Index - Third Quarter

• Cookie statistical distributions (September 17, 2011)
• Glenn Shafer's talk and possibly bypassing the non-enumerable states problem (September 23, 2010)
• Conditions for action-application (July 28, 2010)
• Coalition or Non-cooperative games? (May 04, 2010)
• Multi-agent planning, critical resource (January 31, 2010)
• What good learners think and do (August 07, 2009)
• A problem statement (August 06, 2009)
• Carrot ninja ball (June 13, 2009)
• Ordering of steps (June 09, 2009)
• Ontologies: a subtlety (April 15, 2009)
• Decision theory for teaching strategies (February 11, 2009)
• What is teaching? (February 09, 2009)
• Educating myself about Education (June 15, 2006)

September 17, 2011

Cookie statistical distributions

Has this ever happened to you: You need to perform a certain function, and you assume a tool exists to do it for you. After all, it is a fairly obvious operation. But then you start looking around, and it seems like nobody knows what you are talking about!

My last entry was about the likeness matrix. I want to be able to say, "Give me a statistical distribution of the people who are like Christy. That way, I can take the people who are in the highest standard deviation of those most like her. Or, I could take the lowest ones at the other extreme standard deviation and have the people most UNLIKE her. I want to examine the distribution to figure out if Christy is a generally "a-likeable" person or if she is kind of an oddball and there are very few people."

Obviously, I don't have very much experince with statistics. This ability to take objects associated with certain points in the curve is not easy to do. I can't find any tools that let me do this!

Posted by Frozone Permalink on September 17, 2011 01:46 PM | Comments (0) categorized under Computer Science & AI
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September 23, 2010

Glenn Shafer's talk and possibly bypassing the non-enumerable states problem

This morning, Glenn Shafer (yes, THE Shafer like from the Dempster-Shafer theory) visited the University of Saskatchewan and gave a seminar entitled, Game-theoretic probability and its applications.

I got a lot out of the talk. Earlier (Pen scratches: elementary game theory) I identified a problem with Decision Theory (DT) for my application purpose, namely, that DT is built around the uncertainty being directed at state TRANSITIONS, while the states themselves are presumed to be well-defined and enumerable. I think that the structure presented by Shafer this morning is freer of some of the baggage that was holding me back.

An important theme in the talk was to contrast two frameworks for probability: Measure Theory and Game Theory.

I might have this wrong, but, my understanding is:

In the Measure Theoretic sense, you basically count up all the leaf nodes in your probability tree and count up the favourable outcomes in order to discover the probability you are trying to measure.

In the Game Theoretic sense, you basically calculate a "starting wager" (which is related to the measured probability above) which would identify the next branch in the game tree that leads to your desired outcome. (?) Your prior/given/assumed/wanting-to-test-THIS-result/ -type information basically points the leaf nodes which identify the subtree.

Shafer's new point is that his presentation of Game Theoretic Probability can be used to construct proofs (i.e. find solutions) even when we don't have cases for everything.

My brain wanted to translate this to "even when we can't fully enumerate all possible states".

I have been trying to use formalisms to bring in "observables" (learner model attributes, etc.) and pre-know processes / tricks-of-the trade/ even production rules, if you will - and some other stuff together to build an adaptive, personalized learning environment.

In an educational system, you CANNOT fully enumerate all possible states, so this is an interesting connection.

You can't fully enumerate all possible states in an education system because the state will represent the learner model (which you are TRYING to change anyway, see Payoff matrix) and will also represent the learning environment, which would also change -- new learning objects get imported, etc.. See also Strategy and Process. I believe my thinking here, and even ability to articulate it, was also influenced by some post-talk conversation with Gord. :)

Posted by Frozone Permalink on September 23, 2010 12:15 PM | Comments (0) categorized under Pedagogical modelling
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July 28, 2010

Conditions for action-application

This entry is a hasty record of a brainwave about strategy, process, and action generation.

How does a game theoretic agent generate its next action? I kept thinking that certainly the action-selection must be a choice for the agent: See, it should be given a list of POSSIBLE actions, and it has to pick the best one. (Perhaps it is another subsystem that generates this set of possible actions.)

I've devoted a fair bit of energy into "Process Modelling", and I keep coming back to the question: If you are following a known process, why is "action generation" such a problem? If you have a sequential process modelled ahead of time, isn't the next step obvious? There should be just 1 choice when you are following a pre-defined process, right?

