In Defense of Teaching Conceptual Understanding in Math

 As an elementary student back in the 1970s, math confused me. And the problem only got worse in high school.

I was taught a series of algorithms, like "carry the one" and "divide, multiply, subtract and bring down" without really understanding why the algorithms worked.

It wasn't until I took my first class in how to teach math that the light bulb 💡 finally came on for me. I learned the concepts behind the algorithms, and what the numbers actually represent. "Carrying the one" actually means taking a ten from the tens column and breaking it up into ten ones. "Punching up" to compare two fractions is actually shorthand for finding a common denominator by multiplying the two denominators together, as I explain in the video below.

I know to many folks, the "common core" approach seems to waste time by laboriously walking students through the "long way" of doing things. But when introducing students to the foundational concepts on the way to the traditional algorithms, I believe students will not only better understand what they're doing with the numbers, but also more easily recall the steps involved in the algorithms. In my opinion, there is nothing wrong with using traditional algorithms as long as students understand the concepts underlying them.

What do you think? How do you teach basic operations in your own classroom?