David shared Evidence Based Design (not sure if this is what he was referring to) as a model. I shared Conditions of Learning – the idea that different types of learning outcomes should be taught differently, and Jim Cangelosi’s (forgive the flashing text) work on designing mathematics instruction for different types of learning outcomes. Interestingly he has advocated the idea of mini experiments as an approach for teachers to learn about and evolve learning.

ATE Central is an example of how a project in NSDL can influence other NSF programs. It brings all of the ATE resources in to one searchable portal. It builds the ATE brand and helps disseminate the projects. ATE is different than NSDL in that they focus on content development, industry connections, and the improvement of training and teaching for workforce development. ATE offers smaller grants and larger center grants. Example national, regional, and resource centers of excellence are geoTech, CARCAM, AgrowKnow. ATE Central has been funded for 1 year. They focus more on events than in other portals. This is partially because ATE focuses a lot on workshops including virtual. They create resource areas on ATE Central for each projects and centers. This has been a big deal to their projects to help them collaborate. ATE has a center that is funded just for evaluation. They send out a monthly update and are creating success stories. She showed videos of people that have found success of students that have benefited from ATE.

Linea Fletcher and Rachel is interested in the life of NSDL projects that continue beyond funding (are sustainable). They want to capture and share these stories. Another focus is on how to capture of evidence of impact across projects. They currently track 320 projects and aggregate and share it in interesting ways.

This work reminds me some of what Justin did with 51weeks – a platform for supporting communication around a conference and the other 51 weeks of the year.

Modeling is important because it is what scientists do. It is also a valuable way to interest and help students learn. You can do problems that are too hard or impossible to visualize, that you just don’t see if you don’t have the computational resources. “The difference between physics and math is that I have fun demos. In physics as opposed to math. We do have answer. It is what I measured”. The Falling Slinky Model: What happens to the bottom when it begins to fall? Physically, it is hard to see. The bottom doesn’t know it has dropped until it gets a message from the top of the slinky. Colliding Galaxy model. There is no way for someone to do this on paper.

Adoptable, adaptable, and understandable. They have to be modular, adaptable, visual, interactive, internationalization, quality control, easy to get to, vetted by other teachers, descriptions of how it has been used. Francisco Esquembre – creator of Easy Java Simulations. He says the most important characteristics are adoptable, adaptable, and understandable. This gives power to the people. This was my theory and excitement in my dissertation study. Give the teachers the tools, and they will create. My findings can be summarized by the 90-9-1 rule. 1% of teachers have the time, interest, and skills to create. Of course more powerful tools make it more possible for people to participate.

He showed an Inferior Ptolemaic Model of what it would be like if the earth was the center of the earth and Venus went around the earth. How could you tell which model is right? People can conjecture and explore.

He showed the Falling Loop Model. A loop that is falling through a magnetic field. Faraday’s law. It creates a current that opposes the falling. Other physicists can open (download) the model and modify it with minimal programming. His students can do this as well. This is similar (but more advanced) to my work in the eNLVM that allows users to configure and serialize applets. They connect EJS to the library to make it easy for people to find, discuss, and share their models. Their library allows users to rate, collect, relate, comment, sort, annotate, and share. Again, the themes of our Mellon work and the ODLMS shows its head. One of the contributors to Open Source Physics has written a text book for which their File Cabinet contains the resources aligned with the sections of the text book. They have build into EJS the ability to browse repositories of EJS models. There is a professor in Taiwan who has over EJS 150 models. Doug Brown, Wolfgang, and Lyle Barbato are some of the key people. A project called Tracker that generates video from EJS simulations. They have also done a Data Tool.

Their stats (Open Source Physics?) are 350 resources, 1700 users per week, 31,000 downloads per month. By comparison, the NLVM has about 110 applets and gets 40,000 users per day.