Well, it's not so simple. Each action would have conditions under which you should apply them, and you have to take the learner's current situation into account.

When you model process, you can't just list a sequence of actions. Also required is the set of conditions under which each action-selection would be best. This is strategy, and this is why I am reading up on game theory. I want to know about action selection, and the application of conditions -- how is strategy encoded? How can this map to pedagogical knowledge? (For more on computational modeling of teaching strategy, see this other entry, Revisiting: What is teaching? Some models)

Gord asked me the other day, "So what does Constraint Satisfaction have to do with Game Theory?" Maybe this is it. Maybe conditions for applying a particular action in a particular situation can be modelled with constraints; I am not sure how you would use language for the fact there are many agents and the constraints may deal with specific ones, relative to your current position.

Posted by Frozone Permalink on July 28, 2010 05:53 PM | Comments (0) categorized under Pedagogical modelling
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May 04, 2010

Coalition or Non-cooperative games?

I am reading Essentials of Game Theory: A Concise Multidisciplinary Introduction by Kevin Leyton-Brown and Yoav Shoham. I'm enjoying it because it is helping me to learn about Game Theory faster than some of the other texts I have obtained. This text does not emphasize mathematical notation. Although I believe that mathematical notation is critical for clarity when working with complex systems or ideas, I have also found that it slows me down when I am still in the "broad sweeping" phase of research. It takes longer for me to extrapolate meaning from mathematical notation than it does for natural language.

Anyway, the purpose of this entry is to comment on the distinction between "Non-Cooperative" and "Cooperative/Coalitional" games. The text suggests that the distinction is about the units of study: individuals or groups.

This caused some eyebrow furrowing on my part. My self-proclaimed interest is Cooperative games. However, I would also tell you that I care more about the interactions between individual agents than I care about interactions between groups of agents.

At any rate, I will keep reading the text. My field is pretty new, so, perhaps all that is needed is an elaboration on some of these concepts.

Posted by Frozone Permalink on May 04, 2010 06:48 AM | Comments (2) categorized under Pedagogical modelling
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January 31, 2010

Multi-agent planning, critical resource

In my problem, I would say that the Learner's time and their screen real estate are "critical resources".

That is, if many agents (the learner, the system helping the learner reach their goals, maybe some learning objects themselves) are acting independently, but cooperatively, they all have to be aware of the shared critical resource which is the learner's attention. They have to cooperate to arrange options on the screen effectively. Ultimately the Learner has the Uberest power to procrastinate or follow their lessons diligently, but, the other agents might be aware of affective and motivational things, too.

This thought occurred to me as I was reading Larbi et al. 2007 Extending Classical Planning to the Multi-agent Case: A Game-Theoretic Approach.

Posted by Frozone Permalink on January 31, 2010 10:19 PM | Comments (0) categorized under Pedagogical modelling
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August 07, 2009

What good learners think and do

I dropped off my daughter at daycare this morning, then I came home and slept from 9:30 a.m. - 1:00 p.m.. I'm definitely feeling better now than I was before! I was just digging through my "to read later, when I have time" email before going to pick her up, and stumbled on this interesting article about student retention that my boss had circulated to the staff, but that I had not yet read. I'm interested in student retention issues because I'm keeping an eye out for building in elements into educational software that keep the experience exciting & fulfilling. (Game designers do this too.)

From Tomorrow's Professor mailing list, Are Your Students On Course to Graduation?, here are 8 things that good learners think and do.

1. accept self-responsibility, seeing themselves as the primary cause of their outcomes and experiences;
   
2. discover self-motivation, finding purpose in their lives by discovering personally meaningful goals and dreams;
   
3. master self-management, consistently planning and taking purposeful actions in pursuit of their goals and dreams;
   
4. employ interdependence, building mutually supportive relationships that help them achieve their goals and dreams (while helping others to do the same);
   
5. gain self-awareness, consciously employing behaviors, beliefs, and attitudes that keep them on course;
   
6. adopt life-long learning, finding valuable lessons and wisdom in nearly every experience they have;
   
7. develop emotional intelligence, effectively managing their emotions in support of their goals and dreams; and
   
8. believe in themselves, seeing themselves capable, lovable, and unconditionally worthy as human beings. (oncourseworkshop.com)
   

Other entries, in chronological order, where I have logged these "pedagogy nuggets" are:

• Educating myself about Education
  
• Modelling teaching strategies
  
• What is teaching?
  
