The Math Forum's Advanced Summer Institute (sum98) began this noon with a graph theory game on the lawn outside the College guest house, Ashton House. Each participant wrote her or his name on a piece of paper. Ken, Steve, and Dave then linked these pieces of paper, as well as two blank "nodes," with masking tape to form a graph with several cycles and dead ends. Folks randomly re-settled on a node that did not necessarily bear their own name. Our shared objective: to move people along the paths of the graph, advancing one person at a time and only to connected unoccupied nodes, so as to achieve a state where each person stood at the node bearing her or his name. To lend some order to the movement, we introduced a tennis ball; whoever held it could advance to an unoccupied node or could toss it to anyone else on the graph. After upwards of half an hour, scores of moves, and many more hypotheses and suggestions, we achieved our objective and retired indoors to a hard-earned lunch.
Following lunch, Steve provided an overview of the sum98 agenda. As a way of demonstrating the Forum's continuing explorations into math education on the Internet, and to encourage participants to realize their own ideas employing Forum resources, he highlighted two projects that the Forum is currently developing, Pages of Math and ESCOT. Steve then distributed "uniquity" game photocopies to further our mastery of each other's names, and to get us to discover something unlikely about one another, or something that is not likely to be true of anyone else in the group - for example, that Annie is a descendant of William the Conqueror.
From here, we moved to the second-floor computer lab in Trotter Hall. After some inauspicious network connection woes, we began tailoring the Trotter PowerMacs to individuals' needs so they could read their e-mail and the like. Steve re-introduced the Online Communication page detailing the what, when, where, and how of sum98. We then walked through BBEdit (v4.5), an HTML and text editor with which participants will construct and edit the project pages in their folders.
One BBEdit feature highlighted was the file pop-up menu, the third of five lavender boxes in the status bar of a BBEdit window: set this from the default "Macintosh" to "Unix," as this will save Forum staff subsequent work in manipulating these files on our Unix server. One helpful HTML tag raised during the BBEdit introduction was the use of server side include (SSI) statements, which allow a web page author to include the same HTML snippet across many pages. For example, the SSI to call the Forum's top menubar into any Forum web page consists of the HTML comment tag
<!--#include virtual="/snippets/sum98.menu.html" -->
As the participant pages reveal, SSIs greatly facilitate a coherent "feel" - both aesthetic and navigational - for a set of related pages.
After participants finished preliminary passes at their project pages, Dave discussed how to use the Math Forum search engines. In addition to the main search engine, which now offers some spell-checking functionality and returns starting points for many of the most common queries, Dave pointed out two helpful pages for assembling web resources: the Power Search engine, which offers checkboxes for many common categories (e.g., elementary level, lesson plan resources) and subtopics (e.g., trigonometry) as an interface for searching the Forum's extensive Internet Resource Collection; and the Search Specific Forum Archives page, which lists many of the Forum's search engines for specific projects, such as the Ask Dr. Math service and the Middle School Problem of the Week.
Suzanne Alejandre then shared her ideas, tips, and tricks for finding resources on the Web. Her page's layout and concluding discussion questions elicited some immediate feedback. Steve called attention to Suzanne's use of categorizing the links she offered on her page, as some research suggests that flowing links directly in the text of a web page disrupts the readability of the page, both aesthetically (people begin to get lost in linked text) and navigationally (they follow links out of text, and consequently don't know what to pay attention to). Bob Panoff spoke of an ongoing dilemma that the Shodor Foundation refers to as granularity - within a hierarchical directory structure of nested pages, how (and even where) on any given page to offer enough explanation so as to satisfactorily preface or acknowledge vertically adjacent pages, yet not so much explanation as to overwhelm the reader. Sarah responded to the layout of Suzanne's page, stating that selected visual elements can be of great organizational help to web readers. Richard thanked Suzanne for offering attribution of the third-party pages her page linked to as a way of honoring the work that they have done. Suzanne responded that authors, themselves, could help visitors recognize the authors' work - by including mailto links that can provide e-mail feedback from web pages via the HTML tag
Suzanne confirmed that mailto links proved particularly fruitful for rewarding children who author web pages.
Returning to the theme of attribution, Bob Panoff shared that the Shodor Foundation, despite politely requesting permission from the creators of third-party images, had received "nastygrams" either placing severe constraints on reproducing third-party images on the Shodor site (e.g., "images must be 2"x3" ...") or outright refusing such requests. Several people then clarified that this might tend to be the reaction of commercial sites with an economic stake in site hits and clickthroughs. Steve concluded the feedback by returning to the larger theme of how sharing materials can build online community. In particular, he recommended contacting the creators of interesting material to invite collaboration, as this can prove far more beneficial for all parties involved than does just linking to their web pages.
After a pot-luck dinner back at Ashton House, we returned to the Trotter lab for a TappedIn session led by Judy, Dave, and Annie. Despite several slow or failed connections, we explored the basics of the TappedIn virtual environment, enjoyed some conversation, and toured the Pascal's Triangle web unit, designed to support workshops given by the Math Forum for Urban Systemic Initiatives. In addition to offering a model for web lesson plans that address the unique needs of students as well as teachers, Judy shared some enjoyable and practical classroom experiences, such as encouraging students to rely on their arithmetic abilities instead of punching at a calculator, and about integrating art into math activities.
- Richard Tchen, Project Coordinator, The Math Forum
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