A familiar image in science fiction is that of the mad scientist working alone. But this image is far from the everyday reality of most scientists and may be the most fictionalized aspect of some science fiction stories. In reality one of the most striking facts about successful science is that it exists by virtue of communities of practice (Lynch and Woolgar 1990; Nelson, Megill, and McCloskey 1987; Pickering 1992). These communities are maintained by communication through professional societies, journals, research institutes, the linking of research with academic courses, graduate student development, team research, interdisciplinary research, electronic networks and data bases, and other organizational and technological mechanisms. Science does more than just employ these communication tools; it may fairly be said that science as a human activity is the progressive unfolding and enlargement of a community of inquiry manifested through various forms of communication and organizations. As Peirce (1867 [1958]) noted long ago, our scientific knowledge of the world is constructed by these communities of inquiry.

Educational research may also be characterized in terms of communities of inquirers. But educational research often lacks many of the linkages that appear essential to inquiry in other disciplines, such as those of the physical and biological sciences. Specialized terminology often serves to divide researchers from one another and from practitioners, rather than to unite them. Institutional constraints often hinder the collaboration needed to construct useful theories. As a result, the science of education that Piaget (1970) called for has not developed as it might.

The situation in education contrasts markedly with that of other applied disciplines. In applied areas such as engineering, medicine, and agriculture, the processes of inquiry, the research values, and the representational devices (mathematical formulas, graphs, diagrams, terminology, etc.) are closely allied with those of the corresponding disciplines within the basic sciences. A consequence of this is that basic and applied research, while not without conflicts, are nevertheless tightly linked.

In mathematics and science education research, practitioners are often cut off from researchers in their process of inquiry, and both are separated from researchers in the sciences and other domains of study. Teachers attempting action research often do so without the support of a collaborative research community. The communities that do exist are separated by discourse and by what they conceive to be the problems that need solving. Practitioners, who have the least formal training, the least financial resources, and the least time, also have the least social support for their investigations.

The lack of social support for investigations of teaching and learning--the absence of a vibrant community of inquiry--leads to specific practical difficulties. For example, many physics teachers view their task as one of communicating standard conceptions of energy and matter. To encourage questioning of these conceptions would contradict their view of their role as teacher. In contrast, many educational researchers would argue for the value of tentatively accepting and exploring both the alternative conceptions that students might hold and the standard ones. Practicing physicists might have their own strongly held and different conceptions of both learning and energy-matter. These differences are not at issue. They could be healthy differences. What is at issue is that there is little opportunity to engage in dialogue about the significance of the different views and for all involved to grow in their understanding within a challenging, yet supportive, community. The high valuation of research and dialogue within the scientific communities does not always carry over to research in mathematics and science education.

We have painted a picture bleaker than is deserved for education as a whole. In fact, our own collaboration is one counter-example. Jack Easley is a mathematics and science educator who has worked for many years from a university position to find better ways to support children’s developing conceptions. Chip Bruce has a background in computer science, but has focused much of his research on using new technologies to support writing. Much of his work has been done in a private company setting. These different backgrounds have contributed to the productivity of our collaborations.

There are also abundant examples of cross-institutional and cross-disciplinary communities in which researchers and educators are working together to effect change through action research. In these projects we see how different perspectives and experiences become assets rather than liabilities, and how mutual support leads to productive collaborations that bring about changes in practice. Unfortunately, many of these examples are restricted to language arts research, but they may provide excellent models for collaborative communities in mathematics and science education..

We will highlight here just two examples of successful collaborative communities for action research in language arts. The first example involves work on elementary school writing and reading in New Hampshire. This research began when Donald Graves, a professor at the University of New Hampshire, received an NIE grant to study the development of children’s writing. Believing that it was necessary to look beyond the laboratory, Graves went to classrooms to observe what children actually did when they wrote--how they held a pencil, how they used the space on a page or the time they were allowed to write. He also began to examine the larger social and institutional contexts for writing, such as the fact that schools spent many times more dollars for textbooks than for materials to support writing, or that purchases for lined paper, which was used for writing, were outpaced by purchases of the blank paper used for ditto worksheets.

