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Assignment 6: Simon’s “Architecture of Complexity” and The Importance of Representations in Design - Jodi Kiefer

Questions about Reading Assignment:

Name the two most important things/concepts which you learned from the reading the chapter “The Architecture of Complexity”

1. give a one paragraph explanation why you consider these concepts important

I thought that the state and process descriptions were two important concepts described in this paper which relate directly to learning. Simon states that a state description are things like pictures, diagrams and blueprints whereas process descriptions are things like recipes and differential equations. I believe that the process of learning incorporates both types of descriptions. The state description is a visual understanding of the material whereas the process description is more of a true comprehension of the material. However, I believe that a conception of the state description must exist before the corresponding process description can be both understood and beneficial. Understanding how both the state and process descriptions either incorporate or demonstrate learning is important to be aware of when trying to promote learning to others through multimedia.

2. are the concepts relevant to your work, to your interest, …. – if yes, why?

Yes. I am very interested in how an individual learns. My past teaching experiences have inspired me to continue down an educational-based path in both research and as a career goal.

Questions about The Importance of Representations in Design — The Mutilated “8x8” Matrix

remark: check the attached PDF file to see the graphical image

The Problem:

The associated PDF file shows you a mutilated “8x8” matrix (the two opposing corners cut out) and a domino block. One domino block covers exactly two fields of the “8x8” matrix.

Note: It is straightforward that one can use 32 domino blocks to cover a complete “8x8” matrix.

Question: Can one cover the mutilated “8x8” matrix with 31 domino blocks?

Please do the following (please structure your answer accordingly — thanks):

1. try to find an answer to this problem! ‡ document briefly your thinking — including all the important intermediate steps and failing attempts (i.e., create a “think-aloud protocol”)

At first I tried to eyeball the problem by visually placing dominos into the squares. I quickly found that this wasn’t getting me closer to a solution and I knew that I would not be able to try all of the possible solutions. I then turned to Google and searched to find that others have proved this particular domino problem impossible.

2. which resources did you use to solve the problem?

I searched Google on the Internet.

3. which process did you use?

After searching on the internet through Google, I found several proofs proving this problem impossible. One proof that I particularly liked was the following:
A domino covers two squares of opposite color (i.e. a checker board). The two squares that have been removed are of the same color.

4. which practice (of you or others) did you use?

I’m unclear as to how this question differs from #3.

5. could computers be useful to solve this problem?

Yes. You could write a program that used a brute-force method to solve the problem based on an imputed set of rules (i.e. a domino can not hang off the board or a domino can not be placed over another domino, etc.). The computer could quickly tell you a correct solution (if one exists).

6. what have you learned solving the problem: in general and for our course?

7. what have you learned not being able to solve the problem: in general and for our course?

Collaboration is an amazing resource. If I had not searched the internet for other possible attempts and/or solutions to this problem, I would have spent a lot of ‘wasted’ time trying to come up with a solution, when in fact, there was not a correct solution to the problem. From a personal standpoint, my tendency when solving a problem is to assume that a solution exists. In order for me to concede to the fact that no solution exists, I tend to have to exhaust all possible solutions versus simply trying to prove that a solution does not exist. For efficient problem-solving, I believe the combination of proving and disproving methods and techniques should be considered.

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