• My pedagogical issues
  
• Revisiting: What is teaching? Some models
  
• A good survey-ish paper for my area
  

Posted by Frozone Permalink on August 07, 2009 01:33 PM | Comments (1) categorized under Pedagogical modelling
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August 06, 2009

A problem statement

I'm fixated on the thought that ideas can be represented spatially -- and by ideas, I mean concepts-to-be-explored-by-a-learner -- and that I might be able to use planning technology to help fold together these ideas in the art that is called tutoring. It requires empathy of the learner's context (empathy that can be enhanced using a computer's superior memory) as well as expertise on the subject matter, as well as knowledge of how to apply pedagogical techniques.

Advances in knowledge engineering give us tools to represent domain expertise. Lots of work is going into student modelling, and I believe there are whole conferences devoted to it. (Mental note to continue my quest to get a better "in" on the world of computer science conferences!) But I am still foggy on what to do with the pedagogical techniques, i.e. how it all fits in. I tried to squeeze it in using a utility function in decision theory. I looked at the idea of tagging micro-pieces of teaching techniques and assembling those into a pedagogical ontology, like this. Recently, I was inspired to look at pedagogy as a "mode".

Where am I now? I'm not sure. I'm in a lot of pain, not just from my throat, so I think I'll end here and maybe flip through some papers. But I'm glad to have articulated my problem from a broader vantage point. :)

(I have a sore throat. It is intensely painful. I can't sleep. Tea with honey seems to help. Since it's the middle of the night, I thought maybe I could at least use this rare time to myself (although pain-filled, alas) to play with some ideas.

Posted by Frozone Permalink on August 06, 2009 12:49 AM | Comments (0) categorized under Pedagogical modelling
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June 13, 2009

Carrot ninja ball

I had a thought - quite a messy thought: I don't know if I'll be able to articulate it -- but I'm going to try here, clumsily. I don't even know how to describe it, so the title of this entry is just some random string of words. Mmmm, carrot ninja ball.

It started with my thinking about the job of the computer: to provide an environment for students to build¹ on their new knowledge, to apply it and keep track of and evaluate it.

So the planner, or a part of it, would include a transition function, i.e. a mapping of possible future states, somehow related to the next-action-to-be-executed. I guess I'm thinking of the student model. The current state would include a definition of what we believe the student to "know". Or, looking at it another way, we could just have the current state keep track of any new knowledge that we just presented to the learner.²

The set of possible FUTURE states would describe the different ways that this new knowledge could manifest itself. My original scribble/articulation of this idea read, "Different ways that what-you-showed-them (i.e. when you introduced new material for the first time) could manifest itself." Right. So, future steps - what you are predicting - are all the ways that you think the student could take what you showed them, and, using the environment and the tools at hand, "build" it. (There's my learning theory side-thought again, hrm.)

There are a zillion ways to build the whole thing (i.e. ways that the student could put their knowledge into practice, to move from remembering to understanding to application or other some sort of progression through levels of learning (sorta relevant wikipedia entry to give an idea of what I'm getting at), I'm thinking about Bloom's taxonomy or Anderson's refinement of it). Dispite that there are so many ways the student can let their new knowledge manifest itself in this physical environment, hopefully you can refine and narrow down the options as you gather more clues about what they are doing.³

Clarifying again. This is like 4 or 5 iterations now of the idea, heh.

The first step of the teaching strategy is to introduce the material. The crux of the plan is to predict how you think the student might create that new knowledge, given their current environment and the tools at hand. Why are we trying to anticipate the student's actions? So we can provide the right tools and prompts, according to the teaching strategy we are following.

So how does the machine's next step fit into the plan-state plan? It's like first there's the introduction, then the prediction of the student's reaction, then the establishment of the machine's next action.... and the machine's next action sort of folds up into the start again, doesn't it, somehow?? Like, the learner's own creation feeds in as input, and the machine's prediction of this and how it should provide the learner with like a mirror so they can see into their own mind/understanding....

I just had this vision of a ball, or that strange loop thing again ("carrot ninja ball -- of course it is orange like a carrot"), rolling from new material, to creation, to reflection... and the ball was rolling through task domain knowledge, because every step: the introduction, the creation and the reflection -- al involves ontology references. But it's like you're chewing them from different angles. Chewing and regurgitation, moving along in a crunchy path like pacman!

