It has been a greatly inspired goal of mankind to answer the question of “How can we become more intelligent through greater problem solving ability?” We see this in the written works as early as Plato, perhaps even earlier, all through recorded history up to the present. We look at great problem solvers as the heroes of the time and pay immense homage to their contributions, hoping to find a piece of this for ourselves. What if there is a better, and yet simple way to gain this ability?
Problem solving is an area with as varying methods as it has means for useful application. One possible means for expression of problem solving is in simple actions of everyday life, such as using a television remote, mathematics, or even getting dressed in the morning. Another means might be the use of problem solving to create a new theory, such as Albert Einstein’s creation of The Theory of Relativity. Einstein thus gives us a smooth transition into the next segment, combinatory play, and a potential method for how we can problem solve more efficiently.
The use of the term “combinatory play”, as mentioned by Albert Einstein, is often quoted, but rarely defined. Einstein himself did not define what he meant by this term, but rather alluded to it’s meaning in various interviews concerning his own thought processes. The main source in which Einstein was cited as using the term “combinatory play” comes from a letter to Jacques Hadamard (1945). In this letter Einstein writes, “…combinatory play seems to be the essential feature in productive thought.” Though Einstein did not define this term emphatically, an unfastened definition has been derived from his work. Combinatory play, accordingly, is simply the act of combining, or relating, unrelated items to solve problems, create new ideas, and even rework old ideas.
The concept of “combinatory play” is not a new one, even for Einstein. Einstein is noted for coining the term, and to a greater extent, for his ability to think in a combinatorial manner that expressed itself in his work. Lev Vygotsky (1990) reminds us that this is, in fact, an old notion that has existed since early man. Additionally he notes that this combinatorial skill “exist not just where it creates great historical works,” but rather is a necessary energy of life.
As we look at the research of Dr. Marian Diamond (1993), we might draw our own conclusions about her research and Einstein’s beliefs about the effects of combinatory play on problem solving. Dr. Diamond’s research shows us that mental enrichment does in fact transform into a thicker cerebral cortex, as well as a higher ratio of nerve cell to glial cells in the brain. On the other hand, impoverishment causes a decline in these areas and can even have a greater negative effect than the positive benefits of enrichment. According to Diamond, the bottom line is, continual enriching of these nerve cells can be achieved through a challenging environment. As we read about this research we might ask ourselves, “How can we define a challenging environment?” “Did Einstein’s use of combinatory play express itself as genius? Or, did his genius express itself in a greater ability to relate, unrelated concepts?” Although “challenging environment” has vast implications, perhaps combinatory play is one such method.
The goal of this research has been to examine the potential relationship between combinatory play and productive thought, thereby testing the hypothesis that combinatory play is in fact a vital feature in productive thinking.
Twenty subjects were selected randomly from a Northwest Missouri college student population to participate in a session of combinatory play. Subjects were selected from lower-level psychology classes. No identifying information was collected in the administration of this study.
A concise computer-based instructional “mini-lesson” on how to perform the combinatory play exercise was presented to each participant individually. Following this “mini-lesson,” the treatment group was asked to conduct a single session of combinatory play, while the control group was given only the aforementioned instructions.
Concise computer-based instructions for how to properly complete “The Tower of Hanoi” puzzle were presented to participants before attempting to solve the puzzle.
A computer-based Java version of “The Tower of Hanoi” (problem-solving) puzzle was used in the administration of this study. This version of “The Tower of Hanoi” (Herzog, 2002) displays the time it requires the participant to complete the puzzle as well as the number of moves used in its completion by each participant.
DESIGN AND PROCEDURE
Participants assigned to the experimental group were given instructions for, and treatment of, a single combinatory play session, followed by instructions for completing the “Tower of Hanoi” puzzle, and finally, completion of the “Tower of Hanoi.” The participants from the control group were given only the instructions for combinatory play exercise, followed by instructions for completing the “Tower of Hanoi” puzzle, and finally completion of the “Tower of Hanoi.”
Combinatory play, operationally defined, is the act of combining or relating, unrelated items to solve problems, create new ideas, and/or rework old ideas, either cognitively or physically.Instructions for the combinatory play exercise are as follows: Subjects were first asked to work within a Microsoft Word document “writing down” random ideas, nouns, verbs, people, objects, etc. Subjects were then asked to combine these items, either randomly or systematically, to produce unique outcomes.
Participants with “total number of moves” greater than thirty-five moves were removed from the statistical analysis. From the combinatory play group, an outlier of 52 was removed. Additionally, an outlier of 41 was removed from the control group.
RESULTSIt was hypothesized that combinatory play does in fact result in greater problem solving ability. The independent variables in this study are the presence or absence of a single session of combinatory play. While the dependent variables are the increase, status quo, or reduction in problem solving completion time and number of moves to complete. Basic statistical analysis was conducted on the resulting data.
An independent-samples t test comparing the average number of moves necessary in the completion of the Tower of Hanoi for the combinatory play and control groups was completed. A significant difference between the means of the two groups (t(16) = 2.138, p < .05) was found. The mean of the experimental group (m = 18.00, sd = 3.0) was significantly different from the mean of the control group (m = 22.78, sd = 5.995).
DISCUSSIONAfter a comprehensive examination of the literature, no research has been found on the effects of combinatory play on problem solving. Research was found concerning problem solving ability, but none could be generalized to this research.
Following are limitation to this study and suggestions for future research. The restricted range of the independent variable is one limitation to this study. Perhaps an increase in the total number of combinatory play sessions would have provided differential results. Additionally, a larger sample size is necessary to ensure the validity of these results, as it is possible that the limitations of the small sample size might have left these results slightly askew. A more representative sample of the general population, such as surveying other disciplines, or sampling subjects outside the college population, might give differing results. Suggestions for future research would include; participants being sought outside the college population, thereby increasing the validity of this work, increasing the number of participants, and finally, increasing the range of the independent variable.
In order for these results to be generalized to the greater population, further research in this area will be necessary. In general, it is believed that combinatory play conducted over a larger number of sessions might provide additional encouraging results.
REFERENCESDiamond, M. C. (1993). An optimistic view of the aging brain. Generations, 17, 31.
Hadamard, J. (1945). The Psychology of Invention in the Mathematical Field, New York: Dover.
Herzog, D. (2002). The Tower of Hanoi (Version 2.0) [Web-Based Java Program]. Retrieved from http://www.mazeworks.com/
Vygotsky, L. S. (1990). Imagination and creativity in childhood. Soviet Psychology, 28, 84-96.