How Important is the Online Facilitator?

Seeing Math offers Moderator-Lite Scalable Professional Development

By George Collison

The architecture of Concord Consortium’s Seeing Math Secondary curriculum expands the limits of existing course design and delivery. Seeing Math tightly integrates five powerful tools, all delivered online: 1) video of student problem solving, 2) video of a national math education expert providing commentary on content and pedagogy, 3) an applet (Java-based software that runs over the Web) that permits students and teachers to explore math concepts in a radically new way, 4) a “Diving In” math challenge, and 5) a moderated threaded discussion area. Based on this powerful course design, the role of the facilitator changes in important ways.

The metaphor guiding course construction was the experience of a visitor to the exhibit rooms of the Exploratorium museum. The Seeing Math experience, like an Exploratorium exhibit, is conceptually and intellectually engaging. The design shifts the online museum guide from instructor or potential content provider to that of a moderator who monitors each participant’s progress through the exhibit, encourages participation, troubleshoots technical difficulties, and, through private feedback, provides guidance on topics that may need more attention.

Structure of the Seeing Math courses

Seeing Math Secondary courses are offered through PBS TeacherLine to a national audience or to PBS member stations. Each course is comprised of five week-long segments. The first week introduces the course and the platform. After a community-building activity, participants engage in problem solving through a Diving In activity, which features significant mathematical content embedded in an interesting problem. An applet displays unique representations of the problem and new ways to think about solutions. Participants can share their solution paths with each other in an online threaded discussion area that supports text as well as pictures and snapshots from the applet. In week three participants view two or more short videos of students tackling the same problem. The students’ impasses and false starts often mirror the participants’ own struggles. In weeks three and four, a math specialist comments on the students’ efforts and highlights important content issues, potential unresolved areas of confusion, and links to current research. In the threaded dialogue, participants integrate multiple solution paths and complexities revealed by the students and the expert commentary, and discuss insights from the linked multiple representations displayed by the applet. As a summative experience, participants design or adapt course activities for their own curriculum.

“Here’s what I valued most about this course: The excellent classmates! I gained so much from seeing other perspectives on our given tasks and issues! I really loved the interplay of our postings and responses, and the fact that all of us had all the time we needed to read each other’s views, mull over our own views, and respond in our own time frame. In a regular class, if you don’t have your thoughts all formulated at the right time in the discussion, you can’t just rewind the tape and ask the question or add the ideas later! It was great, too, for the shyer of us to have the anonymity of a posting, rather than a face-to-face interaction, and the knowledge that even the most vociferous critics couldn’t sneer in our faces, so we could all share our insecurities, questions, and even occasional criticisms with increasing comfort.”

The role of the moderator in Seeing Math Secondary

The Seeing Math course design follows the Concord e-Learning Model, which describes nine key characteristics of quality online courses. The role of the moderator in our model diverges signif- icantly from that detailed by Feger and Zibit in The Role of Facilitation in Online Professional Development: Engendering Co-construction of Knowledge. Feger and Zibit build on previous researchers and detail three areas of “teaching presence” or focus for the online moderator: 1) instructional design and organization, 2) facilitating discourse, and 3) direct instruction. The “co-construction” moderators they describe employ a facilitator-mediated discussion design that includes supporting lesson study processes, supplying teacher resources and context, and coaching and addressing cross-grade issues. This model falls short of the goals and achievements of the Seeing Math design in notable ways. The co-construction model proceeds dependent on significant levels of moderator analysis, input, and intervention that potentially hinders independent thought and development.

The Seeing Math design recognizes that highquality expertise is needed to foster deep engagement in the content. The Seeing Math architecture offers alternative, scalable sources for this important course element by expanding on key ideas, conceptual conflicts, ambiguities, and unresolved issues within the text surround, video commentary, Diving In activity, and student video. The expert commentator in the videos takes on many of the characteristics of a co-participant in the group, and also serves to assist the moderator by focusing the discussions. Access to this valuable window on content depth shifts the moderator out of the center of discourse with the participants. The applets, using linked multiple representations, also provide a powerful way for teachers to approach old ideas in new ways. The Seeing Math discussion boards abound with teachers’ discoveries within this media-rich environment.

Dialogue analysis

For approximately half the participants, Seeing Math was their first online course. Statistical analysis of the dialogue in three Seeing Math course sections offered in the spring of 2005 revealed an unusual moderator profile. The participant to moderator response ratios were quite high, ranging from 19:1 to over 100:1. A single, targeted comment by the moderator often generated considerable discussion among participants. The software platform required that the moderator place the initial post in each thread. This post was scripted by the course authors and provided in the facilitator’s guide. It highlighted the main themes for discussion and the important conceptual tensions evident in the student and expert commentary. In a study of three courses, 1,529 posts were made by a total of 53 participants. The moderators posted 39 scripted messages and 18 unscripted messages for an average participant to moderator postings ratio of 27:1. By comparative word count, moderators occupied only between 1% and 2% of the public discussion areas. Over 50% of the postings occurred in threads containing 11 or more posts, and the average word count of a participant entry was 108, indicating considerable participant activity in the online discussions.

Moderator-lite is not moderator-easy

Seeing Math moderators exert considerable formative influence on the course outside the discussion area as well. They spend significant time resolving technical issues, such as diffi- culty installing video players or the proper version of Java to use with the applets. They also give weekly feedback to participants in their private discussion areas. Moderator feedback includes highlighting participants’ contributions that received significant attention from other participants and suggesting where more effort to communicate or articulate ideas could benefit others in the course. Moderators received seven weeks of training based on the ideas in The Online Teaching Guide and Facilitating Online Learning, which familiarized moderators with “voice” and “tone” and a set of critical thinking strategies. Technical training was also included.

Structure of the Seeing Math design: The moderator’s critical functions—providing feedback, reading dialogue and facilitating discussions, offering technical support, and communicating privately with course participants— effectively surround the five key elements of a Seeing Math course.

Implications for future video cases for professional development: Getting to scale

Judah Schwartz, Ph.D., has offered a vision of mathematics education and professional development on the Web. He has looked beyond ordinary tinkering to the effective use of well-designed cognitive tools, which engage the user in dynamic visualization, concrete manipulation of abstract mathematical objects, and discourse that is stimulating. Schwartz’s vision is realized in the five elements of Seeing Math professional development. Supported by a media-rich context and interactions with significant mathematical ideas, Seeing Math participants work together to generate new ideas, build new connections, and extend their understanding of both math content and pedagogy. The ability to learn from each other greatly increases the likelihood that large-scale implementation of professional development in secondary mathematics is feasible.

George Collison (george@concord.org) is an Associate of the Concord Consortium and Senior Curriculum Author for the Seeing Math project.