So the plan-state plan starts with the node that represents that you introduced the concept. Neighbour nodes represent the laying down of tools as the student creates. The machine has to ensure appropriate tools are available.

The teaching strategy could dictate the system's reactions to the learner laying down tools, by questioning or challenging or affirming, etc..

Err. I was right, that was clumsy. But I can't expect new ideas to come out perfectly. SO there they are, hopefully I'll be able to work them into some structure, making ties to decision theory or AI planning to tame the beast and make it do its job. :)

And the baby is awake now, so that is good timing!

---
¹ I'm having a side-thought about biases towards different learning theories: constructivism, etc.. I really should compose an entry about those, too, because I keep wanting to refer to the thought.

² Another side-thought: I know that every state transition will not involve the latest action being "introduce new material". But I don't know if I want to restrict or define the "introduction of new material" to be an ACTION, per se. But I guess it is. Hrmm. Anyway.

³How is this different from the "prediction of misconceptions and taking actions to correct them"?

Posted by Frozone Permalink on June 13, 2009 09:53 AM | Comments (0) categorized under Pedagogical modelling
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June 09, 2009

Ordering of steps

I often start writing entries with an excited feeling, because I like to explore ideas that I've never talked about before. But between those thoughts and the time I sit down at my computer and click "New Entry", these other questioning thoughts sorta peer out of the bushes chanting things like, "That idea is so obvious, and so silly, it makes you look like a n00b." To those little gremlins, I say, "shoo! shoo!". I've got work to do, here!

So I'm still working my way through that book I mentioned last time. I read about sub-goals, and how these transform into "adding a new action to the plan". I also read about action ordering, and about causality between actions. And naturally I'm trying to relate all of this to the process of teaching.

From what I recall from the literature, traditionally a sub-goal in instructional planning manifests itself as a discovery that the student is missing a piece of knowledge, so you kinda have to plan in a "catch-up" lesson to work through before continuing with your overall plan of teaching them something "bigger".

I wanted to spend some time thinking about how else these "ordering of steps" (i.e. adding new actions (sub-goals), adding ordering constraints and other plan-specific things) might relate to my problem.

Earlier, I mentioned IMS LD, and I'm at a point now where I want to take a closer look at it. Can I pick out "activity ordering" from these technical specifications and discover how these might relate to AI planning? (Hasn't anyone written a paper about this already?)

On my first crack, I guess I'm looking at Learning Design Levels A and B.

And now the baby is awake. Sheesh! Grumble, grumble, snippet researcher.

Posted by Frozone Permalink on June 09, 2009 02:15 PM | Comments (0) categorized under Pedagogical modelling
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April 15, 2009

Ontologies: a subtlety

The word "ontology" has become a buzz word. It's too bad, because my research interests are veering in this direction, an i feel kinda.... yucky.... to be researching something "trendy". Oh well, it's minor; I can't stop following this path just because it's starting to become more popular in recent years. =)

Anyway, I'm noticing that different papers use the term "ontology" to mean subtly different things., I wanted to file away this mini post to clarify what I mean by the term in my work. I first learned about the term in a philosophy/metaphysics course, and that will forever influence my use of he term in computer science. Your ontology is what exists in your world. It is an organization of the concepts you can refer to.

I was just reading a paper that said something to the effect of, "the ontology is a description of educational goals". I disagree, and that's what prompted me to record this entry. I think that task domain ontology references form an important, even a central part of the educational goals. However I think that it's a different component that specifies *what level* you are shooting to have the student experience a concept. For example, your ontology might refer to concepts in geology such as types of rock (metamorphic, igneous, sedimentary), but what you want the student to do with that information (example: use the term in a matching game vs. describing the process to a fellow student) is part of a different representation. (Possibly employing another "ontology of levels of learning"!)

This whole issue is a little ironic, if you think about it. The point of an ontology is to help machines intercommunicate and have a way of letting them know if they are referring to the same concept. Yet, the word "ontology" itself has its ambiguities.

Posted by Frozone Permalink on April 15, 2009 04:08 PM | Comments (0) categorized under Pedagogical modelling
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February 11, 2009

Decision theory for teaching strategies

I'm trying to wrap my head around decision-making under uncertainty using decision theory and Markov decision processes. After a lot of tumbling and turning, I realized that I'm trying to compare and contrast two things:

1. optimal policy construction, and
   
2. Markov decision processes (MDPs).
   

These are 2 ways (not the only 2) to tackle decision-making. This post is going to be about #1 -- I'll tackle MDPs another day. As for policy construction -- I began my hunt with the notion that you would start with an influence diagram such as the one here.

