constrained sequence of techniques or topics.
- Collaborative problem-solving: "The Noon Observation Project" and "The Great Penny Toss" linking students around the globe.
- Problems in context, applications of mathematics, mathematics as a live discipline, relevant (Godzilla problem), problems supporting modeling.
- Being current and relevant sustains momentum of thought. How to catch student interest? Interest as more than motivation. It also makes it easier to approach what may otherwise be assumed is out of reach: advanced research, science in the news. Connecting learning to the world outside the classroom.
- Pursuit of interests & independent inquiry
- What we see: students culling from the Web, asking questions, publishing results
- What's not happening: help with questioning and other inquiry strategies. Not getting help knowing what techniques they’re learning or how to build knowledge. Reflection is missing.
- What we need from NCTM writers and others: review of the resources, collect the best, and assess the organization of materials to see if it matches the priorities and frameworks called for.
- Construction: growing by creating and interacting and communicating.
- The Web supports joint ventures/partnerships in learning and teaching among students, teachers, parents, and others, with roles shifting in the process.
- Continuing professional education: online courses, shared course materials, etc.
- audience for student & teacher work
III. WHAT ARE THE CHALLENGES?
- Access/Infrastructure: there are not enough reliably working computers in classrooms to do what's needed when it's needed.
- Quality, amount, and effective organization of mathematical material.
- Professional education in the use of technology and models of implementation are needed.
- Math notation and the display of mathematics are underdeveloped on the Internet.
- Computers can be a time sink.
- Presenting a core curriculum or curriculum process that teachers can hold onto while elements are rearranged or that supports change/evolution.
IV. MATHEMATICS ENCOURAGED BY THE INTERNET:
(geometry, calculus, and discrete resources in abundance)
Not encouraged: algebra
V. NCTM STANDARDS ISSUES STRONGLY ECHOED ON THE INTERNET:
Which topics to teach?
Sequencing of topics and conceptual connections (NCTM writers as guides)
Mastery of computation vs. problem-solving/inquiry/question-asking
Communication in mathematics
What does teaching/learning [homework] look like when one can look up the answers?
VI. WHAT DO WE KNOW ABOUT TEACHERS ON THE WEB?
[In approximate order] They want: to find resources, to know how to teach _x__, answers to math questions, to make lessons, to find colleagues/an audience, to learn about a textbook/reform program, recreation.
We're investigating the role teaching experience plays in the use of the Internet, currently studying some possible gender effects. Who is more likely to spend more time exploring and trying to implement?
Independent learners overcome hurdles. Indications are that there's a lag of 2-3 years before others come along, attracted by the success and results. Some teachers want sequences, curriculum fit. Others want to gather and construct. The Internet facilitates both. It's a good medium in which to publish.
Collaborations and team-based approaches help teachers produce material. Exploring these ideas through ESCOT projects, leadership development program, etc.
Politics and opinion-slinging easily assert themselves in open discussion groups. Topic-specific groups and narrow subscriber bases are more likely to yield grounded conversation in mathematics concepts and classroom activities.
Many teachers seek or need broader mathematics education.
Learning new techniques and technology is hard for many. We're studying for whom, and under what conditions. Learning can be by doing discipline-specific work (one of many reasons why Standards materials need to incorporate technology references). Students and teachers often switch novice-expert roles in this respect, which is threatening for some and offers new opportunities for others.
We need models of use/integration/implementation in the classroom.
Teachers/researchers/parents often do not evidence the learning strategies in discussion groups and in workshops that we want taught to students.
Elementary teachers may appear to be less apt to use new technologies. This could be correlated with the relative dearth of materials and mathematics at their level, in addition to differential allocation of money in schools.
Teachers want challenges and activities for their students to do.
Teachers are not generally writers. The majority are better situated to share their students' work, tell stories, and reflect on these, with lessons and conceptual frameworks supplied by others.
VII. WHAT DO WE KNOW ABOUT STUDENTS ON THE WEB?
Students seek answers, interesting problems, games, and manipulatives.
Good questioning strategies are more visible in Problem-of-the-Week mentored environments than in more anonymous settings where there's not much back and forth.
Students create, construct, and shape spaces for themselves. They get into showing each other pages and discussing ideas encountered. Active engagement. But does it also lead to depth of understanding?
Students are motivated by real-life situations, although this may have been more visible before Problems of the Week became more institutionalized. They are also motivated by the novelty of the medium, self-expression, and access to experts.
We're investigating the role of interest. Interest doesn't predict who will arrive at a solution, but the qualities of the problem-solving approaches appear linked to interest, with students who have an interest in math working over time, asking more questions, using multiple approaches, seeking feedback, taking breaks, etc.
Significant use of the Internet takes place outside of class.
Anonymity provides safety to recover interest in mathematics.
The Internet is about communication, and there is much practice writing mathematics and writing about thinking and experiences.
In the Problems of the Week, the problems closest to traditional textbook exercises get the greatest number of submissions. We're investigating the hypothesis that this results from teachers being more likely to assign these problems.
The easy access to problems and projects on the Web helps to draw in the family (which raises the question about whom we're writing Standards for).
More elementary students do problems because they're required; then because they're interested.
There are more students participating from schools/classroom accounts, but next most frequent are personal or family accounts. Many homeschoolers are making use of these resources and showing their appreciation. How will the opportunities presented for learning via the Internet outside of the school context affect schooling?
VIII. IMPACT ON THE STANDARDS PROCESS AND WRITING
The fact that anyone can publish and that many can have access to so much material suggests an even stronger emphasis on the Standards as a process involving culling, organizing, framing, articulating what is needed, and providing opportunities for development of new resources. The Internet is an ideal vehicle for publishing the Standards because it lends itself to evolving material, to making use of the good work of others, to providing structure while enabling local configuration. What is needed is a foundation for others to build on and a process for contributing and commenting, coherent organization of what is available, and assessment of the value of materials--the Standards as an enabling process.