Jim Jenkins asks about how attribution and copyright works when you copy resources from one system to another. In Send2Wiki we address this by embedding it in the database. In eNLVM we track the source and attribute it in a status bar along the bottom.

nlvm^.5 nsdl^.3 math^.7 learners^.2 education^.8 “grand challenges”^.7

The advantage of identifying and modeling interests are that instead of modeling the average of a persons interests, you model specific interests. Then when you match people or documents, you match them with specific interests instead of the average of their interests. You can see the benefit of this when you consider what the average of math and bicycling is? Alex and I have discussed this issue, but have not yet implemented it. I’m interested to see any research that compares the two approaches.

So some of the questions related to modeling a learner using term vectors are:

• How many interests you should model?
• How do you discover the interests?
• How many terms should you include in each term vector?
• How do you do modeling and recommendations efficiently?

In Ed Fox’s presentation we are listening to Peter Brusilovsky talk via Second Life about the kinds of data that they use to model users including: search, tagging, comments, resources they have created including paths (Walden’s Paths), collaborative recommendations, and social navigation (guides users to most active resources). They uses these models to provide recommendation of content and other users. CUMULATE is their group modeling framework. They are tracking of browsing and problem solving. Steve demonstrated a bunch of tools they have in Second Life for Ensemble.

We are addressing similar approaches in Folksemantic. “Systems support personalization by adapting functionality to individuals, by allowing users to customize the system, and by supporting human interaction inside of the system.” We allow people to register their bookmark, blog and other feeds. We also will be using click, search, comment, and share data to model users and provide recommendations.

Dr. De Strulle is talking about the report Fostering Learning in the Networked World: The Cyberlearning Opportunity and Challenge.

Highlights of the report:

• Crossdisciplinary approach – use
• Platform perspective – adopt & integrate with existing platforms – support
• Learning across the lifespan – achieve decentralization while retaining what we know about learning and education
• Promote OER
• Sustain innovation – build on previous work so that it has life beyond its own project

Cyberlearning – learning mediated by technology (formal ed, informal ed, brought together by networked computing and ICT). Think about life long learning.

We need to think about redistributing learning over time. Cyberlearning is not restricted by the constraints of schools. Not limited by time, location, formal-informal boundaries.

Arlene comes from a Virtual Reality background from the military and illustrates cyberlearning through examples. She’s using examples of virtual worlds, earth systems sensors providing real time data. One example shows a person explore a 3D model of climate change including historical data.

Example: interacting with a dynamic model of a virus as one million atoms interacting with each other.

Haptic table a tool that lets people who can’t see, you can feel the images. Assistive technologies allow people with learning challenges to participate. Virtual laboratory allow people to practice surgery using remote surgery tools. This allows people to practice procedures repeatedly without the consequencies of real mistakes. The future workforce will require that people have skills to use technology. University of Pennsylvania. The GLORIAD network is an optical network that supports cooperation between scientists, educators, and students. It is an example of cross-institutional networks of faculty and students through the use of collaboratories. This helps faculty members focus on educational issues. Science museum virtual reality allows students to become emerged. This is essential to create cognitive presence in the learning environment. Game-based learning is being used to train our troops. It affords tremendous transfer of knowledge and individualization. Research is increasingly showing the power of effectively designed game based instruction. Game based learning increases public engagement in science and policy. Next to LaGuardia airport there is a plot of land that is set aside for a park. They have created a virtual version of Second Life and have invited the community to help design the park in that environment. Part of the design decision is the discussion and learning about the science of water and land related to land use. New mobile small devices have been created that allow data to be gathered in remote situations and provide access to STEM content. Mobile technologies are a democratic device because they allow everyone to access to all kinds of knowledge and to participate in the discussion. It allows people to learn information about their very location, for example the tree that they are looking at. It also allows remote communities to easily communicate (e.g. classrooms around the world). Adler Planetarium lets students look through the best telescopes in the world in real time and report them to the scientists. Technology based learning allows learning and teaching to be tracked and evaluated. The use of avatars in virtual worlds is an area of major research. She pointed us to additional reports: Cyberinfrastructure for Education Workshop Series, NSF Cyberinfrastructure Vision for the 21st Century.

What surprises did you encounter implementing cyberlearning?

