Electronically published with permission of the authors.

This is a draft, subject to change.

Written for News from the Center for Children and Technology , which is distributed free of charge.

Newsletter Editor: Katie McMillan

Contributor to this Issue Dorothy Bennett, Margaret Honey, Naomi Hupert, Terri Meade

Center Director: Jan Hawkins

Newsletter Design Antonella Severo

For more information about CCT/EDC or to add your name to our mailing list, contact us at 96 Morton Street, seventh floor, New York, NY 10014; 212.807-4200.

On-line learning, on-line communities

Telecommunications resources are becoming more readily available in schools, and student-focussed telecommunications programs and activities are proliferating. But using telecommunications technologies as tools for professional development is a subject still infrequently addressed. Teachers with in-school access to modems, computers and phone lines may be searching for useful curricular resources, engaging their students in pen-pal relationships with other schools or in multi-site science or social studies investigations, and exchanging e-mail with friends and relatives in distant parts of the globe. But relatively few teachers are using this technology to participate in structured educational experiences.

One possible explanation for the paucity of on-line professional development opportunities for teachers is that while many of us have discovered how to chat, joke, query, and argue on line, the kinds of substantive, sustained discussion that is central to learning can still be elusive in on-line environments. This issue is relevant for student learning as well - particularly as the idea of "virtual schooling" gains momentum. But most on-line activities for students are still mediated by teachers, who build on students' on-line experiences with discussion and elaboration in the classroom. Teachers looking for professional development opportunities are less likely to have someone present to play that role for them. So the task of providing a structured, rich, and inviting environment for learning within the on-line experience becomes all the more important.

In this newsletter we focus on the challenges of creating on-line learning communities for teachers. CCT researchers, in collaboration with the Bank Street College Mathematics Leadership faculty, are creating just such an environment in The Mathematics Learning Forums project. The Mathematics Learning Forums are one of a number of projects funded under the umbrella of the Annenberg/CPB Math and Science Project. The Forums offer K-8 teachers intensive eight week seminars on content and teaching issues in mathematics. The Forums are designed to help teachers introduce new mathematics teaching practices into their classrooms in accordance with current nation-wide mathematics reform efforts (see the bulletin board section for more information on the NCTM national standards).

About the Mathematics Learning Forums

The emphasis in the Mathematics Learning Forums is on using telecommunications to support a multifaceted learning process, which uses discussion among peers, discussion with a faculty facilitator/moderator, in-class experimentation, readings, and videos to bring teachers in contact with innovative teaching techniques for K-8 mathematics. Each Mathematics Learning Forum is offered over a telecommunications network, making it possible for teachers to communicate with colleagues throughout the country. Each Forum focuses on a particular area of instruction, such as mathematical content, student learning, teaching strategies or assessment techniques. An important part of the Forum is the use of videotape as a common "text." These videotapes provide participants with a way to examine classrooms in a range of school settings, and a concrete context for reflection on what is happening in their own classrooms. Articles for discussion and materials for in-class activities are also used, and on-line discussion builds on all of these resources (see page X for an outline of a typical eight-week forum).

Excerpts from introductory messages posted in a forum about patterns...

Welcome everyone! My name is Anne and I am a graduate faculty member at Bank Street College of Education. I will act as your facilitator for this forum. I came to Bank Street College after 30 years of elementary school classroom teaching and high school mathematics teaching in New York State Public Schools.
...it might be a good idea to get a sense of each other as teachers of students across this country: from Rhode Island to California. What are the things we'll find out we have in common in our teaching situations? How will we find we differ in our needs, strengths or concerns about math education? ...I look forward to your opening thoughts...
Hello, this is Helen from Austin, Texas. I am a first year fifth grade teacher. I have a self-contained class with 22 students. I have taught first, second and third. This is my first attempt to use the computer for anything.
Hello everyone. It has been so interesting to read about you all. My name is Michelle. I teach with the Department of Defense Dependent Schools, presently stationed in northern England. I teach 6-9 grade math classes, including Algebra I. Our school's curriculum is the same as any stateside school, just located in one of the most beautiful places in the world.
We are located quite far north. Because of that I am more aware of a certain pattern than when living stateside. The days are getting very short here. Soon we will have only about six hours of daylight, if the sun chooses to shine. The upside is that in the summer it is very light until almost 11:00 pm.
Best wishes to you all!

The goal of each forum is to help teachers do mathematics with their students, and to talk about mathematics with colleagues participating in the forum. Forums are hosted by a faculty facilitator and focus on the "how" of mathematics teaching, providing on-going support to teachers as they implement new approaches in their own classrooms. Throughout the eight weeks of the forum the facilitator's role is to raise questions, guide discussion, and provide reflective commentary. Participants exchange ideas, share concerns, and learn from one another's practices as they converse with colleagues and build an on-line community. Through doing and talking about mathematics with a community of peers and a faculty facilitator, teachers are supported in developing a new understanding of the learning process. Participants are encouraged to pay close attention to the learning of their students, their own learning and the experiences of their on-line colleagues.