Soon many others joined and extended this research community. Lucy McCormick Calkins conducted a two-year study in a school in Atkinson, New Hampshire, which led to the publication of her widely-read Lessons from a Child: On the Teaching and Learning of Writing. This work was a collaboration between Calkins and the teachers, Carolyn Currier, Pat Howard, and Mary Ellen Giacobbe, and the principal, Jean Robbins, in Atkinson. But it also involved university researchers, such as Graves, Susan Sowers, and Pulitzer Prize winning author Donald Murray, who also taught at the university. As they worked together to develop better ways to support the teaching and learning of writing they also learned more about writing. Ideas such as the widely used writing workshop emerged and expanded through work in the classrooms.

Those involved shared many things, including the belief that good teaching must be based on listening to children. They also believed that writing was important as a means of self-growth, as a way to learn, and as a way to participate in a social world, not just as a set of skills to be demonstrated on a test. Because of this they all felt that they should be writers, as well as people studying or teaching writers. This writing was not necessarily for publication, but for constructing their understandings of what they observed and of their own writing processes.

At the same time, participants brought different experiences to the new community. Some taught professional writers; others taught children in kindergarten. Some focused on creating publication outlets for children’s writing; some were more concerned with connections between reading and writing; all had to confront questions such as "But what about spelling?" Their collaborations became multiple and soon extended far beyond the initial projects in southern New Hampshire. The ideas and publications from this work continue to pour out (e.g., Atwell 1987; Hansen, Newkirk, and Graves 1985; Newkirk and Atwell 1988; Roderick 1991). This research, collaborative and action-oriented, was deeply grounded in real classroom practices and in the understanding of children. These are some of the reasons that it has transformed writing instruction in many schools around the country and throughout the world.

Starting in 1981, a group in Cambridge, Massachusetts began developing Quill, a computer program to support the teaching and learning of writing (Bruce and Rubin 1993). The Quill project replicated some of the experience of the New Hampshire writing research. In order to design a program that made sense in the classroom the researchers needed to start by working in classrooms. The research became a true collaboration between software developers, writing researchers, teacher educators, school administrators, classroom teachers, and others, including, of course, the students who used Quill and continued to push its limitations.

Perhaps the most successful work with Quill occurred in Alaska. As in other sites, collaboration meant finding ways in which people in diverse institutional settings could bring their special expertise to bear on common problems. Ron Scollon initiated the Alaska Quill project in part because of his extensive work with and concern for the education of native Alaskan children. He was soon joined by Carol Barnhardt, who shared those concerns and was working closely with schoolteachers in Alaskan villages. Almost from the beginning, teachers such as Bonnie Bless-Boenish began to shape the project as well.

Teachers in Alaska who worked in small villages were also concerned about communication: How do you stay in contact with people hundreds of miles away, when there may not even be a road connecting with them? This shared need was one of the reasons why communication through electronic networks was already established at the time the Alaska Quill project began. It was thus natural to explore how networking could be used to support the project. Soon there was an Alaska Quill communications network, built on a clumsy patched gateway between two established networks. But the patch was not an issue. What mattered was that people felt a sense of community, and a shared mission. Because they felt these things, they used the network to share discoveries, teaching ideas, tips for equipment use, and often, frustrations they all experienced. As with the other writing projects described above, discovery and improved teaching grew inseparably out of the interactions of a diverse, but united community.

This is not surprising, since as Dewey outlined so well in Democracy and Education (Dewey 1916 [1966]), "community" and "communication" share more than just the same Latin root. Through communication we are able to establish what is common (another descendant of Latin "communis") among us--our shared beliefs, values, and goals. These shared things are the basis for our communities, which are in turn established, maintained, and expanded through communication. Communities for action research around language learning make sense because participation in the community is part and parcel of the object of the research. Students, teachers, and researchers used the Alaska Quill network not just to carry out research on other phenomena, but to embody the very processes they were engaged in studying.