Cathy Manduca – Pedagogy in action. Implementation in the Geoscientists. Implementation as a library. The goal is to help teachers and faculty to make better choices about education. If teachers and faculty had more information and examples about methods in subjects they teach, they would make better decisions about which methods to use and the barriers to adoption would be lowered. They created a catalog of teaching methods connected to examples. That was widely used by lots of people, so they created a service structured as a library. People can draw from the library to embed them in their websites and contribute content. Tracking demonstrates people are using the resources. Interviews give evidence that the site has given them new methods and confidence to try them. The resources speaks directly to teachers and supports adoption of the technology. Pedagogies and actions. Their project highlights cyberlearning comment such as teaching with data, models, visualizations, and games. You need to treat it as learning (remember all of the standard instructional design issues). The design takes advantage of teacher motivation PBL where the problem is what I’m going to teach today and collaborative allowing. The innovation have been able to allow teachers to author web pages. Cloning allows you to copy content into your website

David Porcello (SMILE Pathway) targets informal education of science and math. Learning Sciences and Informal Environments, people, places and. It talks about 6 strands of learning: learners experiencing, exploring, participating, reflecting about science. Recommendations include: learning objects should have learning goals, be interactive, have multiple ways to approach and use iterative design. Front line staff need support to actively discuss questions for diverse cultural views. SMILE is a central place for hands on science activities. NSF is building a lot of tools that include lots of personal content, mobile access, and widgets. It sounds a lot like what we are proposing for the ODLMS. SMILE is creating tools and services to support these in informal learning. They want to encourage people to use the SMILE tools. Focus on the educator and their needs.

Kim Lightle – Middle School 2 portal patheways. Teachers, students, and policy that affects teaching at the middle level. At Ohio State, Serena Nair is working with students to design learning environments for students. Mary Henton is looking at the policy of how to change what happens in middle schools. At the MS2 project they have built a portal for teachers. They are using a Ning based platform to connect content important to for teachers to know about in a way that it is all based in the technology. As teachers are learning about systems knowledge they are in wikis, in forums, and blogging. They are becoming part of a virtual learning environment for teachers. Surprises: Kim is not convinced that the “Digital Native” actually exists. Kids can buy shoes. Example: many 21 year old teachers didn’t know . Architecture of participation. If you build it, they might not come. They are putting content in lots of places to people will find it: Curriki, Indigo. “We are “. Object centered sociality – when you build a social network, you have to have content to build it around. The more complex the object, the more gravity it has and the more discuss. They have 570 registered members. Objects that have attracted attention are about integrating technology. It is interesting what people are looking for. The average age of registered members has 15 years of teaching experience. We should focus on second stage teachers. That is where we should focus (teachers who have figured out how to manage and are saying, I need something more). People found about the portal through friends primarily. One size doesn’t fit all. CBANS – Concerns based adoption model helps you understand what the needs of teachers are at a given stage. A social network allows differentiation by allowing people at each level to congregate and help each other. Book: Daniel Pink a whole new mind. He talks about symphony and about stem. We should focus on creative aspects of stem, not recal. Design for the future, not the past.

Bruce Mason, Director of Compadre. It is a service organization for teachers and learners in physics and astronomy. They try to bring people together to learn and find new methods. One of the biggest challenges of running Compadre. He wears 3 hats: Faculty member – don’t like change, showing them really cool stuff they can do is cool, but it will take a lot of work to get them into their classroom. Developer – he helps develop resources, faculty members evidence that approaches work and the materials and plans to easily fit new resources into what they are doing. We need to bring the results of past educational research into the world of cyberlearning. A community of educators that focus on the learning is powerful. The idea of a platform is a big challenge. Just last week 2 publishers came with learning platforms, but they already have Desire2Learn at their college. NSDL member – we really need to provide these services, not just a library and content. More important is that we show others how to develop content and use the tools. This should part of our sustainability model.

