ESCOT Summer Workshop 2001
Day 1

ESCOT Summer Workshop 2001 || Math Forum Workshops

Today's attendees: Mark, Jeremy, Bill, Jody, Leslie, Dave, Suzanne, Wenming, Chris, Alex, Seth, Kristina, Gene

Welcome/Introductions: Jody led the introductions and then reviewed the agenda to ask for input and suggestions for changes as we started the workshop.

Chris shared his thoughts with the group about how fortunate we are to have some time to reflect on the three years of the project. He hopes to have a clear idea of what has come out of this work and have a consensus of our successes/failures.

Jeremy and Chris have an over arching goal for this workshop - seeing that there is some kind of ESCOT legacy. They want us to think about the end of the three years there are some artifacts that have some value to the public. The most tangible way is by taking some of our more successful ePoWs and repackaging so that they can be reused by teachers outside of the PoW context with support materials with ideas of how the ePoWs can be extended. Also make them customizable so that teachers can tweak them for their specific needs.

Gene recommended that Chris and others take the time to write the results of this workshop and defining a legacy into the final report for NSF. Leslie noted that without a serious time of reflection, the change is not implemented.

Chris also said that we want to set the stage for future work. The "possible futures" topic in the agenda will be part of that discussion. Jeremy added that the third part of the reason that we are meeting is to have a time to celebrate after having so many accomplishments during the three years of work.

Third Year Highlights:

  • ePoWs
    Focus on designing, developing, and deploying ePoWs. For this second school year, we published 2 problems per month for a total of 16 problems.

    Combined with 1999-2000 ePoWs, the total number of interactive problems produced by ESCOT is 46.

  • Mentoring
    Mentored responses per ePoW ranged from 5 to 44, with an average of 24 for each ePoW, although it is possible that many more students tried the ePoWs, but did not submit a response.

    Technical problems with loading some of the ePoWs.

  • Component Camp
    In January ESCOT hosted a successful "Component Camp" for developers in Half Moon Bay, CA.

  • Applets
    A significant new technical challenge posed by this year's ePoWs

  • Java Worries
    Using a browser/Java combination to deliver interactive tools to students continued to be highly burdensome.

    Unfortunately, a robust, widely-available, developer-friendly runtime is likely beyond the scope of any NSF research project, and conversations with Microsoft and Sun indicate that there is little commercial interest in resolving the problems.

  • Evaluation
    The Math Forum is studying:
    - the role of context in student work with software-supported ePoWs.
    - longitudinal patterns in students' work with software-supported ePoWs
    - the impact of these PoWs on students' mathematical thinking
    - Integration Teams through interviews and an analysis of team communications during problem production

  • Web Site
    Over the last few months the ESCOT public site [] has been completely overhauled.

    The new design is intended to live on after the end of the ESCOT grant and provide a place for the public to access our ePoWs and other products and publications.

  • Outreach
    Invited talks at UC Berkeley, Intel, an International Workshop on Advanced Learning Technologies, NECC, AERA, and the National Academy of Sciences.

    Papers (a variety presented to various scholarly journals)

  • End-game Activities
    An interactive session for CSCL 2001

    Reflective paper targeted for ...

    Technical paper on the evolution of the ESCOT interoperability architecture targeted for IEEE Software

    How-to paper on deploying Java applets to classrooms targeted for the JOMA

    Evaluation/design paper on creating effective learning experiences through applets

Possible Futures of ESCOT:
Chris wanted the group to have an ongoing conversation about this after presenting some ideas of what is on the immediate horizon.

Opportunity Institutions Players
TRAILS Colorado, ETS, MF All of us
MMAP Stanford Shelley Goldman
MathScape   Susan Jenson (works with Glen Kleinman)
Everyday Math University of Chicago Andy Isaacs
Teacherline PBS  

TRAILS is not likely to be funded. Chris said that the proposal was one of 5 highly recommended ones. They are funding the first 2 or 3 but we are number 4. They would have to find another 4 million dollars in order to fund TRAILS and that is unlikely.

Gene asked that Chris and Jeremy send him the reviewers' comments. Chris said they had not yet received them but that he had asked if he could supply more information or clarify anything and the response from NSF was that there had not been any problems with the proposal. They just had not funded that many.


