Designing and Delivering Professional Development Summary

Sunday - Friday, July 1 - 6, 2007

Sunday, July 1, 2007
The program began with introductions of the participants and of the leaders, Gail Burrill, Jim King, and facilitator, Johnny W. Lott. The fifteen participants were from California, Colorado, Maine, Minnesota, New Jersey, New Mexico, Texas, and Washington. They included experienced PDO leaders, PD³ leaders, and others involved in professional development in a variety of ways. Jennie Bay-Williams of the University of Louisville, President of the Association of Mathematics Teacher Educators was present for the first two days.

To set the stage for a discussion of reasoning and proof, participants were sent a reading by Gershon Harel and Larry Sowder on proof that will appear in an upcoming National Council of Teachers of Mathematics research volume. Participants were given an opportunity to respond to the article with their initial thoughts and were asked to keep considering it during the week. An underlying question for potential professional development is how to deal with reasoning and proof at different levels. A problem involving mathematical induction and the use of recursion or closed formulas was discussed. The goal for most days was not to solve the problem but to consider the process.

Nicole Davis, from the Seattle team, gave a presentation on complex instruction and group learning (see file). The participants solved a problem involving compactness and how it might be defined, then reflected on the interaction of the groups as they were working on the task, in particular considering the discussion and interaction that was useful among members and the strategies and behaviors of the facilitator to help the groups make progress.

One feature of the sessions for the week of DDPD was the use of comment cards with three questions: (1) what did you like about today; (2) what bothered you about today; (3) what else would you have liked to see today?

Monday, July 2, 2007
The DDPD group participated in the PCMI SSTP program and spent a small portion of their time together at the end of the day reflecting on what they had observed/ This was followed by problems presented by Johnny Lott and Gail Burrill (see the Japanese pattern problem), which gave the participants a time to work together, to consider how different patterns might emerge from simple problems, how the patterns might be expanded for teachers from lower grades to upper grades in professional development and how reasoning and proof might be involved at different levels.

Tuesday, July 3, 2007
The day began with a continuation of the patterns and reasoning from the previous day where participants described their solutions and discussed whether reasoning frim the picture could be a proof. One example (that the growth was the sum of the squares, which could be observed by cutting the pattern apart and rebuilding it as a square) provided a good explanation of the relationship between the stage number and the growth of the pattern but did not actually reach the level of a proof (one suggestion was to reposition the blocks so that what was added to the new stage was clearly visible and could be generalized). Darryl Yong from Harvey Mudd College then presented an outreach effort by his PDO. An Imagine Math day for area students and their teachers structured by the PDO members has been held for the last two years. The day is organized around a mathematical theme; the one shared was the Graph Complexity Project from 2006 (see the facilitator's guide for the activity).

Wednesday, July 4, 2007
There were no sessions on the Fourth of July. Many participants enjoyed the Park City parade.

Thursday, July 5, 2007
11:00 AM - Extra Session
The discussion focused on characteristics of professional development such as the following:
Necessities for Professional Development

• Identification of audience
• Meet with audience, what are needs
• Set realistic goals
• Work on timeline to reach goals
• Choose style of professional development depending on goals
  Examples
  
  • For community - consider the example of Darryl Yong, Harvey Mudd College
  • Planned In-services: content knowledge, pedagogy; blend?
  • Conferences and workshops
  • Attending; building conferences and workshops to present
  • Writing materials
  • Others

• Placing professional development in work day
• Range of teachers from elementary to high school with all different mixes
• Teacher buy-in; administrative buy-in
• Time for professional development
• Prioritizing for professional development
• Outreach by teachers to parents, community and to other teachers
• High turnover rate of teachers in some districts
• District goals and individual goals may not mesh with professional development goals
• Work with administration on resources and time for professional development
• Use of money to get most out of it
• Maintaining teacher interest in professional development during year
• New standards for school districts and state and how to keep current
• Balance the needs of audience during professional development
• Scaling up/Sustainability
• Human capital - how do you keep using the same people over and over?
• Narrow focus on of immediate problems
• External issues
• District wants versus teacher wants

Johnny Lott passed out a set of problems called Chunks of Gold: The Best Mathematics Problems Ever Reproduced for DDPD at PCMI.

1:00 Extra Session
At 1:00 in the tent, individuals wanting to meet with Johnny Lott were given time to discuss issues that were facing them in the coming year. Individuals from New Mexico, Colorado, Iowa and Minnesota met.

4:30 Normal Session
Brian Hopkins of St. Peter's College, New Jersey, presented a mathematical content topic used in his New Jersey PDO that presented a vision of bijective proof used in some discrete problems. He has used the content to encourage the PDO teachers to think beyond the bounds of traditional material in classrooms.

Friday, July 6, 2007
Henri Picciotto presented a reflection on proof from his experience in the classroom, where one of his suggestions was that investigating the situation prior to working through the proof made the proof more meaningful for his students.

The group reflected back on the original discussion about proof and its role in professional development. The notion that proof should be developed across student's mathematical experiences was raised as critical, but it was also noted that this should be appropriate for the level of the student. One of the key elements that both teachers and students should be aware of is that while it is important to "tell the truth" it is not always necessary to "tell the whole truth" and that often a proof has to be trimmed down from the full mathematical argument to be suitable and understandable by students at an appropriate grade level. Participants reflected on their overall experience at PCMI and its value for their own work.

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