Questions: The cost of higher ed has multiplied. New technologies are being laid on top of them all and we are being charged for them all. How will cyberlearning address this? The open opportunities to do new things rather than replacing or substituting. It is far more expensive to not teach well. How do you evaluate student learning while technology is changing so rapidly? Use stable measures of learning consistently measure each technology. Teacher confidence is impacted heavily by reading websites. What does participation mean? What are they getting out of the experience?

In my part of our presentation I plan to talk about Teacher Training and Curriculum development. Here are some links I plan to use / reference:

• Overview of the eNLVM
• eNLVM eModules
• Curriculum development / teacher training case study
• How to rite good applets
• eModule research materials
• Transformation of Functions (example observations)
• Probability and Relative Frequency (example of simulations)
• What’s My Line (example of reinforcing group discussion with hands on experience)
• Patterns, Relations, and Functions (example of adapting by adding questions)
• Digging Dirt (example of open-ended, manipulative supported, grounded instruction)
• THEORY FOR AUTHORING TOOLS THAT SUPPORT TEACHER ADAPTATION OF MATHLETS
• Presentation on the eNLVM
• When Teachers Reuse and Remix Interactive Online Resources
• Interesting Interactive Math Websites

Teacher Training. A process I have used with teachers:

1. Demo a lesson
2. Discuss / critique the lesson together based on a rubric
3. Have teachers observe students while the lesson is taught
4. Debrief the experience
5. Revise the lesson
6. Reteach

Training Goals. My goals are for teachers to learn:

• Content knowledge
• Instructional strategies
• Familiarity with using high quality materials
• Where to find high quality materials
• Material evaluation / selection
• Help them enter a community
• Implementation issues
• Barriers / workarounds
• How to adapt existing resources
• How to evaluate student learning
• Processes for continuous improvement

Developing Interactive Math Curriculum

When developing curriculum, one of the first thing designed are the elements and structures of design and the processes of design, whether they be ad-hoc or structured. Curriculum design structures include time, learning outcomes, content models, instructional strategies, messages, representations, and media elements such as pages, displays and controls. Important design activities include:

• analyzing content,
• identifying desired learning outcomes,
• recognizing common student errors and difficulties,
• developing an overarching design,
• using design tools that allow for quick inexpensive prototyping and iteration,
• putting off expensive development as long as possible,
• using modular approaches,
• expert review,
• testing with real users,
• iteration

Considerations for Designing Interactive Math Curriculum

The design of interactive math curriculum should take into account the affordances that the medium can offer. These include efficient rich, dynamic, and linked representations, exploration, simulation of physically in-accessible situations and events, guided practice, immediate feedback, easy revision, recording sharing and replay, collaboration at a distance, linkages to real-time data, data sampling, and complex computation.

Contexts of Use

• Group presentation – projection, activity, discussion, worksheet
• Classroom station
• Computer lab (self-paced, pairs)
• Home work (self-paced)

Three Levels of Adaptation

• Activity instructions (via web or worksheet)
• Problem sequence (via web or instructions)
• Virtual manipulative (via configuration or code)

Multi-Disciplinary Teams

• Mathematician – Make sure the concepts / content / terminology / representations are correct
• Instructional Designer – Translate ideas into concrete technology designs
• Programmer – Develop virtual manipulatives
• Educator – Instructional sequences, strategies and types of activities
• Classroom Teacher – Access to students, anticipate student responses, guide implementation

Some Observations

• When an interactive model is on the screen, students ignore the text
• Text must be short and to the point
• Questions that require responses can help focus attention
• Transitions (going to lab, setting up equipment, getting people started, etc) waste time and need to be taken into account when designing experiences
• Always test out exact usage before going live and check again in the morning
• Developing virtual manipulatives is expensive
• Leverage existing manipulatives
• Choose areas where the impact will be greatest
• Teachers are much more likely to adapt than create activities

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.

While attending the 2008 Mountain West Ruby Conference and needing something to hack on I decided to take a crack at the project. I already hacked Google Translate for Send2Wiki so I figured it would be a snap to do for this project. My plan was to take the search text, run it through the translator for each of the languages to search, then pass the translated queries off to the Google search sites for each of the languages and then pass those pages through Google translate to get English versions of the pages. I soon found that Google has already done most of the work for me with their cross-language search.