  • Reform-oriented middle school math text
  • Planning a new edition
  • Wants to involve more technology
  • Need a long range vision: 6-7 years before publication
  • Close to SRI

Mathscape is based in Boston at EDC. They have a very good handle on supporting teachers, parents and students in using the program. They are sending in a proposal today and some people at ESCOT were listed as consultants.

Everyday Math is a successful reform-oriented elementary school text. It is considering integrating some technology. There are exciting possibilities around manipulatives. Chris has had promising discussions with Andy Isaacs, who has some healthy skepticism.


  • PBS wants interactive mathematics contents for its Web site
  • Thinks we can produce it efficiently because of ESCOT experience
  • Licensing terms already in place
  • Waiting on PBS reorganization

Jeremy's conceptual map of possibilities:

ESCOT Directions: ---->
curriculum revisions (ESCOT as a support center)
math and science partnerships (improving pedagogy in schools)

Teacher Professional Development/Teacher Enhancement

Digital Library project (Math Forum/ESCOT partnering)

Scaleable research (IERI)

Handheld technology

Touring the Sites:

Suzanne explained the Teacher Support pages on the Math Forum site including a new one that she has been working on that arranges the problems by NCTM Standards:
    Teacher Support Pages
    Teacher Support Pages - NCTM Standards Index

Chris gave a tour of the new and improved ESCOT site He pointed out the following features:

Classroom User
Teacher Author

in the middle is an animated gif which is changed periodically

top left hand corner resources include authoring teams, component tools, main standards, interactive problems



Chris distributed a paper with thoughts on how to repackage ePoWs. These ideas were compiled by Yoni Kahn last month. Some of the ideas must be pretty difficult to accomplish but they will be a good place to start

You can download the MS Word file with Yoni's suggestions or view the page on the Web:
The Polyrhythm problem:

The challenge is to come up with a way to coordinate two rhythms to match the mystery rhythm. Leslie said her students were working in 2's and 3's. Some students were more rhythmically experienced than others. Some students were so random in their tries that it was funny to watch their efforts. The classroom noise was high.

We looked at the suggestions that Yoni wrote for Polyrhythms:

Allow teachers to add as many rhythm lines as they want, and allow them to choose the available options for rhythms (1:2, 1:3, etc.). Allow teachers to create their own mystery rhythm for students to experiement with. Along those lines, students could also make up their own rhythm and trade it with other students in the class, who will try to discover what it is.

Providing the technical infrastructure that allows the teacher to customize.

The kids wanted to go fast and yet when the went fast they couldn't figure it out. Some students wanted to hear only one drum at a time. They didn't have that feature, so they set the pattern the same on the two rows.

Another idea is to just be able to bring up the applet. Suzanne said it would be very easy to just make a page with links to the applets. The rough draft is

Chris asked if anyone might have ideas for a process to go through this systematically. Jody suggested breaking up into several groups and have each group take a subset of the problems. We talked about what teachers need, want, and/or have time for and what we could do to support that.

In some contexts we want to give control and in some cases we want to give it to them so that they have a more open-ended problem. Fun to have a library of the "master" applet but have the tweaked versions available to have others see.

Chris asked if there are problems that could be refined without the applets. Would that be better to leave as a legacy? Jeremy asked Leslie what she thought.

Write a problem that you would like another group to solve. Leslie would have them write their problem in a Word document and then email to each other.

Bill is thinking how could you do this problem without the applet. He said that the students could easily clap it. We all demonstrated that it could work. Suzanne said that this idea would be great to have on the page in case the technology didn't work and they needed a back up time.

Chris said that having the "war stories" available for teachers could be of value. We talked about the use of the Discussions area on the Math Forum site.

Next we looked at The Hispaniola Water Shortage:

Changing the art work might be something that could be done.

The numbers that come up at the bottom. The numbers can't be printed. The issue of the length of time that teachers have for a class period and the problems that arise when student work cannot be saved or printed was discussed.

Marabyn was the next applet to be considered:

Mark explained the applet and the basic problem. We watched as Leslie and Dave worked through the problem. Bill said that this brings a better level of understanding.

How would you want to use it? It might be nice to have it where you could adjust the speed so if you were to use it again you could have variations. Mark said the bus speed, walking speed and the position of the house could be adjusted.

