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Design, Learning, and Collaboration Assignment 5 Jonathan Marbach #try to find an answer to this problem! Well, that was fun! 1. document briefly your thinking – including all the important intermediate steps and failing attempts (i.e., create a "think-aloud protocol") The first thing I thought to do was to print out the grid and 31 dominoes and try it! Since we were asked to try a collaborative approach, I asked my housemates if they wanted to try a brain-teaser. I first worked on the puzzle with Hilary, and we tried some pattern based approaches but each time it disintegrated into random trial and error. All these attempts of course failures. Hilary became quickly fed-up with the little dominoes and got out a pad of paper to work it out on her own while I continued with the pieces. All of our efforts ended in two empty squares at a diagonal. From there I approached the problem like one of those puzzles that you slide the squares around in, pushing the pieces around to try to get the empty spaces to come together. Of course, I had no luck. Hilary, in the meantime, had come up with an attempt at mathematically proving it wasn't possible which sounded pretty good to me so I decided to move on to letting another housemate give it a try. Although Chris was too wrapped up in his Martha Stewart cooking show, Erik attempted the problem. At this point I had come to accept that when solving a complex problem like this, collaboration was a lost cause because the solver was focused so intently on envisioning how the layout would unfurl that it left little brainpower for communication. A few times though, during commercial breaks, Chris would make a suggestion or critique of Erik's layout, so collaboration wasn't totally unsuccessful. Erik was working with patterns too, trying to find one that was "mirrorable" so that if one half the board was complete, the whole thing would be. Another interesting angle Erik worked from was to minimize the impact of the missing corners by trying to construct an empty square in the center. Greg gave it a try as well but quickly gave up saying, "I think Hilary is right." Not wanting to give up, I tried a few more methods such as winding the dominoes around in a spiral from outside to inside, but still found no solution. Then I thought again about what the assignment said, "Try a collaborative approach". [Not an exact quote of course...] And that's when it hit me. Although I realized it would take the fun out of looking for an answer, I realized I could look up an answer on the web. Sure enough I found a page that said it was impossible and explained why, but I must admit that the explanation left me slightly unsatisfied. 2. which resources did you use to solve the problem? I used a printout of the grid and dominoes, Hilary worked out ideas with pen and paper, and ultimately I resorted to searching the web for information. 3. which process did you use? I mostly used trial-and-error but it was founded in pattern seeking. 4. which practice (of you or others) did you use? I'm not sure what you mean by a practice. 5. could computers be useful to solve this problem? Maybe a computer simulation of the dominoes would be easier to work with than the little pieces of paper that I cut out, but ultimately all the machine could do to solve the problem would be to evaluate all possible permutations of domino placement on the board. This of course would be quite a lengthy process. 6. what have you learned solving the problem: in general and for our course? Hilary's dislike of the movable pieces on the board further supported the idea that people will want to approach solving a problem in varied and possibly conflicting manners. You can't assume that the methods for solution that you lay out will be accepted or adopted by the problem solver. Also, for some problems, interpersonal collaboration is not well suited. This kind of problem required the solver to think deeply and independently. Being able to discuss the problem with others at a general level was helpful, but working on a specific solution would require the solver to focus and visualize extensively, thus limiting his or her ability to communicate. In addition, social exploitation did not apply because noone in the house had any knowledge that could contribute definitively to the problem. Hilary's rough mathematical argument for why it was impossible wasn't convincing enough, so the social aspect wasn't advantageous. Ultimately though, outside knowledge - from the Internet, determined the fate of the task. 7. what have you learned not being able to solve the problem: in general and for our course? Well, in general, I would say that it is good to know up front whether a problem is solvable or not. If we could have proved the impossibility of coverage, we could have saved time and effort. I'm not sure what the relevance to the course is though.
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