Maniac Monday: Teaching Math Concepts or Rules and Procedures?

photo by d3 Dan www.flickr.com

Recently, my stepson who is in third grade completed a unit on rounding and estimating that I thought might get the better of his dad, his mom, me, and Logan, but we made it through! One of the first things I said to my husband when we were working on Logan’s homework and studying for a test was that he had no idea what rounding and estimating actually mean. He knew something about some rules where if one of the numbers was four or lower, he was supposed to go down. . .but down to what? He knew that rounding to the nearest ten meant that he would have a number with a zero in the ones place. But if the number was 42, he was choosing between 40 and 20–the 20 coming from the 2 in the ones place. He was totally confused.

So, having a background as an elementary teacher, I thought, Margo to the rescue–I’ll fix this. Ahh, not so fast. We made a number line, counting by tens, across the top of his page, and I said, “Okay, which two numbers does 42 come in between on this number line?” Yes, he got 40, but then he still pointed to 20, and I knew he had no idea of the basic concept of rounding and estimating. He was just focused on those rules, and he didn’t have the rules right, so this math worksheet was a total disaster. By the end of the week, he was rounding to the nearest hundred with hours of practice with my husband and me, and then more practice with his mom the next week. We used the number line and the rules he learned. And of course, this experience got me thinking as many of them do.

Logan obviously needed a combination of both–a basic understanding of what it actually means to round a number to the nearest ten and the rules on how to do this. He didn’t understand that taking 42 and rounding it down to 40 means that 42 is actually closer to 40 than 50; and if you have to add two numbers in your head at the grocery store, let’s say, it’s easier to add multiples of 10. However, when I tried to scrap every rule he had learned and just go to the math concept of which multiple of 10 is 42 closest to, he was totally lost. (What do you do with 65 then?) He had no rules or procedures to turn to when he was stuck.

This reminds me a little of the phonics/whole language argument when I was in college, preparing to become a teacher. Some people thought phonics was the way to go; others thought whole language. I thought kids needed both to learn to read. That’s what I think about math, too. Kids have to understand basic math concepts like that a plus sign means to put two groups of objects together and find how many there are all together. But they can also memorize these addition facts, so they can do harder addition problems without struggling over math facts. Children need to understand that 1/4 means you have part of an object that has been divided into four parts, and that 1/4 is less than a whole. Then when students are asked, “Which is greater? 1/10 or 1/4 of the pie?” They can easily choose because they understand what 1/4 means and what 1/10 means. They can also learn the rule that the larger the denominator the smaller the pieces; but if they have the concept in their heads, they can also rely on that to find the correct answer.

In my opinion, we have to teach children the concept behind the rules and procedures first, and then teach the math rules. How about you? What do you think?

Or maybe Mathopolis can help!