Calculators
I came across a math problem on YouTube the other day. Apparently, it was asked during a high school math competition somewhere in Europe. The problem is as follows:
The student is tasked with finding the area of the newly created figure. I am not a big puzzle guy. I usually only pay attention to puzzles that address more essential questions, such as our failing intuition regarding probability. This test question did get me thinking about another topic that is of some interest. Namely, the use of calculators in high school and college math classes.
I have a software program built for analytic geometry, I use it often. When I looked at the test question, I immediately knew how to solve it. That is if I were to use the computer. A programmable calculator would also prove helpful in quickly solving the problem.
My question is this: Is it essential that I know how to solve that problem with just a piece of paper and a pencil? That is the debate math teachers have been having for as long as there have been programmable calculators and sophisticated software programs. I remember hearing many differing opinions about graphing calculators used in math classes, especially during tests.
As I sit here today, I know how essential it is to understand the programming of “black box” programs, especially those used for statistics. Back when I was a student, we derived all the equations to prove that they were legitimate. After that, we all hit buttons on the computer and let it do all the work. Never again did I calculate any of the answers myself.
Do I think it is vital that I solve the problem with just my brain and a pencil? Maybe a few times. As long as I, or anyone else, understand the logic of the problem, I see no harm in letting the machines do the work.
Here is the answer to the problem, it took longer to import the image than to create it.
And there you have it. I rely heavily on my computer and its software. Of course, I understand what is going on in those lines of code, which is probably the most important thing. Let the debate rage on. As for me, Three Cheers and a Tiger for Team Calculator.
