Experiment Write-Up

­Abstract

I decided to conduct the Tower if Hanoi study. The study was conducted in order to determine if grade level had any affect on number of moves taken to solve the puzzle. It was also performed in order to determine what problem solving strategies work and why this relatively simple puzzle was so difficult. This research involved having participants try the classic puzzle game: the Tower of Hanoi. Participants had three disks on peg A that they needed to move to peg C. The two rules were that only one peg could be moved at a time and larger disks could not be placed on smaller ones. After their results were recorded, participants were asked what specific strategy they used. We found that there is almost no correlation between grade level and number of moves taken in solving the Tower of Hanoi. However, we did find out why the Tower is such a complicated puzzle. It has a series of intermediate steps that must be performed in a certain order. Participants must complete the puzzles in their mind s before starting it in order to complete it in the east number of moves. Envisioning the intermediate steps seemed like the biggest problem. It was interpreted by this study that these problem-solving skills are not based on age, they are based on the individual. Some tenth graders performed better than seniors, not as a result of age but because of individual differences.

Introduction

After reading about the Tower of Hanoi experiment (Medin, Ross, & Markman 2005) and abstract thinking that the puzzle forces (Knoblock 1990), the study was conducted. In the Tower of Hanoi, there is a starting point, an end point, and space in between to solve the problem. It has a series of an intermediate steps, which due to memory limitations, makes this simple problem difficult to complete in 7 moves. Before we conducted the study we believed that because older students have a more developed ability to think abstractly, that they would be able to solve the puzzle more efficiently than younger students. This study was conducted with students that were not randomly selected and has no particular scientific merit. This study shows that there is no correlation between grade and number of moves taken to solve the Tower of Hanoi.

Materials and Methods

21 students, 7 sophomores, 7 juniors, 7 seniors, who I selected were studied. Each participants completed the puzzle online at: http://www.softschools.com/games/logic_games/tower_of_hanoi/  This website game keeps track of both time and number of moves. I recorded their grade level and their results. The subjects were not randomly selected and there were no experimental or control groups. After they completed the puzzle, I asked them what their specific strategies were. Results were plotted on a scatter plot to determine the correlation between grade level and number of moves.

Results

We found that there was little to no correlation between grade level and number of moves made to solve the Tower of Hanoi. Through the question asking for strategy, we learned that the most common problem was becoming fixated on keeping the tower together and focusing on the end result instead of the intermediate steps.

Discussion

Due to the fact there was no correlation between grade level and number of moves used to solve the puzzle, it can be interpreted from this study that problem-solving skills used to solve this puzzle are not a result of age, but rather a result on another factor that contributes to individual differences. After each participant completed the study, I asked what approach or strategy they used to attack this relatively simple puzzle. There was a common strategy, to keep the tower together. The mental block that takes place is that participants see a starting point, they see an end point, they know how to make intermediate steps, but they don’t know which intermediate steps to take. The most critical aspect of this game is moving the smallest disk to peg C instead of B. To do this one must realize that they need disk two to go to peg B in order to get Disk three to peg C. Most of the participants that didn’t do it iin the minimum number of moves, failed to think two steps ahead and were not economical when it came to moving disk 1. The abstract and diverse thinking associated with creativity must be correlated with the ability to envision a series steps.

Literature Cited

Medin, D.L., Ross, B.H., & Markman, A.B. (2005) Cognitive Psychology (4^th ed.). Hoboken NJ: Wiley

Knoblock, Craig A. (1990) Abstracting the Tower of Hanoi. Carnegie Mellon University