Math 1510 Blog:
So, maybe you aren't like me- and you did great in math, and it was never a problem for you. The fact is that even if you are a math pro. you still may be able to pick up some good tidbits through this site. First off, I would like you to answer a question on the right side of the page about 8 friends.
This question really got the ball rolling for me- it made me realize how robotic my former education shaped me to be when it comes to math and problem solving. Granted, I'm not a rocket scientist- or a mathematician... but I am going to be an Elementary teacher- and after this question, I realized just how easy it is for teachers to just teach methods and techniques without revealing the reasoning or real life that goes with the problems.
After working at question #1, you may have found your brain trying to solve the problem by reverting back to methods that may have been impressed upon it. Did you try to multiply? Did you break the problem apart? These are important steps to working towards a correct answer... in fact, it is said that we must all go through a process before we can actually solve a problem.
The process is described below:
A problem is a situation for which the following conditions exist:
1) It involves a question that represents a challenge for the individual
2) The question cannot be answered immediately by some routine procedures known to the individual.
3) The individual accepts the challenge.
To associate this with the problem posed on the right we can say that a question (8 people, how many handshakes?) was asked and perhaps represented a challenge to you. Perhaps you already knew the answer or perhaps you have learned the proper methods of solving it through a math class- but you still had to read the question that was represented. Next, you may have needed to use a procedure to solve it. I did as follows:
I know that 8 people shook hands, and the first person shook 7 people's hands (they don't shake their own hand so we can't count 8). Each time decreases by 1 since the person previously shook the next person's hand. I then add up all the shakes, getting 28 total. The chart below reflects this:
People Shakes
1 7
2 6
3 5
4 4
5 3
6 2
7 1
8 0
Now I know there are other methods I could have used (equations with "n" representing an unknown number or "s" representing shakes... and for larger problems I would have done this... but for me this is how I had to break it down at first before learning the equations). So, lastly- we see that the individual accepts the challenge and tries to solve the problem... Kudos to you guys out there who tried to solve this problem- great attempts!! If you answered 64... do you think this could possibly be from the methods that were impressed upon us as young people? Use multiplication, use division, use formulas, etc.- but now we can see that there is more to it, we can't look at it initially and plot in a formula. We need to break apart problems and study them, and when our brain gets all jumbled up (like mine often does!)... we need to look for help and research how others have solved problems. By doing this we will gain the skills needed to figure out things we never knew we could before!
So, I suggest we all look at math from a new light... instead of seeing it as something that was imposed upon us at a young age- let's see it as a mighty tool that we can use to solve everyday challenges. We must take the challenge, solve the problem- and triumph! It's like a computer game or Wii game, we love them because they challenge us- we try to beat the game. Let's use math in a similar way- take the challenge, beat the problem... and you will feel a great sense of accomplishment.
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