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.
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).
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...
Anne
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.
Helen
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!
Michelle
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.
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.
Anne
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."
Dorothy
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...
Sheila
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.
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.
Sheila
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.
Jim
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?
Anne
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.
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.
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...
Anne
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.
Sheila
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
doubleÉ
Dorothy
...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.
Jim
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.
Sheila
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.
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.