The only thing cross-language search doesn’t do for me is collate all of the language results into a single results page. You can only search for results in a single targeted language. Anyway, between sessions (a coder has always got to brag about how fast he can work right I threw together a Multilingual Google Search Mashup that does the job. As I put it together, a couple of things almost immediately stood out:

• Wikipedia owns the top hit slot for many searches. Because their pages are essentially equivalent in the different languages, listing that entry for each of the languages isn’t especially useful.
• Interleaving search results is difficult. Rather than try to figure out an intelligent way to order in real-time the search results from the various languages, I just give the first two from each language and provide a language for getting more. I’ve got ideas for interleaving results, but none of them are too easy. Notice also that I haven’t included English in the search, which is probably where the most relevant pages will actually come from.

These issues makes me wonder if a different approach would be preferrable. Perhaps Google could annotate search results with relevant pages in different languages. This also makes me think about Google’s search result ordering. Google search results appear to be determinative (if you execute the same search twice, the same item will show up at the top of the list). While this may be what we have come to expect, my experience with writing OER Recommender makes me believe that it isn’t necessarily the best or the fairest thing to do. When ranking pages it is often the case that the scores of the top two or even 10 pages are statistically indistinguishable. So why should the one that happens to have a .00000001% higher score always show up first. My approach with was to identify a strata of rankings for those “highest ranked pages” that are virtually indistinguishable, I randomize the order. This seems fairer since it is quite natural for users to click on the first item in on a search results page, thus biasing it to become more and more popular.

“It was too easy to make a mess in Smalltalk” Ward Cunningham (Dynamic languages allow you to be undisciplined.)

Fundamental dilemma. Bad code will fundamentally slow me down. But when faced with a deadline, we go ahead and write bad code anyway. Showed productivity vs time curve. As a project wears on you become less and less productive. The only solution is to clean up the code.

Possibilities:

• Grand redesign in the sky?
  • It will take forever
• Incremental improvement
  • Always check code in better than you checked it out.
  • Never let the sun set on bad code.
  • Test First! – Provides the necessary flexibility.

RSpec & TestUnit – unit testing frameworks. Write your tests first. Target 100% coverage.

Showed an example of building out a command line argument parser. Starting with handling boolean arguments, then other data types.

Discusses the problem with if-else statements:

• They tend to duplicate themselves. If you want to change the code you need to duplicate it in lots of places.
• The original design pattern did not scale.
• Violates the DRY principle and the Open Close principles. Applications should be open for changes but closed for modification. Design so that you can add functionality without changing existing code.

Refactor when you smell a mess (festering pile) not when you have a mess (as early as possible). So there is this fine balance be over-engineering and keeping your code clean. So clean it when it starts to smell and not before.

Similar to writing essays, we should re-write code periodically.

Incrementalism

Don’t make massive changes in the name of improvement.

• TDD: Keep the system running at all times! I am allowed to make a change that breaks the system. Every tiny change I make must keep the system working.
• Running tests helps point out all of the places that changing the code impacts.

Get into the feel of running the tests continually. Autotest is a product that allows you do this.

Continuing his demo he showed how by creating marshallers he was able to move most of the data type specific code into one place.

Software is about separation of concerns. Segment code that changes according to how often they change. Put things that change a lot in a different place than those things that don’t.

Was it worth it? (refactoring his demo code) If you are worried about function and function alone you should not be in this business. If you are not a craftsman you shouldn’t be here.

The Green Band (A wrist band he wears)

• Professionals write tests first
• Clean their code
• The only way to go fast is to go well

Making a mess is not faster.

I attended a discussion group facilitated by Damon Bahr of BYU that focused on finding the balance between teaching for procedural and conceptual knowledge. I also attended a presentation by Blake Peterson of BYU that reported research comparing the presence in US and Japanese preservice training of discussion related to classroom management.