What then of action research communities for mathematics and science teaching? The picture of separateness between school and university is a little bleaker in mathematics and science education than it is in reading and writing. This could be because participants may not conceive participation in an action research community as being both a means for supporting that research and an essential element of the research itself. Sociologists of science have emphasized the importance of community and communication in many areas of scientific research (Latour and Woolgar 1986; Lynch and Woolgar 1990; Pickering, 1992; Star, 1988), but that insight has not been accepted fully in some realms of mathematics and science education research.

However, action research communities in science and mathematics are emerging as mathematicians and scientists volunteer to help schools reform. For example, the National Academy of Sciences and the Smithsonian Institution train leadership teams in elementary science composed of school administrators, teachers, and scientists, and the National Science Foundation urges research groups in the sciences to collaborate with public educators in educational reform projects. Educational researchers, e.g., the National Association for Research in Science Teaching, (Shymansky and Kyle 1991) have collaborated with scientists to plan science education research in a new mode, including action research. We tell a story, here, of an inter-institutional community that emerged from research projects in primary school mathematics. It demonstrates the need for new kinds of alliances, organizations, or perhaps new kinds of institutions to effect educational change.

The story begins with a paper called "Teaching by listening" (Easley and Zwoyer 1975), which showed how children were able to engage more deeply in the process of mathematical thinking when they were encouraged to articulate their own, perhaps unconventional, ideas and not just listen to the teacher. Through this telling, the children often revealed aspects of their thinking that could provide invaluable guidance to the teacher. For the teacher, this approach called for a new way of thinking about the teaching of mathematics, one in which the teacher’s role was not to transmit mathematics to children who knew little, but to listen to children as a first step in nurturing their construction of mathematics theories.

Studies of teaching by listening continued with the support of an NIE grant (organized by Zwoyer in 1977). The purpose of the grant was to learn more about the ways K-3 children discover and talk about their concepts of number and numeral. Easley led a team of clinical interviewers who worked directly with children. A mathematician (Peter Braunfeld) examined the number system in relation to what the clinical interviewers were learning from children. A mathematics teacher educator (Harold Lerch) studied the use of hands-on mathematics materials by teachers. The successful collaboration among educational researchers, teachers, mathematicians, and children meant that the collaborators learned from each other and that the results of the research had a richness and grounding not possible through more separated research. One finding was that there was a large gap between mathematics educators and children's ways of thinking in mathematics.

Easley and Bernadine Stake then began work with primary teachers in places as diverse as Chicago, Kankakee, and Urbana. Early in this research they learned that when experts demonstrated their best methods in the teachers' own classes, they relied on backgrounds of mathematical ideas and a confidence with mathematical dialogue that the teachers did not share. Thus, teachers were often unable to emulate these innovative teaching methods. Moreover, the teachers were not learning how to learn as teachers. Demonstration and imitation was not an effective way to foster learning to teach.

The research revealed great differences in mathematical ideas among children, teachers, administrators, educational researchers, and mathematicians. These differences are perpetuated through lack of communication among the groups. Each group is isolated from effective communication with the others about how to improve teaching and learning.

The researchers decided to address these learning and communication problems directly. They called a meeting of volunteers from the adult groups mentioned above. Enjoying the prospect of breaking out of their institutional isolation, members volunteered to meet for two days (Friday-Saturday) every fall and spring and have been doing so ever since. A new institution, called DIME (originally Dialogues in Mathematics Education), came into being from an effort to break down communication barriers between groups who played different roles in existing institutions. Communication opened up with two other groups: mathematicians, administrators, and, in one classroom after another, also with children.

