Math, technology, education, and beyond

I still find it so amazing that there are students of mine that worry more about how to do something than why it is they are doing it. Case in point: I have recently introduced a lesson on variance and standard deviation. The students did well and following the process to find the standard deviation. They were even able to remember the formula for it. However, when it came to questions that asked which set of data had the most variation or what a range of scores were when we knew the mean and standard deviation, not many knew what to do. All it took for me to get the idea through to them was to ask what standard deviation is.

Unfortunately, most gave the answer, “The square root of the variance!”

I responded, “That’s how you find it, but what is it?” Blank stares. “Okay, look at your notes.”

Ten seconds later, 15 hands shot up. “It’s tells how far scores deviate from the mean.”

Now, they had an understanding of what was being asked in these questions. This brings me to the fact that it is still so difficult to get students to think about why something is, not just how to do it. One way I try to get students to think about math is to ask them how to get to Harrisburg. Some say to take 422. Others send you out to Interstate 81. Others will choose back roads. I ask them why they chose that way, and whether one way is more correct. The students say that they’re all correct, as we end up in Harrisburg each time. However, one will usually point out that depending on how quickly you want to get there and what time of day it is, you might want to choose one way over another. If it is in the height of rush hour, traffic moves more slowly on 422, and when it merges into 322 and then I-83, it gets even more backed up. But if you go to I-81, traffic tends to move better.

Now we have an understanding about how to get to Harrisburg, not just directions. I can now relate to my students that math is the same. If you only know a process, you don’t get any of the understanding for it. We now take a look at the formula for finding standard deviation and take it apart. Using the order of operations, you can go through the process step-by-step to see how it works. Understanding of the individual parts leads to an understanding of the whole. Those that take the time to look at all the pieces will have a much better understanding of mathematics as a whole.