Your decision problem is modelled as a graph. The square nodes are decision nodes. The diamond nodes are utility nodes. The circle nodes are the same as the nodes in a bayesian network. Circles can point to diamond and squares. Squares can point to diamonds and circles. Only one diamond allowed per diagram.

A policy (I learned to represent policies with the greek letter delta, δ ¹) is like a "rule of thumb" for the action you choose when faced with a decision. The optimal policy is the policy that gives you the greatest utility (from the triangle node). You can think of the policy as being connected to the decision nodes (the squares).

One thing that has confused me for a looong time is that your random variables (circle nodes) can be either "states" or "observables/evidence". Recently I had a little epiphany where I thought of the states as your ontology and your observables as your epistemology.

I'm perplexed about the application of a decision network like this. Would you use the same network over and over? I guess you would have to build a network for each type of decision you'll need to face. And, the only time you'd re-use the same network is if you face exactly the same sort of decision again. Although you could modify the values in the CPTs (conditional probability tables) if you had better information the next time around.

Anyway, a "policy" is something that you can apply to your decisions, and the policy tells you which direction to go. It is a function from states to actions. Basically, for all decision nodes in your network, (all squares), your policy is the set of decisions to make -- one decision per decision node. (So, is policy construction always an offline problem?)

With that background in mind, I want to return to the paper I was reading last time. Remember, my whole quest right now is to figure out, "What is teaching?".

In this paper, I think I was a little mislead by their usage of "pedagogical strategy". I was thinking, "oh, are they modeling how to gently guide a student vs. material that's new to them vs. challenging a student to get them to become even more familiar with material they've already been introduced to?" But after reading the paper a couple of times (and I could still be missing something -- the material was pretty dense and a lot of it very technical) I think what they meant by "pedagogical strategy" was "the order in which concepts are introduced". To me this is only a small dimension of a teaching strategy. It's like, this is the "content planning" without "delivery planning".

I was also a little surprised to learn that these researchers used artificial students. I didn't understand what was being measured with the artificial students -- which part of the system was being "tweaked" by optimizing against different types of students, and where they got the "student types" from. (Thinking, 'hey, could I ever use artificial students in my experiments?').

I missed out on learning about "Reinforcement learning" and how they were using MDPs. I still have so much more to learn before I can really grasp a lot of the research that is going on.

On the bright side, this paper did force me to take a closer look at decision theory.

Anyway, my journey about finding teaching strategies continues. I also feel like I'm getting closer to picking a thesis topic. (HA! I know, I've been saying that for years..... ugh.... lol). But, I'm confident enough this time that I might put this statement on my "About Me" page: I'm interested in how to model teaching strategies such that an abstract task domain ontology can be taken and "filtered through" the teaching strategy. This way, you'd have a universal machine that can teach. Scientists all over the world can continue to make discoveries about physics or math or chemistry or astronomy or geology or medicine or anything, and any Jane Doe could learn about it if she wants because she'd have a(n artificial) tutor to help her explore the material whenever and however she wants. I'd like to figure out how to take a learning object and weave it into an instructional plan that is conscious of overall themes and stories that can stretch from lesson to lesson to create an enjoyable, meaningful experience.

¹I have also seen pi (π) used to denote a policy. I don't know if there is a difference or if it's just inconsistent notation.

Posted by Frozone Permalink on February 11, 2009 03:22 PM | Comments (0) categorized under Computer Science & AI
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February 09, 2009

What is teaching?

I started reading a paper ([Iglesias et al., 2009] Learning teaching strategies in an Adaptive and Intelligent Educational System through Reinforcement Learning). On the first page, the article starts talking about how to define a teaching strategy, or rather what a pedagogical strategy specifies, exactly. The authors say that it "specifies how to sequence, how to provide feedback to students and how to show, explain or summarize the system content", and they reference the Murray paper (which I too have referenced before, indirectly!).

I stopped reading the article here because I wanted to brainstorm for myself what I thought a computational model of a teaching strategy ought to address.