The most recent DIME meeting had 14 elementary teachers, 1 elementary principal, 3 mathematics education specialists, 1 speech therapist, 5 university educators, 2 mathematicians, 1 physicist, 1 education undergraduate student, 2 education graduate students, 1 museum educator, 1 art student, and 2 educational consultants. Other meetings have included secondary teachers, scientists, and members of other professional groups. More than 8 school districts in three mid-western clusters have been involved. Regular DIME meetings, originally held in Urbana, soon began in southeastern Michigan and Carlinville, IL. The enthusiasm and attendance has remained high, despite the increasing difficulty for teachers to get professional leave to attend on Fridays.

Visitors at DIME meetings were frequent. Eventually, DIME teachers broadened their concerns to other areas of the curriculum, first to science teaching and learning, and then to literacy and the arts. To reflect this expansion of interests, the name of DIME was changed to Dialogues in Methods of Education.

Collaboration in classroom action research was central to DIME from its inception. Because of the previous research showing children’s ability to grow through responding to challenging problems, and the work showing the importance of dialogue in learning, an initial focus was the use of challenging story problems in small groups. This approach has remained an important theme in DIME meetings, and has been adopted and adpated, in one form or another, by most DIME members. Although it has spread as a method, it remains as an hypothesis to be explored, rather than a practice to be adopted without critique. This is true of all the methods presented in DIME meetings; methods are not to be copied but examined and improved.

While teachers shared story problems at DIME meetings, that sharing did not give them enough problems to sustain their own reform efforts. They were on their own to find more. Many were able to invent sources of more such problems. Cross-age interaction of mathematics students in problem solving (developed by Rhonda Priest in Carlinville, Illinois) provided a ready source of good problems. It meant tutoring help for the younger children in her class, and had substantial learning benefits for the older students and their teacher. Approaches such as these were shared at DIME meetings, adding to the ongoing dialogue about teaching and learning.

Over time, DIME members adopted a number of general principles. One was the listening to children notion that had informed the earlier research of Easley and Zwoyer. They saw the value of clinical interviews, which respect and help us understand the ideas of children, no matter how bizarre they may seem from a standard adult view. They also saw came to understand that differences in mathematical ideas exist among cultures, and among children. Perhaps most importantly, they saw that dialogues between people of different views are valuable as a basis for understanding and improving our own views on any subject, from mathematics to the role of a teacher.

An example of a current issue in DIME discussions is the explicit or implicit choice of themes in mathematics instruction. Textbooks typically present a fixed sequence of operations, skills, and facts, so arranged that what you study today may be perceived as absolutely essential to what you study a day, week, month or year later. Teachers often stress other themes they find appropriate to mathematics. They may stress discipline components with a moral tone such as neatness, promptness, following directions carefully, doing your own work, etc., which they perceive as making a big difference in success throughout later study of mathematics.

Could they stress, instead, general themes of a more mathematical nature? One example might be the computation by decomposition of numbers until the results of appropriate operations on the component parts are known, followed by reassembly of the results as needed. A similar theme is decomposition of shapes into elemental shapes. Another useful theme is measurement. Each of these is powerful, and has the property of relieving the student's dependency on sequence or discipline themes. Within DIME, all of these possibilities are treated as possibilities to be explored, critiqued, and shared, not as new methods to be imposed.

Over the 12 years of DIME's history, several offshoot projects emerged:

• Several local DIME groups were formed and met for varying periods of time.

• Teachers collaborated with educational researchers in various action research projects (Easley and Taylor 1990; Easley, Taylor, and Taylor 1990).

• Groups of teachers collaborated on research proposals. One of these investigated problem-solving dialogues in groups of children. Another is developing materials conforming to NCTM standards across a district.

• Three writing conferences were held; seven teachers published articles and presented conference papers about their teaching innovations in educational journals.

• A newsletter has been published for 12 years, giving news about meetings and publishing articles on classroom practices and research.

DIME members have valued informality in the meetings and have not been inclined to institute bylaws, offices, committees, or other organizational trappings. Nevertheless, a shared culture has emerged in which implicit rules govern key aspects of social interactions. We have identified three such rules that facilitate communication among the members.

