I recently listened to a podcast from a Mathematician named Marcus du Sautoy in which he talks about how, although we hear so often growing up not to take shortcuts, we should indeed take many shortcuts, and we do it all the time. And he has a point. Although I could multiply 456.76 and 341.08 by hand, it is much easier to do with a calculator, and if there is one nearby, I will always grab it. So, why is it so often taught at home and school to not take shortcuts?
Well, it is important to figure out when it is okay and when it is not, which I’ll try to pin down here.
Shortcuts All Around Us
Shortcuts happen all the time, and everyone takes them. Using a formula to do a math problem is a shortcut. For example, there are formulas to help us add a series of numbers up instead of adding them together one at a time. Buying a Christmas tree at Home Depot instead of growing it yourself is a shortcut. Driving a car instead of walking is a shortcut. The internet is perhaps the biggest shortcut, as Marcus du Sautoy points out. So was language, to improve communication. These are not bad shortcuts.
But some shortcuts are bad. Copying answers off of someone else’s homework is a bad shortcut. Cutting in line is a bad shortcut. Robbing someone’s property instead of working to earn the money and then go buy it yourself is a bad shortcut.
Others are harder to categorize, at least for me. Taking diet pills instead of eating healthier, for one. Getting wealthier from owning stock in companies that don’t seem to do anything useful for society is another. Taking the escalator when there are stairs right next to it… Are these good, bad, or do we need to look at each circumstance individually?
What Makes a Shortcut Bad?
I think in order for a shortcut to be bad, it needs to do one of these things. If it doesn’t, I say take the shortcut.
- It intentionally misleads someone into believing that you put in hard work when you did not. You know, like copying answers from someone else. Or plagiarizing someone else’s work from the internet. Or taking steroids to win a strength competition.
- The hard work was exactly the point of the exercise. Lots of people are thrilled to make it to the top of Mount Everest. Would they be just as thrilled if a helicopter dropped them off at the top? Of course not. I feel good after a run because I put in the work. I could just take the shortcut to my front door by never beginning the run, but that doesn’t feel very good at all.
- It is unjust or harmful to someone (either you or the others around you). Cutting in line goes here. Copying answers can go here as well. Robbery and many other crimes are bad shortcuts in this regard. I think a diet pill that harms your body while it makes you skinnier would go into this category as well. Even though it might not hurt anyone else, we should avoid shortcuts that harm ourselves too.
So what about things that don’t seem bad, like using a calculator? Why can’t we use that shortcut?
When your teacher wants you to not take the shortcut, it is probably for a good reason. There are some math teachers that never let their students use calculators. There are others that always let their students use the shortcut. I have seen the problems from each one. On one hand, if you never let your student use a calculator, they will definitely end up spending time resenting all the “wasted” time they have to put in to do something, when the shortcut is so close by. On the other hand, if they never learn their multiplication tables because they always just use the calculator, they will feel and be, helpless when one is not around. They will also feel stupid, and their confidence level is never as high as for the student who knows their tables. I have seen this snowball into feeling inferior in other areas as well.
Shortcuts, Goals, and Incentives
So, it is probably best for a teacher to make sure their students know their multiplication tables, and then let them use their calculator for some cases in which the lesson is not actually focused on just multiplying a couple of numbers together.
My parents did this well when I was younger. I really wanted a digital watch, and they told me I would not get one until I learned how to read a clock’s hands. That way I could use the shortcut after knowing how to find the time without that shortcut.
I also try to do this with my kids. For instance, I tell them they can see the movie after they read the book. By the way, I did not invent this idea, as you well know. Someone else did the hard work parenting so I wouldn’t have to do all the trial and error on this one. I appreciate the shortcut, whoever you are!
Shortcuts are all around us, and everyone uses them all the time. If you want to take a shortcut, just make sure it doesn’t violate one of the three rules above. After that, enjoy.
Oh, and here is the best part: if you want to take a shortcut, but one doesn’t exist yet, you can put the effort into creating the shortcut. And maybe that shortcut will save lives, or be the foundation of a great business. Working hard to find shortcuts is a marvel of its own…