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Nathan Balasubramanian's Response to Assignment 6

Read chapter 8 in Herbert Simon’s (1996) The Sciences of the Artificial “The Architecture of Complexity: Hierarchic Systems”

1. Name the two most important things/concepts which you learned and give a one paragraph explanation why you consider these concepts important.

The two most important concepts that I had reinforced and learned were:

• Human problem solving is fundamentally a selective trial and error process, and

Adaptive organisms, like humans, act purposefully on their environments to find correlations that bridge blueprints (world as sensed – existing state of affairs) with recipes (world as acted – desired state of affairs).

The reason why I consider these important is because they provide a sound rationale for using a systemic approach to problem solving. I always believed that cues and/or guesstimated solutions were critical to facilitate learning. Simon underscores its importance by using the notion of selectivity, which is activated through feedback and prior knowledge. He cites Plato’s Meno to support the idea that all kinds of inquiry and learning take place through mere remembering or recollection.

2. Are these concepts relevant to your work, to your interest, …. – if yes, why?

These concepts are relevant to my work because I believe in teaching my students core concepts and skills that they might find use in their lives. To achieve this, I typically present challenging problem solving activities in the classroom to motivate and kindle their systemic thinking abilities. For instance, they might work in teams to design boats that can travel the greatest distance in 30 seconds, carrying a 23 g load. Each team (of two) is provided with just 10 cm of aluminum foil, 1 plastic straw, 30 cm of masking tape, and 25 minutes to prepare for the challenge. To assess their different levels of understanding and performance in problem-solving, I use Kurt Lewin’s recommendations and present learning goals as a movement from the present level to a desired level along a directed line continuum (illustrated below with Simon’s views incorporated).

Adapted from Balasubramanian, N. (2005). Improving student achievement through scaffolded science and technology instruction. Manuscript submitted for publication.

To evaluate the learning activity and student achievement, I perform a rudimentary Lewinian force field analysis on learning goals with my students – and make them list various forces that helped or hindered their learning (for a sample of student responses, see RC Soccer Tournament Post-Activity Learning Summary)

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

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?

Remark: the major objective of this assignment is that you spend some effort trying to solve this problem and answering the questions below — it is not so important that you will succeed solving the problem!
Also: Engage in some collaborative efforts solving it
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”)

I printed out two copies of the template. As Simon remarked, I “acted” using a straightforward “trial-and-error” method and sketched domino blocks (ovals) between the squares/fields. Both times, I ended up with two fields that could not be filled. In the first attempt, I had the fields adjacent to the opposing corners empty. In the second, I had the first and last field in the first row empty.

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

When two successive “trial and error” attempts – starting at the center first and end next, failed, I advanced to “selective” trial and error. I began looking for patterns and the second attempt I realized was close. I found that if one of the “opposing corner” had NOT been cut-off, I would have solved the problem. As an avid “Internet Checkers” player, I realized that if this 8 x 8 matrix could be visualized as a checkers board, then cutting off the opposing corners was equivalent to cutting off two identical colored squares. This transformation from a sterile 8 x 8 matrix to a vibrant checkers board provided a meaningful context to solving the problem.

3. Which process did you use?


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

“Prior knowledge” of a checkers board

5. Could computers be useful to solve this problem?

Yes, because the 1-3 domino block, along with the identification of alternate colored fields, can be used to write a computer program that would show that it will be impossible to reach the required goal state – covering the mutilated “8 x 8” matrix with 31 domino blocks.

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?

Not all problems can be solved and being able to visualize them using “prior knowledge” helps.

Nathan Balasubramanian

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