How do you divide one number by a different number? I was taught to do it using long division. Long division is considered to be a “traditional” algorithm (or methodology). It looks like this:
Our children, however, aren’t being taught long division (or aren’t being taught it to mastery). They’ve been taught various “reform math” approaches, such as this one:
What’s the big deal about that? Sure, the reform method is clunky, eking its way to the answer rather than getting there efficiently. So what? The field of public education appears to love it, so why not teach it to the children and not worry about it? Here’s why.
The reform method doesn’t work well with larger numbers. It isn’t efficient. It doesn’t include decimals. It adds too many steps, allowing for more possibility of error. It’s difficult to later switch students from that method to the more-efficient algorithm. And – most important – the reform method often leads to wrong answers. Despite what reformers seem to think – a correct answer is the entire point of a mathematics calculation. Math is a tool that we use to get a job done.
Not long ago, I was explaining this reform approach to some college folks. A young math professor was listening in, nodding his head and saying, “Uh, huh. Uh huh,” in that encouraging way people do when they’re in agreement. “You don’t sound shocked,” I said to him. And he wasn’t. He praised the reform approach and appeared to prefer it. I was surprised, but I thought perhaps he wasn’t familiar with its complications; he claimed to be seeing it for the first time. So, I asked him to do a problem for me.
Dividing 396.3 by 16 is simple for those who were taught long division. However, for those using the reform approach, the decimal poses a problem. Using long division, this is how the problem is done:
Long division efficiently provides a complete answer to the problem. On the white board that day, however, the young math professor used the reform method. His answer: 247 remainder 9. Whoops.
I pointed out the inadequacy of his answer, so he wrote more at the top of his work. His new answer was this:
I also commented on this new answer, so he kept writing. His next answer was this:
Not only was this additional information confusing, it was still incorrect. Later, he fixed his initial subtraction error (43 – 32 = 11, not 9), but didn’t complete the problem. His final answer was this:
Someone in the room (not me) wrote a huge question mark next to his work.