Hi Ken:

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> Hello,
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>>
>> You say: "The SCG approach is different than what we, as computer scientists and mathematicians, are used to." Do you say that because in mathematics you did not hear about refutation (or falsification)? Mathematics is about showing formally that for certain claims
>> a refutation is impossible if the scholars play perfectly. Those claims become theorems.
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> I may have poorly worded that sentence. I meant that during CS and Math classes, when assignments ask students to work in groups, we generally work together to achieve a solution, not so much as playing a game of refutations and finding a winner.

I see what you mean. SCG creates a controlled scientific discourse between the scholars with the goal to find the best solution to a computational problem. This is different from just coming together ...
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>  
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>>> In our class; however, I feel that SCG is kind of hidden in the background during class sessions; and they really bite during the homeworks. Some work as a pair; some work alone; and some may work as a trio. I believe it may be more effective in larger groups because the homework problems are actually hard.
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>> I will make SCG much more explicit during class sessions. And I will explain the theory behind it in a better way.
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>> It is interesting that you suggest larger groups. How large would you make them?
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> I do not really have a preference. The homeworks are hard and considering works in other courses as well, at times, solutions and or claims may be hard to come up with. This may be due to a lack of understanding. So for example, one of the homework assignment was related to a diameter and some distance formula. I think it may be the 3rd or 4th homework. The solution was basically in the shape of a flower. But when we tried to come up with something, it's not quite so easy. Some worked for few nodes, but adding more really didn't help. And so working in pairs limits the knowledge going back and forth.

We can change the course to accomodate your suggestion. We can add wikis in which we play multi-player SCG games. Then larger groups of students can get together and learn through multi-player SCG. I will do this this semester.
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> I believe this struggle helps later on because we get a better understanding of limitations and the kind of approaches that won't work. At the same time, there may be a lost of interest and focus to solving something if the answer is too hard to come by and we, the team, has no further ideas.
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 I can see that. There is a fine line between becoming disappointed and having a big "aha" moment.
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>>> The class sessions had some very interesting times, but I may find them more effective if the time were used to work out more SCG protocols rather than reading off powerpoint slides. I believe we, the class collectively, can go to the site and skim through the slides so we can focus on the actual material and or any concerns/issues we, the class collectively, had. 
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>> So you are saying we should play more the SCG game in various algorithmic domains rather than covering material from Powerpoint slides. You believe that creates a better learning environment.
>> I believe you are right. Learning by doing is the best way to learn.
>> But from the instructor's perspective it is a resource issue: preparing a "traditional" lecture takes less time than preparing an SCG-based lecture.
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> I believe that the class can be more interactive. Powerpoint slides are fine and useful to demonstrate concepts; however, reading off Powerpoint slides tends to be less effective because by the time an instructor reads them, those who are present and are attentive would've already read them.
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>>> I believe that some of the refutations in the homework assignments were silly because the correct answer is already known.
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>> I don't follow why they are silly. Consider the statement which is known to be true (called the
>> Four Color Theorem) : All planar graphs can be colored with 4 colors.
>> If you defend this claim, you will be given a planar graph and you will have to color it with 4 colors.
>> Although you know it is possible, it is much harder to come up with a coloring.
>> Do you consider constructing the coloring silly?
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> I consider that if a team member answers or even the team collectively answer the question successfully, the refutation protocol is silly because you can make up a fake one. Brandon and I normally sit down and read the assignments together prior to working on them. If at the time we can already spot the solution, then how should the refutation protocol be played out?

    
 When the claim is: Exists x in X ForAll y in Y: pred(x,y)  and you have a solution how to construct an x in X then you are in the best position to defend the claim. If your partner had the same idea, then I agree that the game becomes uninteresting because there is general agreement that refutation is impossible.
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> Ken

Thanks for sharing your thoughts with me! This is helpful for this semester.
     
-- Karl