On Teaching Thoroughness in Math

The reader may know that I teach basic arithmetic to Kameron, an Early Grammar student at HSCA. Ever since I started working with Kameron, I have noticed a few virtues that are honed while solving basic arithmetic math problems. These virtues will certainly serve him well when he encounters more complex problems later on and they are also useful in other areas of life. I hope to one day write a Core article about each one of these many virtues but for today I will focus on one in particular: thoroughness.

Recently, Kameron has been working on division with remainders. It is amazing how many steps we do (and, as adults, skip over) when we solve a division problem. When I first started teaching him, I unconsciously left out a few steps. As I saw him attempt to solve his first division problem, I quickly realized that I needed to give him a procedure to follow, so that it would be very clear what was expected at each step. As a result, he has a very systematic way of completing a division problem. He does not skip a single step, and he nearly always solves the problem correctly.

This made me realize just how critical it was to give him a step-by-step procedure so that he could be thorough (i.e. do everything step-by-step and check his work at the end of each step). By leaving out a few steps, all I was teaching him (without meaning to) was to solve the problem faster, not accurately. Ultimately, we want him to be able to accomplish this task quickly. But by being thorough, he is really ingraining these patterns into his memory, which, after all, is the real goal of the exercises. With careful repetition of this procedure, he will soon be able to retrieve the answers from his memory more quickly, and his calculations will be both fast and thorough.

So, realizing that at this stage in Kameron’s development it is better to be thorough, how could I instill this virtue further?

I have found at least one activity that will help him (though I am always looking for more). I like to call it the needle-in-the-haystack homework. In every class I let him do problems in his exercise book. In the past, if he made a mistake, I simply corrected him on the spot. I think this may have had a negative influence on him. Ultimately, it is up to him to be careful, not his teacher; if he gets used to me always correcting his mistakes, it will cause him to rely on me to tell him when he is not being thorough enough, not on himself. I don’t want that. So, instead of correcting his mistakes for him, I now patiently watch him, and if he makes a mistake, I simply note it to myself and wait until he completes the exercise. Then, for homework, I assign him to look over what he did in class and ask him to spot the few mistakes himself without telling him where or what they are.

I hope this has caused the reader to be more aware about the role of this virtue in his or her life. For, though thoroughness is certainly necessary for math, how much more do we need to be thorough in driving, conversation, prayer, and worship? My hope is that by instilling this virtue in him now, he may apply it to his whole life, and not just math.

Comments are closed.