• it's about what you're making the student do
  
• it could include the LOC of control, a la [Vassileva & Wasson, 1996]
  
• the frequency of interaction between the system and the student (i.e. are you giving them lots of time to reflect & build on their own, or are you "holding their hand" by questioning and guiding a lot? This is related to the point above, I guess.)
  
• group dynamics: when different members are called to do different things, a la SI style
  
• a model of how to "step back" to let the student struggle, vs. how to jump in and hint, how the system figures out *what* to hint (vs. the point above, which was more about modelling the frequency of the interactions vs. how to model the interactions themselves)
  
• when and how to be the "trixter" and put forward a deliberate incorrect piece of information to give the student the chance to say "hey, there's something wrong here!" so they can build up a little bit of conviction
  

Okay, I'm going to keep reading the paper now. It'll be neat to see how much of my thoughts overlap with what these authors have done. I also appreciate how deeply they've gone into implementation details (as I flip thorough the rest of the paper) because that's where I've really been struggling: how to turn wishy washy ideas into proper SCIENCE. (Reminded of my posting with the pink fairy at the end... lol, I'm such a kid!)

Posted by Frozone Permalink on February 09, 2009 10:14 AM | Comments (0) categorized under Pedagogical modelling
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June 15, 2006

Educating myself about Education

I began my research about Education by starting with a question:

What would the College of Education teach a first-year student about how to be a teacher? What topics would a course like "Education 101" cover?

I hunted around, hoping to find a course website with assignments or even a reference to a textbook... but no luck. I even (very) briefly considered enrolling myself in the college and signing up for a couple of the courses, heh heh.

Somewhat defeated, I switched tracks back off of Education towards my home territory in Computer Science. I dug up this paper written by my favourite German researcher, Carsten Ullrich, and read about how his ActiveMath computer system models pedagogy in Pedagogical Rules in ActiveMath and their Pedagogical Foundations. He makes reference to an Educational Technology researcher named M. David Merrill, who has worked on an excellent and thorough review of instructional design theories in First Principles of Instruction. Hurray!

From skimming Merrill's work, I found these particularly interesting, also in brackets I've marked Ullrich's hooks back into Computer Science terminology:

• Instructional design theories:
  • Problem - "Learning is facilitated when learners are engaged in solving real-world problems."
  • Acivation - "Learning is facilitated when relevant previous experience is activated." (Learner recalls, describes, applies)
  • Demonstration - "Learning is facilitated when the instruction demonstrates what is to be learned rather than merely telling information about what is to be learned." (Examples)
  • Application - "Learning is facilitated when learners are required to use their new knowledge or skill to solve problems." (Feedback/error diagnosis)
  • Integration - "Learning is facilitated when learners are encouraged to integrate (transfer) the new knowledge or skill into their everyday life." (Motivation)
• Student modelling
  • Topic mastery levels / Learning outcomes
    • Knowledge / Comprehension / Application
  • Cognitive modelling
    • individual tends to organise information into wholes or parts
    • individual is inclined to represent information during thinking verbally or in mental pictures

Reading about Scenarios in the ActiveMath system was also very interesting:

• Overview Scenario - general overview of course concepts
  
• Guided Tour - can take 3 different angles on the course, one for each of Bloom's Knowledge/Comprehension/Application
  - Knowledge Scenario - runs the student through a dimension of the course (or can be thought of as a separate course altogether) that enables the student to recall/describe/name concepts
  - Comprehension Scenario - generates a course that enables the student to explain/identify/grasp concepts
  - Application Scenario - generates a course that enables the student to apply/use concepts.
  - Union Scenario - Honestly, I didn't understand this one. I quote from the paper, "The fourth scenario, in principle the union of the above scenarios, teaches the student about the chosen concepts without focusing on a cognitive domain. These scenarios use the ActiveMath extension competence-level of the OMDoc [6] metadata. Using this metadata, an autho can cencode whether the learning outcome of an element mainly targets knowledge, comprehension, or application." ....Perhaps this is the one that adapts each concept to the learner.(???)
  
• Excercises-only Scenario
  
• Concepts-only Scenario (exam preparation)
  
• Rehersal Scenario - shows the learner learning objects that they've already seen
  
• Terse scenario - removes all well-mastered content
  
• Polya-style proof-presentation scenario - not much detail on this one
  

I think I'll go get another cup of coffee and read Merrill's paper more thoroughly.

Posted by Frozone Permalink on June 15, 2006 07:40 AM | Comments (0) categorized under Pedagogical modelling
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