This vision of providing tools for teachers to create online content is similar to what I envisioned for my dissertation work which led to the eNLVM. My eyes were soon opened to the fact that most teachers do not have the time or skill to create online content, especially from scratch. I suggested to Turadg that if he wanted to encourage better and more problem submissions that they could provide example problems from which teachers could base similar problems. I also pointed out that there is already a massive supply of math problems in textbooks that could be tapped. He and others present mentioned concerns about copyright. To me, this is not a problem. By looking at a math problem you can extract the essence of the problem or it’s “problem type” and use that to easily generate many more of the same type of problem with different cover stories and values. Of course, until you solve a problem it can be difficult to know that the problem has similar solution structure as another. This is the basis for a project I would like to do some day: a library of math problem generators coupled with math test generators that leverage the problem generators and their alignments with standards and textbooks.

Ido presented a study that measured metacognition, specifically help seeking behavior. He began by flaming simple recall as a learning outcome, showing the example of the YouTube video of the child who can point to the names of the countries that her parents name. He did this probably because a PostDoc sitting in the presentation focuses on fact learning (Chinese). Ido’s study compared a new measure to the “assistment” measure used by Carnegie Learning’s tutors as predictors of learning. It seems to me that they pretty much measured the same things, and both are somewhat good predictors of learning.

This is an interesting area. Information seeking is a metacognitive skill: knowing when you know enough to proceed and when you don’t. Having the will to not take the lazy out when you know enough. Knowing where to go to find information you need. The picture is actually much more complex than this. When you are first learning something, or solving a novel problem, it is expected that you would need more information. Better problem solvers and learners recognize this and seek the needed information effectively. As you learn more in an area, you don’t need as much help and so you should stop relying on it. In a situation where making a wrong decision could cause someone to die, the good problem solver relies on additional sources to verify that what they think is a good decision is actually one .

Measuring information seeking behavior is an important way to measure problem solving ability. Unfortunately, school, and even worse, school testing situations, are very unnatural problem solving situations where information seeking behavior is called cheating

I resonate with David Yaron’s concern that we teach the wrong things in High School and introductory College courses, focusing on teaching students to follow mathematical procedures rather gain a conceptual understanding of the content. I shared my theory a cause:

1. We emphasize in our teaching what we test
2. We test what is easy to test
3. Testing simple recall and procedure following is easy
4. We emphasize simple recall and procedure following in our tests
   
5. We emphasize simple recall and procedure following in our teaching
   

The remedy is to develop automated measures of higher level thinking: conceptual understanding, problem solving, design. He agreed in part but challenged that we don’t know or agree what problem solving is and have an even harder time measuring it. I agree in part, but think we do know something and can begin heading in the direction of trying to measure problem solving and higher level thinking.

Problem solving is what we do when we don’t know what to do.

Problem solving involves recognizing and defining a problem, searching for relevant information, forming appropriate subgoals, selecting appropriate strategies for accomplishing subgoals, executing procedures, monitoring progress and redirecting efforts when appropriate, recognizing when satisfactory solution has been arrived at, and interpreting the results of problem solving efforts. Interestingly this relates to the conversations I had at the PSLC later in my trip.

Yaron, who sits on the AP Chemistry board, also indicates that even if we had good automated measures of higher level thinking it would take a long time for them to be widely adopted and that a revision approach is more likely to succeed than a revolution approach.

How does one begin to participate in a community?

If you accept my characterization of a community, you begin participating in the community when you begin caring about the same problems that the community cares about. If you wanted to create an entry path for people to join a community, you could create a sequence of problems to solve and resources to begin solving them including records of past attempted solutions.

• Playing with something is a better way to begin learning about it than to be told all about it.
• When people begin creating things they begin learning the language of design.
• It is OK that most of what people create is no good, at least they are learning the language of creation.
• The tools you create shape what they can and do create.

After returning from the hotel last night we sat and brainstormed about what we are and can create based on what we are doing. A lot of the discussion centered around defining the problem. Here are some possible problems:

• What are future educational scenarios and how can we help shape / facilitate them?
• How do you form successful online communities (ones that have lots of members who regularly contribute and gain value from the community)?

I woke up thinking about these questions.

Can we create a space where people can pose and solve problems?

Can we glean principles from Ze Frank, MySpace, and the MathForum’s problems of the week that could help make that space successful. Why do people like MySpace?

• (Power) They can create what they like
• (Show Me) They can show it to their friends
• (Feedback) People can comment on their pages

I’m personally interested in creating such a space and online community for math, science, and technology.

I envision a place where people can pose and solve problems using interactive models. Connect this to current news involving math and to the history of math discoveries. Provide tool sets that let people quickly create, play with, and adapt with interactive models. Provide podcasts that engage learners in problems, invite them to work on those problems, see how others work on those problems, and pose their own.

COSL’s interests are of course much broader than math, science, and technology. They are all topics. So what is generalizable to all topics. I think a space people can pose and solve problems. Here is an idea that came out of thinking about that general problem.

What if you had a catalog of every problem that you had ever worked on?

What if that catalog additionally included links to web resources you accessed when trying to solve it, and any notes you made about your efforts and potential solutions? What if you could share that catalog with your friends and with communities that cared about the same problems?

It seems like that would be valuable, but how would such a thing get created. What if you had an agent that monitored (and stored for your private use only) a record of all of all of your searching and browsing activity. The agent analyzes those activities and clusters them based on concerns. It allows you to annotate those clusters with tags, notes, and explanations so that they can be more useful to you and others. It organizes and ranks web resources based on how long you spent at those pages, how often you came back and so on. It lets you contribute those problems and answers to relevant communities. It recommends relevant web resources, communities and users.