Excepts from posted messages during the initial introduction of the forum content; in this case, the forum group was discussing patterns and their relationship to daily life and to mathematics...

So let's begin by sharing our experiences with pattern. How does pattern enter into your life? Have the children in your classes had any experiences with pattern in their past school experiences? Do they encounter patterns in their life outside of school? Do they use patterning in any way to learn about their environments? Do you have any sense of how patterns might relate to mathematics? Have you ever observed a child engaging in a patterning activity? What did you see? ...I hope your responses will yield insight into your students, your schools and your philosophy of teaching mathematics.
Yes, there are seemingly endless things that represent examples of patterns. Earlier in the school year, we collected data on the rising and setting of the sun so the students could use the data and connect it with a larger or more global picture of a pattern that drives the wind and ocean current which affects our daily lives.
If I were to use one word to describe pattern, perhaps it would be "orderly."
I've really enjoyed reading everyone's responses to Anne's "How does pattern enter into your life?" questions. I'm going to answer this question from another perspective. Pattern governs our lives because pattern is routine. All of us have a Monday-Friday pattern that differs from our Saturday and Sunday pattern. For example, sleep, eat, dress, work, play, etc. Yes, our students have experienced pattern in their school history. For example, they receive grades every nine weeks, change classes every 50 minutes, bring instruments to school on Wednesday, wear scout uniforms on Fridays, etc. Outside of school students experience pattern in after school activities, meal time, T.V. shows, etc. Students use patterns to learn about their environment in the science classes...

The Forums are activity-based, grounded in issues that arise through real practice. During the eight-week forum teachers plan, revise and implement activities with their students. The content Forums focus on elements of a topic within a content area, rather than providing a broad overview. These Forums are designed to introduce selected aspects of an area of study to teachers, and to introduce a variety of teaching strategies and approaches to the particular topic. Forums focusing on teaching, student learning, or assessment emphasize teaching strategies and approaches to mathematics that build on teachers' current practices and understandings.

Practical and pedagogical advantages of on-line learning communities

There are a number of practical and pedagogical advantages associated with building virtual learning communities for teachers. On the pragmatic end is the convenience of telecommunications. Because teachers spend the vast majority of their working hours with students in classrooms, there is little time available for professional exchanges with colleagues. Telecommunications affords teachers the option of communicating with colleagues at times which are convenient to them. The asynchronous nature of communication in this medium means that teachers can establish a rhythm for the exchange of ideas that meshes with the routines of their professional and personal lives.

Excerpts from posted messages, discussing the first reading assigned in the Patterns Forum...

Well, I really liked the article. It was concise and needless to say that since I'm always behind with things, articles that are clear and concise are great. To be honest, I had never thought of pattern as leading to function. This was a very interesting concept for me to think about. I had never thought of using a graph to show patterns. This is really neat, and I'm excited about trying this with my math class.
I couldn't agree more with the explanation of why we teach patterns. I believe that recognizing patterns helps us all make sense of the world around us. My frustration is in helping those children who do not naturally "see" patterns. What do other folks do for these children? I've often been at a loss except for exposing the children to many different kinds of patterns repeatedly. I hope to get more insights into how to help children see patterns through this forum.
In your responses to the first reading, those of you who have experience with very young children noted that the desire to find pattern and build meaning is very natural at this time. Then others of you shared that older children have somehow lost this enthusiasm for building their own understandings. What could have happened in the interim years - third through sixth grade - that could cause this? Dorothy doesn't believe that math is somehow special and only a few specially gifted children can master it. Do you agree with her? This is a crucial point...Why do some student get through the interim years mathematically intact and some lose their interest and enthusiasm?

On the pedagogical end, telecommunications offers an environment in which teachers can reflect on the nature of their professional work. Composing messages to a community of colleagues gives participants the opportunity to think about their work, to speak about the challenges associated with trying to bring about change in the classroom, and to learn from others who are also sharing their experiences. The process of promoting self-reflection and understanding by discussing the experiences and understandings of others is a phenomenon that well-designed telecommunications projects can actively support.

Building an effective learning community

In the course of working on the Mathematics Learning Forums project, we are learning a great deal about how to design effective virtual learning communities for teachers. Building a "safe" environment, creating rich and descriptive representations of practice, designing content that is flexible, and constructing a sound technical environment are all necessary components of this process.

Creating a safe environment.

