After morning hikes we swam in the lake which was surprisingly pleasant.

The older kids and I explored polygamy cave.

My Dad and I backpacked into White Pine lake where we ran into beaver. One beaver (I’m assuming the mother) made quite a show repeatedly slapping her tail on the water.

Seth made a compass course for those of us who are directionally challenged.

Good times. Now get back to work!

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

The Masters in Entertainment Technology (MET) program brings together people from multiple disciplines to work together on intensive entertainment technology projects. He said that this is the head fake; the MET program is designed to help people learn to communicate together and work as a team. It only made me wish I could be back in school doing their program! Now if I can just convince Julianne

Drew explained that they Randy likes research and had pretty much moved Alice and his group back to the CMU campus for some time even before the last lecture. While Alice is a good tool for introducing programming to novices, it is not the tool of choice for developing production quality 3D games. The ETC now uses Panda3D heavily with Jesse Schell one of the primary contributors on staff. Panda3D is the open-source, python programmable, game engine used by Disney to develop games such as Toontown and Pirates of the Caribbean.

Very cool! I could have kicked myself when standing outside waiting for the bus I realized that I failed to take out my camera during my tour of the ETC.

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.

JCDL 2008 trip continued: I talked with Bryan Chapman about aligning content with standards (see his paper Exploring Educational Standard Alignment: In Search of ‘Relevance’). He pointed me to the CNLP’s Curriculum Assignment Tool and to the Teacher’s Domain cross walking service as potential sources of tools and providers of standards alignment. I have the idea that if we could create a backbone set of standards that was as superset of all of the state standards and then align content with that set of standards, then it would make it dramatically easier to provide answers to a teacher’s query for resources relevant to what they are teaching.

Bryan believes that it is nearly impossible to develop effective crosswalks between the standards. Different standards focus on different levels of detail and address different levels of outcome. They use the same words to mean different things and some standards assume the context of their location in an hierarchy rather than restating it. This still seems like an interesting problem to try to solve, maybe even something that recommender technology could be applied to.

Tuesday morning I got in a run along the Allegheny and saw up close a few of the 466 bridges of Pittsburgh as well as the inclines.

After years of keeping them in boxes, I recently got out my University Physics and Math books and put them on my shelves. Just getting them out inspired me :-). This morning while testing the Open Yale Courses feed that I had added to OER Recommender, I ran across the Fundamentals of Physics course. This led me to R. Shankar’s home page, where I noticed an old friend, Shankar’s book that I used in my quantum mechanics class at the University of Utah. I also smiled to see him list his

Most important contribution to physics

“Discovered a small parameter that justifies most calculations performed in physics: 1/ego, where ego is the author’s ego.”

Very clever. It is cool to see a self-deprecating physicist. The description of his other book shown there: Basic Training in Mathematics rang true to my experience. My love and interest while studying at the UofU was always Physics, but I ended up taking so much math that I decided to go ahead and major in Math as well. While doing so, I found that almost everything I learned in my Math classes I had previously learned in my Physics classes :-).

Problem solving is what you do when you don’t know what to do. Problem solving requires recognizing and defining the problem, selecting an approach, breaking the problem down into sub-problems, selecting procedures for solving those sub-problems, executing those procedures, evaluating and diagnosing progress, recognizing when a solution is satisfactory, and interpreting results. Note, if practice makes perfect, we better give students opportunities practice in all of these aspects of problem solving, not just simple recall and algorithmic procedures.

Common wisdom says that we should wait until people have developed the basics before we ask them to solve problems and do higher level thinking. I reject that notion. Higher level thinking may not so much be “higher level” as it is “different level”. Kids at the youngest ages can and need to be given opportunities to engage in real problem solving. Maybe, part of why kids learn to hate math is because we spend so much time focusing on “repeat what I just said” and “do what I just did”, to the exclusion of authentic problem solving.

“Theories are like toothbrushes, everyone has a theory, but no one wants to use someone else’s theory”

This is true within a given field such as artificial intelligence / cognitive science in which the PSLC work is based. It is even more true if you look across multiple fields such as education (teacher preparation), cognitive science, instructional design, and math education. Each of these fields have something to say about learning and teaching math, but the languages of their literatures are as different as English, Urdu, Chinese, and Russian.

I recently presented on the PSLC and this framework at a recent USU Math & Stat Journal Club meeting (see my PSLC Theoretical Framework Trailfire Trail). In our discussion it was brought up that sometimes teachers object to the type of instruction that is typical of the PSLC model tracing intelligent tutors because it is not open-ended or exploratory. My reactions to this criticism is that the tutors are not meant to replace all instruction. This type of instruction is very effective at teaching procedural (algorithmic) skills consisting of a sequence of steps. It turns out that a lot of the math what we expect middle school and high school students to learn (and demonstrate on standardized tests) is of this nature.