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
(4th ed.). Hoboken NJ: Wiley
Knoblock, Craig A. (1990) Abstracting the Tower of Hanoi. Carnegie
Mellon University