Wes’s Presentation
Wes gave a helpful overview of the main services of the MathForum. While I have visited there periodically it is so big that it is hard to get my mind wrapped around all that is there. Perhaps the most interesting things to me are the Problem of the Week (POW) online mentoring.

One of the challenges they are currently facing is sustainablity. They have mentors who respond to student responses to problems of the week. Because they recieve 300+ responses each week, they need a way to reduce the cost of doing so. Approaches to this that they are considering include: (1) Enlist University Professors and others to respond on a voluntary basis, (2) Start charging for the service. Data from a recent survey they conducted indicates that ~30% of teachers and students even care about the moderating. Another option I discussed with him is to try to automate some of the work. I proposed the following process:

1. Analyze past student responses to see what the degree of clustering of response types is.
2. If there is sufficient clustering, perhaps the work could be divided into two tasks, first sorting student responses, and then writing a response for each of class of responses.

Anderson and Koedinger’s research on feedback is that diagnosing errors in detail and giving detailed customized remediation based on the type of error is not nearly as important as getting learners back on the right track. Of course a lot of this research comes from studies of immediate feedback which, it doesn’t appear that PoW mentoring is. Something to consider anyway.

He presented briefly on the Math Tools DL. He gave the vision that they hoped to utilize what they have learned from the somewhat naturalistic evolution of the Math Forum to apply to the development of this new resource.

I also discussed with Wes the possibility of analyzing some of the NLVM log files to contribute to a characterization of different types of online communities. Here are some hypotheses I would like to test in regard to that:

• Sessions that last ~30-45 minutes are more likely to be from classrooms then sessions of different lengths.
• Multiple IP addresses from the same domain are likely from a given class.
• If students in a class access many different resources in the NLVM, they are likely “playing”. The teacher’s use of the NLVM is not for the purpose of supporting specific learning outcomes.
• In contrast, students all accessing the same small set of resources, is likely targeted use.
• Repeat usage can be gauged by looking at repeat visits of same domain over time.

My guess is that there is a lot of playing going on. We would like to increase the amount of purposeful use. This will likely increase when objective focused sets of activities are made available. Currently the library is what I like to call mathlet centered as opposed to objective centered. So far, using TADRIOLA I have created a few lessons that are objective centered.

One interesting hypothesis that Wes shared is that being busy is part of what it means to be a teacher. It is part of their identity. It is also a way of being comfortably secure. When a teacher is busy, life is hectic, but at least they can deal with it. When you ask them to do something new, and they respond that they cannot because they are busy, that may be a way of saying, I’m comfortable doing what I’m doing, I don’t want to try something new. That is not to denigrate the fact that teachers are in fact busy. There is lots of data to show that. Wes pointed out that despite their business, never has a teacher turned him down when he asked them if they would spend an hour with him to do an interview. My experience has been similar. In general, teachers have been very gracious to spend time with me.

I talked with Wes about analyzing the qualitative data that I gathered. He indicated that in a similar analysis he conducted a few years ago, he found teacher types that characterized teachers according to their skill and comfortability level using technology. He found that technical skill was highly correlated with pedagogical expertise. I’m guessing that my data doesn’t exactly bear that out.

I told him of my guess that while many of the teachers that I worked with indicated interest, I doubted that many would follow up. I hope that I am wrong. He responded, that with the sample size I had (~80), he expected that there would be only 1 or 2 among them who would take the initiative to lead out in innovating with the technology.

Sanne’s Presentation (PPT)

The main thing I got out of Sanne’s presentation related to problem representation. He talked about how a problem is represented, or how a person represents to themselves has a major effect on how effectively and efficiently they can solve it. This ties in heavily to what we have been doing on the NLVM. Providing visual, dyamic, and interactive representations of problems that make them easier to conceptualize and solve. Good representations obscure details that are not needed to make decisions and accentuate details that are important for solving the problem.

Dr. Merrill’s Presentation

As usual, Dr. Merrill’s presentation was passionate and thought provoking. He pushed for theory building and empirical validation. I am all for that, however, there are questions other than will students learn from this? that are important, such as will teachers use this? will students use this?