Stressed out? Try some math!
On top of the demands of work and school, daily news of the COVID-19 Pandemic brings us has created a lot of stress in our everyday lives. When I am stressed my wonderful partner will give me a math problem.
“What?” you say, “A math problem? That would make me more stressed!”
Sadly, it is true that for many people the mere thought of solving a math problem stresses them out. But hang in with me for a few paragraphs and I’ll explain why that is not so for us and how math works as a de-stressor for me. Perhaps it can also help you, too.
How many people have used counting sheep or even counting backwards to go to sleep? In my personal experience concentrating on one thing, by counting backwards from 1000 for example, can occupy just enough brain power for a moment that I let other thoughts go. In other words, counting provides just enough “cognitive load” that I let go of thoughts that are preventing me from sleep.
As an example of a ‘just right’ mathematical tasks, I like to play with 99 + anything. 99 + 3 is 102 because 99 and one more makes 100 and just two more is 102. 99 + 56 works the same way. Use any starting number you want to and you will find a pattern. Try 67 + anything. What patterns will arise? I encourage you to do these in your head. I also enjoy multiplication puzzles like 4 times anything or 50 times anything. For example, 50 times a number is the same as 100 times the number divided by 2.
There are several problems that Number Theorists have yet to solve, but are easily studied by a common person. Here are a couple of examples of famous problems that make what I call “just right” for relieving stress. A “just right” problem begins with an easy idea that you can use simple mathematics to begin to explore. The Collatz
Conjecture is a famous unsolved problem in mathematics that anyone can explore using a sequence rules: a) pick any whole number (1,2,3,4,5,6,7,….) b) if your number is even, then divide by two and if the number is odd then multiply by 3 and add 1, c) if the next result is an even number, divide by 2, if not, multiply by 3 and add 1. Keep doing those steps until you get an answer of 1. The conjecture is that any whole number selected will always end at 1. Another interesting question related to these sequences is the predictability of the length of sequences given any number.
Okay, so let’s give a number a try using the rules involved in the Collatz Conjecture. Let’s try starting with 10.
Example with the Number 10
· So, 10 is even, divide by 2 and you get 5.
· Five is odd so multiply by 3 and add 1 and you get 16.
· 16 is even and now divide by 2, that’s 8 so divide by 2 again and you get 4.
· Four is even so divide by 2 again you get 2 and then 2 again and you get 1. Done!
Number theorists record these sequences to look for patterns and the pattern we created here is: 10,5,16,8,4,2,1- a 7-number long sequence. Doing this in your head is fairly easy, the rules are simple and you have to concentrate just enough to keep the numbers straight, but it is complex enough so that other thoughts cannot intrude. This meets my criteria for a math stress reliever. Another thing to notice is if I had begun with the number 16 a larger number, my sequence would have been shorter at just 5 numbers in length (16, 8,4,2,1).
Try a couple of numbers yourself to see. Try it while you are walking somewhere, or sitting on the couch trying to not check your phone for news alerts, or even, trying to fall asleep. Share the love! Play around with the conjecture with a friend so you both are not looking at the news!
I have used this website to do some math on my own as well as curate for lessons with my students as well as families. The description directly from the website explains it best:
“
NRICH is an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge, part of the University’s Millennium Mathematics Project. NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering all stages of early years, primary and secondary school education - completely free and available to all.”
References
Cuthbert, B., Kristeller, J., Simons, R., Hodes, R., & Lang, P. J. (1981). Strategies of arousal control: Biofeedback, meditation, and motivation. Journal of Experimental Psychology: General, 110(4), 518.
Baijal, S., & Srinivasan, N. (2010). Theta activity and meditative states: spectral changes during concentrative meditation. Cognitive processing, 11(1), 31-38.
Thanks Tony for finding my de-stress zone and for the counseling reference help!