In order for teachers to feel comfortable sharing the challenges associated with their professional work, it is crucial to build an environment where people can say what they really think and feel. Faculty facilitators who are attuned to the dynamics of on-line conversation are essential to the process of creating meaningful learning communities. Facilitating a forum involves paying close and careful attention to the words of all participants; it involves acknowledging both differences and similarities among participants, and finding aspects of conversation that can be built and expanded upon so that substantive exchanges occur.

It is hard to exaggerate the importance of an effective facilitator to the success of an on-line community. In addition to the choices that they make during the course of the actual forum, it is helpful if the facilitator brings certain qualities to their role from the start. If they are comfortable with the technology involved, then they can intervene when minor technical problems arise, and can guide people through nervousness or uncertainty about this aspect of the project during its early stages. Perhaps more importantly, experience with telecommunications means that the facilitator has had an opportunity to develop an on-line voice - that she has a style, a "tone of voice" she is comfortable with, that she feels represents her effectively and appropriately. When the facilitator offers this kind of established presence on-line, participants gain a clearer impression of who the facilitator is, and learn from her model how to present themselves effectively on-line.

Another important part of the facilitator's role is the choices that they make in how they structure their interactions. This process is influenced by the facilitators' prior experience as classroom teachers; each facilitator draws on techniques they have developed in face-to-face classroom interactions to create their on-line style. Does the facilitator provide a public voice, by only posting public announcements and never communicating through private e-mail with individual participants? Does she use private messaging occasionally, or frequently? And how should she pace the movement from early activities, that focus on introducing participants to one another and learning about each other's contexts and teaching experiences, to the activities that focus on the material to be covered? Different facilitators will address these decisions in different ways, and there is no single answer. However, in the Math Learning Forums we are learning that facilitators who bring prior teaching experience to the task, and who encourage the personal, introductory portions of the forum are often most successful in building substantive discussions of the content area later in the forum. The importance of establishing a base of knowledge and understanding among participants should not be underestimated.

Designing flexible classroom activities.

An important part of each forum is a set of activities that are designed for teachers to carry out in their classrooms. Classroom activities offer opportunities for teachers to experiment with, observe, and reflect on how their students work on and talk about mathematical issues. Project staff have found that while the character of the conversation among the facilitator and participants is important, the quality of the classroom activities teachers are asked to carry out are important too. The most important characteristic is flexibility - teachers need to be able to interpret and implement the classroom activities in ways that make sense for their students and classrooms. Teachers participating in the Forums teach in a wide range of environments, so activities need to be adaptable to a variety of teaching circumstances. (See the following pages for an example activity and some of the discussion it generated.)

Some practical issues that need to be considered when forum activities are designed are the logistical differences facing the geographically dispersed forum participants. Varying school schedules and varying curriculum designs mean that some teachers may be taking a forum on fractions while they are teaching something very different. Teachers' level of access to manipulatives, their comfort with taking on new classroom techniques and approaches, and their level of autonomy in the classroom all contribute to how they approach new math activities. Additionally, teachers' own math backgrounds vary widely, as do their students, so keying new activities to an appropriate level of difficulty for each new forum group can be a challenge.

Consequently, forum activities need to be presented as open-ended and adaptable - as a set of ideas and suggested structures, rather than as a step-by-step set of instructions. No two classrooms are alike, and particularly in an on-line community that draws together teachers from many parts of the country, allowing teachers to make the activities fit their own circumstances is a wise strategy for professional development.

Creating an inviting and flexible context for forum activities is also important. Activities need to be not just presented, but introduced - background material explaining where the activity came from, and how it relates to issues being discussed in the forum help bridge participants from conversation to active experimentation. Activities most often present an idea or question that can be addressed on a number of levels, sometimes of increasing complexity. Explanatory material needs to make explicit that these are not so much goals as possible points of entry, and possible areas for further exploration if students are able to pursue them. In a short, eight-week forum, it is difficult to avoid the urge to focus on goals, but the forum activities are most successful when they are viewed as explorations rather than exercises with clear beginning and ending points and simple criteria for success or failure.


Here's the second assignment for Week Two of the forum: look in your forum packet and find the description of the Tower Puzzle. Try the activity out for yourself. You may wish to invite a colleague or two to join you so that you can discuss your approaches to this activity and experience the enrichment that comes from listening to others' perceptions and learning styles. What insights, if any, did you gain about patterning in mathematics?
How will you provide for an experience for your students to gain and share their own mathematics insights after working on this activity?...it is a fine line that the teacher walks, in terms of providing enough structure to allow the students to do the activity but not giving so much direction that the students are being led down one particular path...
Well, I've tried out Activity One - Tower Puzzle. I must be honest and admit that I haven't had any insights yet as to where the pattern is. The problem I had wasn't with the activity, but rather with the lack of time available. I love to do problems like this, but I love to go off in a corner and just ponder for awhile; unfortunately, there was no time this week for me to do this. I was very frustrated with my performance...
The students worked on the activity for the full hour class period and their response when leaving class was "This wasn't like having Math today - it was like having recess from math." Oh, they did make me feel better when they solved the problem in fifteen moves. Actually, the first group had nineteen moves but when they went back and did the problem a second time, they solved it in fifteen moves.
Here are some responses from my students on the Tower Puzzle:

Eric states this: I did see a pattern in the number of moves it takes to move the tower of any number of blocks. The pattern is the following: the number of moves equalts two to the power of whatever the number of blocks in your tower you're moving (for example, if you have six blocks in your tower, it would be 2 to the 6th power) and then you subtract 1 to get the number of moves...

