By Katie Van Dettum
Freshman year of college. The times of adjusting to college, figuring out where your life is headed, and overall attempting to stay sane even with all of the changes in your life happening. One of those changes happens to be trying to figure out how to solve problems now that you’ve taken your first steps into the scary world of being an adult. As a junior, I have learned a few things when it comes to solving problems that I can pass on to incoming freshman. Specifically, when it comes to studying and doing homework. College has caused me to readjust my strategies in order to become a more productive studier and a better student as a whole.
Now, if you’re wondering what I’m talking about when it comes to solving problems in regards to studying and doing homework, I’m talking about something called divergent thinking. The name divergent doesn’t mean being a part of more than one faction in a dystopian society in this case, as it does in the young adult book series. Rather, divergent thinking has to do with the potential, originality, and creativity in regards to problem solving . Or the definition in the form of a direct quote, in the case Silvia et al’s, “Divergent thinking is central to the study of individual differences in creativity” . This can be done with mediation, as a method of achieving focus, but meditation is not something that is required .
To quote a study conducted by Gilhooly, Fioratou, Anthony, and Wynn, “Analysis of protocols from the think aloud group suggested that initial responses were based on a strategy of Retrieval from long term memory of pre-known uses” . For example, if you’re working on something that has to do with Algebra in a class along the lines of Math 095, and you’re learning about how to factor polynomials. It is best you talk through the problem as you’re doing it. Take the problem step by step, and saying each step aloud as you are doing it.
For example, as a way of using divergent thinking, let’s take the problem, 5x2-50x+120 step by step and get a better sense of what I am referring to.
Step One: Divide by 5 to get 5(x2-10x+24). Dividing 5 reduces the problem to its lowest terms. However, don’t forget about the 5, as it will help you with your quest later on.
Step Two: Think of the numbers that multiply together to get 24. However, these numbers have to add up to negative 10. The only pair of factors that multiply together to get 24 and add together to get negative 10 are negative 6 and negative 4.
Step Three: To check the problem for correctness, simply retrieve previous knowledge of the FOIL (First, outer, inner, last) method. This method is where the creative parts of divergent thinking comes in, as this step can be done with arrow pointing to which terms are being multiplied or writing out the letters of FOIL and writing the multiplied terms there. Whichever method you decide to use doesn’t matter as long as the correct end result of the problem is achieved.
Step Four: After using the FOIL method, remember that no problems are completed without combining like terms. There are a set of like terms, which are negative 4x and negative 6x. Add those two terms together, which gives you the middle term from the problem you factored, negative 10x.
Step Five: Remember that 5 which was factored out at the beginning of the problem in order to have the problem in its simplest terms? That still needs to be taken care of. All that has to be done is multiplying 5 by x2, negative 10x, and 24 in order to reach the original problem.
Factoring is based off of prior knowledge of multiplication and addition. If it is really thought about, factoring polynomials is basically the FOIL method in reverse. Instead of combining two polynomials together with the FOIL method, they are being taken back to their original quantities. There is a reason why math teachers will say that math is cumulative, as multiple concepts build on each other, allowing students to use their prior knowledge in order to solve the new information given to them.
If you are skeptical about divergent thinking or have questions similar to what Nusbaum and Silvia, ask in their first line of their research study on divergent thinking, “Does a person have to be smart to be creative? . In my personal opinion, intelligence does not matter when it comes to creativity. Creativity is something that is for everyone regardless of intelligence.
Divergent thinking also factors in there being more than one way to solve a math problem. There being more than one way to solve a problem is another common math teacher phrase, as similar to math being cumulative, that is something that happens to be true. Even if the textbook says one thing, it is more than possible for you to come up with a completely different method. Every person has potential to solve any problem in their way. It doesn’t matter if they have quite a bit of creativity or not a lot of creativity. In the math classes I’ve taken in the time I’ve been in school, I’ve used the occasional different method than what the textbook or teacher told me to do. As long as the problem was solved and the correct end result was achieved, it was more than fine for students to be like Fleetwood Mac and go their own way in regards to problem solving.
So there you have it, divergent thinking and how it can be used as a strategy to help with homework. Be dauntless and may the problem solving odds be ever in your favor.
1: Runco M.A, & Acar, S. (2004). Divergent thinking as an indicator of creative potential. Creativity research journal, 24(1), 1-10. Retrieved November 12, 2018 from https://www.researchgate.net/profile/Mark_Runco/publication/8902778_Creativity/links/54256bfe0cf2e4ce94037f94/Creativity.pdf
2: Colzato, L. S., Szapora, A., & Hommel, B. (2012). Meditate to create: the impact of focused attention and open-monitoring training on convergent and divergent. Frontiers in psychology, 3, 116. Retrieved November 12, 2018 from https://www.frontiersin.org/articles/10.3389/fpsyg.2012.00116/full.
3: Silvia, P.J., Winterstein, B.P., Willse, J.T., Barona, C.M., Cram, J.T., Hess, K.I., Martinez, L., Richard, C.A. (2008). Assessing creativity with divergent thinking tasks: Exploring the reliability and validity of new subjective scoring methods. Psychology of aesthetics, creativity, and the arts, 2(2) 68-85. Retrieved November 12, 2018 from https://www.researchgate.net/profile/Paul_Silvia/publication/232480788_Assessing_Creativity_With_Divergent_Thinking_Tasks_Exploring_the_Reliability_and_Validity_of_New_Subjective_Scoring_Methods/links/00b4951ae147e610ad000000/Assessing-Creativity-With-Divergent-Thinking-Tasks-Exploring-the-Reliability-and-Validity-of-New-Subjective-Scoring-Methods.pdf.
4: Nusbaum, E.C & Silvia, P.J. (2011). Are intelligence and creativity really so different? Fluid intelligence, executive processes, and strategy use in divergent thinking. Intelligence, 39(1), 36-45. Retrieved November 12, 2018 from http://libres.uncg.edu/ir/uncg/f/P_Silvia_Are_2011.pdf.
5: Gilhooly, K. J., Fioratou, E., Anthony, S. H., & Wynn, V. (2007). Divergent thinking: Strategies andexecutive involvement in generating novel uses for familiar British Journal of Psychology, 98(4), 611-625. Retrieved November 12, 2018 from https://uhra.herts.ac.uk/bitstream/handle/2299/2373/901145.pdf?sequence=1.