Alex suggested the "blind watchmaker's approach." Teachers would sort of evolve it without having any programming background.

Jeremy summarized and said that maybe we have come to the decision that teachers don't need to be given the opportunity to change things but if there were variations available to choose from that would be a nice addition.

Chris said that there is a site that teachers can use to make pages that have a set of links to use with students. It might be interesting to suggest this to teachers as a tool to use in conjunction with the ESCOT applets TrackStar.

Mark talked about the Search and Rescue, Part I applet

He said that ideas to add to it would be to customize the flight plan and that would go hand in hand with the addition of a new map.

Evaluation: Student Learning

Ann Renninger said that she is working with a lot of different kinds of data and that she is doing an overview of that data and then at the end questions can be asked.

An overview of the kinds of questions and the issues that have been raised. Ann introduced Eric Freedman who worked with the interviews. Abram Lipman also did a lot of the work (not here).

Two types of questions:
  1. What cognitive and affective patterns describe student work with online interactive mathematics
  2. What is the impact of different levels of scaffolding on students' work with these problems.

    These two questions surfaced as a result of conversations from last summer's workshop. The evaluation from year 2 came out of the questions being asked by participants of integration teams.


    Compatibility between information students are expected to learn and what they already know is influenced by how students understand the problem (including the applet):

    • When I (Ann) talk about "problem" we are talking about the mathematical story as well as the applet.
    • What the task requires, math understood and strategies suggested
    • Roles of components in providing support/potential
    • Students understanding of tasks is generally influenced by:
    • Interest, gates types of connections students can make
    • Competence, informs expectations about what the problem entails
    • Self-concept, informs students' sense of possibility about being able to do problem solving
    • Scaffolding: How much help does a student need to work on a problem?

    Studies of the ESCOT Testbed, year 2

    1. Problem contexts that do and do not include a story (story, no-story study)
    2. Individual think-alouds (think-aloud study)
    3. Work with a peer (partner study)
    4. Work with a peer facilitated by a student teacher (partner and mentor study)
    • Questionnaire (interest for, competence in, self-concept about mathematics)
    • Teacher ratings of student performance and effort in regular classroom setting
    • Student achievement reported by teacher, based on standardized measures

    Study condition (assessed (a) mathematical thinking [connections to, strategies for, autonomy in work with problems], (b) guessing strategy, and (c) problem solving [understanding of concept, mental map, analytic approach, planning, resilience/resourcefulness] as appropriate

    We also have interviews/reflections - picking up on what the students' reflections for the problem integration team

    Ann turned on the VCR to display students working through the Hispaniola Water Shortage problem.

    An adult prompts: What are you thinking? The students explains what they are doing step-by-step.

    The example is very systematic. This is an example of a mental map.

    Another two students were shown who were quietly talking about their ideas of how the problem worked. One student was explaining and the other one said "Ohhhhh."

    Ann said this is an example of the students really thinking together, they are working really hard. Typically the problem takes them about 20 minutes.

    The third group is an example of playing An interesting finding is that we have put interest into. Regardless if they like math or do not like math, the students like to work with the problem.

    The question is what kind of work they are actually engaging in.

    There is a real range which plays out in the analysis. Strategy use is a difference between students. It doesn't matter if they have interest in math or not to work with it. There is a connectiveness with a problem. There are some differences with gender and level of competence.

    All of the problems this year rate as level 3 difficulty which is an improvement over the previous year.

    Girls are likely to be strategic (using strategy use) Girls are better at describing their strategy.

    Everyone wants to figure out how to work with weak students. You're seeing gender, strength and competence differences. A study that helps you decide how to change things to target improvement for weak students.

    It's great that we got them all engaged, how do we get them to do equally well?

    What was learned from the interviews:

    Students said the applet was helpful mainly because it:
    • helped them to visualize the problem
    • was more interactive and hands on
    • gave them immediate feedback
    • was more fun and enjoyable

    Most students in the story/no-story study felt that the story generally helped them understand what the problem was about.

    In discussing how they solved the probles, many students indicated they used a strategy of "guess and check" or "trial and error."

    The primary difficulty students had with understanding the directions was figuring out what the problem was about.

    Eric generalized a variety of problems that students reported with the applets.

    Guess, check and refine.

    Day 2 || Day 3

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