One rule is that everyone has something to contribute. A moderator ensures that every attendee gets a chance to take the floor, at least once during the two-day meeting. This may be to share student work, to show a videotape of classroom interactions, to report on a conference. to share a new teaching method or curriculum materials, or to present a professional problem and seek advice, such as how to work better with teachers in the school who operate from a different pedagogical philosophy. Although interactive dialogue is the norm, others wait their turn to make their presentations. This rule can be viewed as the logical extension to adults of the teaching by listening principle that emerged independently in the research on both language arts and mathematics learning,

A related rule is that divergent views are always accepted. DIME members generally espouse teaching by listening, hands-on learning, cooperative groups, the use of manipulatives in mathematics, problem-solving, whole language, and other progressive educational practices. But they do not view any of these practices as perfected or final, nor as dogma. Moreover, they extend their philosophy of learning to adults. Thus, both new and old members are given ample opportunity to articulate their ideas and to explore the consequences.

A third rule is that no standpoint, e.g., formal educational research, is privileged above all others, and no standpoint, e.g., the beginning teacher, is devalued. The goal is not to find a single truth and no one method is assumed to be adequate for determining the best approach to teaching. Instead, members work to discover what each perspective offers, viewing their own accounts of teaching and learning as provisional and subject to revision in the light of continued dialogue.

A fourth, rather specific rule, is that no one can make a second point until the group has a chance to discuss the first point. This was instituted in response to some early meetings in which some members had a tendency to make speeches. People talk naturally, and even heatedly at times, about each others' concerns, often late into the evenings.

A fifth rule is that good learning activities can foster dialogue. Participants at DIME meetings often visit schools in session, and new kinds of communication are experienced between adults and children. At a recent DIME meeting, participants visited the Wiley elementary school in Urbana, where teachers had been working in teams with university students to develop kits to support interdisciplinary science learning (Fortschneider, 1992). DIME members observed students using the materials the Wiley teachers had developed. Freed for the moment from the need to manage their own classroom, the visitors were able to observe the use of the kits, talk with students about their projects, and listen to their developing conceptions of scientific phenomena. Although worthy as curriculum materials, the kits served the more significant function of enhancing dialogue among teachers and between teachers and students.

Discussions within DIME and reflection on the DIME experience have highlighted two contrasting models for teacher change. The first of these was tried in the early days of DIME, but is now seen as having limited usefulness. In this model, innovative activities are developed, perfected, and then disseminated. The forms of the dissemination may vary greatly. For example, student textbooks implicitly define a type of teaching and are thus one way to spread desired forms of teaching. Teacher's guides provide even more direct guidance for teachers to follow. More recently, videotapes and videodisks provide models of teaching excellence. Scope and sequence charts can be used to define the content and order of teaching, and thus serve as another route for dissemination. Observing expert teachers and imitating their practice is another route.

Figure 1 represents this approach schematically as the Demonstrations Model. In this model, innovative activities or teaching approaches are developed, and then, through an essentially imitative process, teachers incorporate these activities into their own practice. The pervasive problem is that, even when the model is excellent, the copy is less than ideal. Part of the explanation for this is that assimilating the practices of another into one's own system is difficult. But a more fundamental issue is that the so-called innovative activities are typically but the surface manifestations of deeper processes. A teacher may have been able to develop activities that work for her and her students because she learned how to listen to what they were saying. But the hours of listening and struggling to understand are not immediately evident in the 20-minute demonstration that grew out of that listening.

Figure 1. Outmoded demonstrations model for teacher change.

A contrasting model for teacher change has emerged through the DIME experience (Figure 2). Here, change is viewed as an ongoing process within a community of inquirers. There are no sharp distinctions between experts and novices, but rather a recognition that each person has experiences worth sharing. Educators in various roles have contributions to make, but ultimately any insights about teaching and learning must be related to what is learned by listening to children. In a learning community model there is no point at which one can say that the method has been perfected and is ready to disseminate. Instead, teachers continually share their insights, their questions, and their frustrations to help each other develop a richer and more fruitful understanding of teaching and learning.

