REASONS FOR THE DEVELOPMENT OF THIS ON-LINE WORKSHOP

We believe that workshops, long a mainstay of professional development efforts for teachers, could be offered long distance by computer. Until recently, the technologies to do so, while on the drawing boards, were just not sufficiently advanced or readily available. But, with the explosive growth of the Internet and the associated technologies that make sending and receiving large amounts of data, pictures, video, sound, etc. relatively easily and quickly, all of that has changed. It is now possible to provide hands-on workshops for teachers (or students for that matter)over the Internet. And, we developed this particular workshop exploration to show how teachers could participate in such a hands-on, manipulative based workshop experience, long distance by computer.

To prepare for this first, innovative on-line workshop presentation, the authors initially presented the ideas in this exploration as a 1 hour more traditional, hands-on, onsite workshop for groups of teachers, to introduce them to Dr. Super's Triangles as a manipulative to teach pre-algebra, algebra and geometry ideas that students in grades 6-12 need to know. The workshop was presented many times in Northern Virginia and at several professional meetings of the National Council Teachers of Mathematics during the period, 1995 -1997.

As part of that workshop presentation, the authors extended ideas about the professional development of teachers who participate in work shop experiences in mathematics education first articulated in the prologue of the book, Teaching Mathematics with Manipulatives, (Allyn and Bacon,1993). They prepared an extensive, in depth resource packet for teachers who had participated in the workshop. The packet consisted of copies of all of the overhead transparencies used at the workshop and a very detailed, sequenced description of the actual workshop, ideas covered, answers to problems posed, teaching tips, etc. Teachers were given this type of detailed information so they would have ample resources on hand in the future, when it came time to incorporate what they learned at the workshop directly into their own teaching.

In early pilot tests with teachers, the structured workshop itself was quite successful. And, over time, the extensive resource packet should be an important key to potentially helping many of them maximize the benefits of the original workshop. In general, once teachers have participated in a workshop, many months often pass before they have an opportunity to try the ideas in their own classroom. And, for many teachers, with the press of day-to-day teaching and other things, frequently it becomes difficult to remember all that happened months ago or to recreate the relevant information. But, from previous experience with resource packets of the type provided for this workshop, by scanning such in-depth information after participating in the original workshop, many teachers will find that they had just the right material on hand to effectively recreate or remember or relive what they had experienced in the original workshop. And, then, from that recreation they are able to incorporate ideas previously introduced in the workshop into their own teaching with minimal curriculum development effort, expenditure of time, etc.

And, as the Internet in recent years has become more available and popular, it became evident that properly modified and adapted, the in-depth resource packet idea, essentially a sequenced workshop itself,could become an on-line workshop experience for teachers or an actual classroom activity for students. The workshop, even on-line, could be truly hands-on so long as teachers had the physical manipulative and a few activity sheets in their possession to use while they were doing the workshop on-line. [Eventually, we will have on-line virtual manipulatives that teachers will be able to use with point-and-click technology, too. But, importantly, we will always be using the physical manipulatives as well, since the concrete embodiment of math ideas is so very important as a first presentation for students. And, we believe, the concrete embodiment must precede or be simultaneous to the visual embodiment that would be presented using virtual manipulatives.]

So, here we are.

The exploration presented here is that final, first, professional development, on-line workshop from Dr. Super's Manipulatives Project of the Meta Media Math Program at George Mason University, Fairfax, VA.

Importantly, this exploration on the Internet is effectively exactly what you would experience if the authors were conducting an in-person, on site workshop with you. And, therefore, once you have completed the exploration on-line, you will have both the experience of the workshop and also the extensive review packet at your fingertips. The packet will be accessible to you, when you need it, either over the Internet or you can easily print a copy to have in your own files.

We ask teachers to keep in mind that having the workshop exploration in the form of an in depth resource packet to use at a later date is not intended to provide a script, per se, that should merely be followed to recreate the exploration for others, colleagues or students. Certainly, if educators desire, they can present the exploration to their students just as it was presented to them. That will work and some teachers choose to do so. But, that is not the primary purpose of this comprehensive set of materials.

The extensive resource packet is a part of this experience because improvements in teaching occur over time through the systematic efforts of teachers to learn new ideas; to think about how these ideas can improve their teaching; to actually write some of their own classroom curriculum materials; to try their materials with students; to revise their materials based on experience with students; and, then as a near final step, to add a new curriculum unit to their long term teaching repertoire.

The operational words here are: over time.

The demands on a teacher's time are such that it is virtually impossible to be exposed to a new idea today and be able to use it tomorrow in the classroom, in anything but a very cursory way. There is too little planning time, if any, given to teachers to make such rapid changes in curriculum or methodology, particularly given the in-depth knowledge often required to do so.

Thus, before teachers can seriously consider incorporating new ideas in their teaching in any meaningful way, there will usually be a long period from the time the new idea is introduced to the time the idea can be used in one's classroom. And, herein lies the dilemma.

Educators have attended excellent, introductory and motivating workshops for years. Often, they leave with the intent of using the new ideas learned. But, when they return to thinking about the workshop's content many months down the road, they realize they have insufficient information (from memory or handouts) at that time to recreate the workshop experience. And, therefore, they are frequently unable to build upon or modify the experiences in the professional development setting for their own classroom teaching.

The resource packet idea described here has been developed to solve this problem. Because the materials are an exact recreation of the workshop presentation, an educator who has participated in a workshop on this topic, in person or on-line, can quickly scan the materials and effectively recreate or relive the very experience they had at the workshop. And, in most cases, this type of "review" will provide sufficient information for the educator to translate the new ideas into actual classroom practice, regardless of the amount of time that has elapsed.

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