Many of us are acting as teachers or teaching assistants for our kids these day. Schools are closed and remote learning is the order of the day. We rely on teachers and teachers rely on us. There is a kind of symbiotic relationship here that is new and different from the past.
And then, there’s math.
I learned math differently from how it is taught today, and I find some of how it is taught today to be confusing. I suppose that research and studies have shown that kids learn math better the way they teach it today, then how it was taught when I was learning it (or for that matter, when Isaac Newton, or Euclid and others learned it). It still often seems nonsensical to me. Thus we hit upon a problem: my kids are taught math in a way that I don’t really get, but I am relied upon to help them learn math in this age of remote learning. I can’t help but fall back on the ways I know.
The Little Man had a math test yesterday involving fraction. The test focused primarily on multiplying and dividing fractions. For one set of questions, the instructions indicated the answers should be given in simplest form. The Little Man was marked off on three of these questions. He gave answers of 7/2, 8/3, and 11/6 respectively. His teacher marked these wrong and said “close” for each one.
The Little Man came to me puzzled as to why these were wrong. “Well,” I said, “let’s look at the definition of ‘simplest form’ in your text book.” We checked and the textbook gave the definition as a fraction in which the numerator and denominator could not be further reduced; that is, they only have a common factor of 1. Well, this was true in all three cases, so I sent the Little Man’s teacher a question, asking for clarification so that I help the Little Man understand his error and avoid it in the future.
His teacher said that his answers were improper fractions and that improper fractions were not in simplest form. I dove into the ancient and dusty parts of my memory to see if I could recall this from my own math classes, but there was nothing there. Maybe she’s right. Still, the definition given in the text book made no mention of improper fractions. It was generalized to “fractions.” I thanked the teacher for the clarification and then said the following to the Little Man:
“Buddy, you basically got these wrong on a technicality–like evidence of crime being tossed because it was come upon improperly. The thing to remember is, if you were an engineer in the real world, and someone asked you to calculate a measurement, and you came up with 7/2 as an answer, that answer is precise and correct, and would have served whatever engineering purpose it was needed for. Your boss would have been happy, and the bridge you were building based upon the calculation would be structurally sound. Sure, the answer was in improper fraction and might not technically be considered simplest form the way 3-1/2 is, but they are mathematically equivalent. You were mathematically correct, and definitionaly wrong.”
This is small potatoes, I know, but it is a frustrating part of being an amateur teacher. It is virtually impossible to unlearn how I learned math and equally difficult to comprehend how it is taught today. For me, math is a tool and I’m not as concerned about the theory. I use all kinds of math every day in my job. 7/2 is just as good as 3-1/2 and in the real world, when we are all trying to be efficient with our time, it also faster to come up with (one less operation to perform). Kelly has been trying to teach the kids how to study–practical advice that will be useful for them in all of their schooling going forward–and something I think was never taught well in my schooling. I am trying to teach practical problem-solving.
Fractions, improper though they may be, are more practical than mixed numbers.