Figure 2. The learning community model for teacher change.

Members of DIME have learned many things. What follows are some shared ideas that have percolated within and beyond DIME. This learning guides us now in continuing collaborative efforts to develop a broader, and more effective educational reform. The "we" in the comments below is meant to refer to DIME members or to any of us who takes on the difficult task of helping children learn. Some of these emerging ideas within DIME pertain directly to teaching and learning:

• Adults often underestimate children’s capabilities for strong mathematical and scientific thinking.

• If children are not challenged by difficult problems they sometimes conform to low expectations.

• Many of us can easily facilitate dialogue among children in large or small groups. Consider, for example, how we resolve a playground crisis. But that dialogue facilitation role may be more difficult to assume in mathematics or science lessons.

• Lack of mathematical knowledge is not what blocks us from listening to and supporting pupils' mathematical thinking. Instead, it is the widespread but questionable assumption that we need to be the classroom authority and judge on all matters of instructional content.

Other ideas within DIME relate to the process of change in teaching:

• We do not invent or adopt new methods "out of whole cloth" but modify known methods to improve them.

• We need good examples, if we are to try something quite different from the methods we know already.

• But examples alone are never sufficient.

• After trying a new method, we need to criticize it and modify it to make it work better.

There are also several ideas in the DIME community regarding the challenge of building communities of inquiry around issues of teaching and learning:

• We don't always share our ways of doing things with our colleagues--especially if we suspect our approach or methods won't be appreciated.

• We find it difficult to work in ways that obviously differ from those our colleagues seem to trust.

• Established institutions impose constraints of time, schedule, or custom that hinder collaboration, communication, and reflection.

• Most of us share in family and household care as well as earn a living. If schools cannot provide the time teachers need for conferencing, then teachers may be on their own to find it.

The examples in this chapter show diverse ways in which people have collaborated in action research communities. We could go on to look at many other examples, such as the North Dakota Study group, the Whole Language Umbrella, and many other successful efforts without formal names and citations. Although these efforts exhibit a variety of histories and forms of collaboration, a common theme is that their structures have emerged from consideration of the needs of the individuals taking part in them. Thus, successful structures follow from the goals, interests, and concerns of those engaged in the action research. A corollary is that dialogue within the collaborative is essential, not just to exchange information, but to shape the participation of the members. It is noteworthy that supportive dialogue thus serves as a teaching approach, as a research tool, and as an essential element for successful collaboration.

The experiences of the literacy-oriented action research communities show that we need to invest effort in creating action research communities for mathematics and science education. We might do this by creating extra inducements for participation in such a community. Or, we might need to ask whether we should enlarge our conception of mathematics and science to encompass the kinds of communication that occurs in these communities. After all, the sociology of science is replete with analyses showing how communication, through talk, conferences, reading, writing, diagrams, charts, and tables, and so on, is at the heart of scientific practice (Latour and Woolgar 1986; Lynch and Woolgar 1990).

Teaching mathematics (or, for that matter, teaching any aspect of the curriculum) is not a skill learned through imitation. That this is so, may be more evident by consideration of learning in less intellectual areas. For example, physical education experts now call for individualized programs in which the learner is urged to "listen to your body" as a necessary condition for deciding what kinds and amounts of exercise are most helpful. Imitation is not enough; the learner needs to build a knowledge base and continue to ask questions about what, when, where, why, and how. If this is true for an apparently routinized activity such as calisthenics, it must be even more the case for the complex and dynamic intellectual task of teaching mathematics. The experiences of the DIME group have reinforced this idea for the teaching of mathematics, and more recently for the sciences. Rather than relying on demonstration and imitation, teacher growth and curriculum development call for collaborative communities of inquiring professionals.

We would like to thank the members of DIME for providing not only the inspiration, but the insights for this chapter. We would also like to thank David Brown, Laurie Beckelman, and Molly Watt for helpful comments on the manuscript.