Yael reports this: I found a pattern. It is a pattern because it happens many times. If you had (for example) four cubes and you figured out how many moves it takes and you want to find out how many moves it takes with five cubes, then you take the number fifteen (the number of moves it took for 4 cubes) and then you multiply it by two and add one, so it equals 31...

Emily states this: the differences between each number doubles each time such as the difference between 1 and 3 is 2 and the difference between 3 and 7 is 4...So, when you look at the differences: 2, 4, 8, 16, there are a few patterns; 1) the differences are all even and 2) they each double…

...Not having any adequate recording system or device for looking for patterns in the moves was frustrating. They did come up with a prediction after we solved for three cubes. Like Joanna's group they thought that the difference would double. I wish I had seen Caroline's recording system. In fact, I think I will try this again this week using her system. I'm also going to be more structured in setting up groups and assigning tasks as Alyce did.
As I mentioned earlier, I have always had a hard time SEEING the patterns in this type of problem. I hope with some of the suggestions from all of you and from my children I will be better able to see the answer.
We also finished the Tower Puzzle on Wednesday...the fifth grade students were getting a little listless; they were frustrated that they had to really think about the problem, and that they couldn't solve it post haste. Comments like:
"it's impossible"
"this is hard"
"should we stop and think first?"
"we've tried that, it doesn't work" and
"we did the same thing last time"
were emanating from each of the four fifth grade groups.
...on Tuesday we'll briefly look at what they discovered and see if they can state it in terms of powers.

Constructing a sound technical environment.

Unlike other professional development projects, the Mathematics Learning Forums is not using a proprietary network or customized end-user software. Our goal has been to find the most effective means of disseminating the Forums for educators who may only have dial-up access to state or local telecommunications services. Providing a highly functional and easy-to-use service is critical to making these learning communities work. Forums are being run as listserves, which are broadly accessible and can be used easily by participants with only e-mail capabilities. Project staff are also working to archive forum discussions and materials in a WAIS database (see glossary, below).

Facilitators have several strategies available to them for dealing with participants' technical problems when they do arise. Technically knowledgeable facilitators can field questions themselves, passing only major problems on to technical staff. Other facilitators choose to discourage discussion of technical problems, advising participants to take any such questions directly to technical staff. We have had good experiences with a facilitator who integrates the whole issue of technical fluency into the day-to-day forum discussions, by disseminating a "technical tip of the day" to her group participants. By anticipating glitches, she has avoided many of them ever becoming real obstacles to participation.

Minimizing the technical difficulty of the on-line experience is particularly important in a project like this one, which depends upon the regular and substantive contributions of its members. If participants are discouraged by technical hurdles, they become less likely to ever develop a natural on-line voice. If, on the other hand, they experience the technology as relatively transparent, they will be far more likely to quickly create an on-line style, and a consistent way of representing themselves that is comfortable.

Finally, it is important to bear in mind that many teachers participating in Forums may have a very particular window of time when they are able to gain access to telecommunications resources. If this window of time is tight, or if the hardware supporting them is less than ideal, their whole experience of the on-line environment may be colored by their feelings of being rushed or frustrated. On-line providers need to minimize such frustration, so that the time teachers have to devote to these activities can be as unstressful and as stimulating as possible.

Other Key Factors for Successful Forums

Bulletin Board

The Center for Children and Technology (CCT) was founded at Bank Street College in 1981. In 1993, CCT changed its institutional affiliation and became a division of the Education Development Center. Over the past thirteen years CCT has undertaken a wide program of basic and applied research as well as prototype design and development. The mission of the Center is to investigate the roles technology does and can play in children's lives in general and in the classroom in particular, and the design and development of prototypical software that supports engaged, active learning.

News from the Center for Children and Technology is distributed free of charge.

Newsletter Editor: Katie McMillan

Contributor to this Issue Dorothy Bennett, Margaret Honey, Naomi Hupert, Terri Meade

Center Director: Jan Hawkins

Newsletter Design Antonella Severo

For more information about CCT/EDC or to add your name to our mailing list, contact us at 96 Morton Street, seventh floor, New York, NY 10014; 212.807-4200.

GLOSSARY: WAIS, listserve, asynchronous

Here are other guidelines to educational network projects.