When is Too Soon, Too Soon?

The Importance of Teaching Why Before How

Have you ever given up on learning something because you thought, "I don't really need to know this?" You might know a short cut or learned something different that makes the learning obsolete, at least to you eyes.


When I was in college, I majored in airport management for a semester. As part of the course work, I had to pass ground school for a pilot's license. Did you know pilots have to know exactly how the engine of the airplane works? I could tell you what the carburetor does, how the spark plugs work, and how the fuel makes the engine run. I learned it and understood it because I needed to know it. This learning was a prerequisite for future learning.

In contrast, when preparing to get my driver's license, I learned some of this information in my driver's ed. class, but none of it stuck with me. The reality was that I had a short cut if my car wasn't running right. It was 1-800-CALLDAD. He always took my car to get fixed. I never had to think about it.

Learning math can be a lot like this, if we let it be. If we teach students short-cuts or tricks before they've developed conceptual understanding, they will not see a reason to learn the reasoning behind the shortcut. In reality, we're robbing our students of important learning opportunities.

For example, if we teach the standard algorithm for addition and subtraction before students have a full understanding of place value, many students will not see the purpose in learning or practicing with place value. You may have heard students say, "I already know this. Why do I have to do it this way?" (i.e., with place value drawings) Students cannot see the bigger picture of mathematics. They cannot see that place value will be important for rounding, estimating, and even multiplication and division. Without place value understanding of whole numbers, how will students ever make sense of decimals?

Learning the standard algorithm too early and without understanding, can also lead to misconceptions that interfere with future learning. Earlier this year, I completed subtraction running records with some of our fourth graders. While I knew that students may have unfinished learning, I found that several of the students I tested, had major misconceptions based on unfinished learning with place value. When asked to solve the problem, 14 - 9, students wrote the problem in vertical form in the air or with their fingers on the desk. They then proceeded to solve 4 - 9. When they realized that they couldn't subtract 4 - 9, they "went next door", crossed out the one, and then wrote the one next to the four to end up with the same problem 14 - 9. Only then were they able to solve it. (This is how they explained their thinking to me.) Some students even did this when they were asked to solve 12 - 11!

It was clear that the standard algorithm was taught too early. Students learned it rotely and followed it rotely. Place value understanding was missing, and, as a result, number sense was also not evident.

What if we put the textbook aside for a moment and taught our students to add and subtract using place value concepts. What if we followed a developmental progression, as suggested by Michael Battista, and provided the time and space for students to make the connection between manipulatives and drawings to the standard algorithm? As students build understanding first with connecting cubes, then with base ten blocks, and finally, with pictures, they uncover how the standard algorithm works and are able to explain it. They have the understanding they need to round numbers, estimate based on place value, and eventually see that place value can also include numbers less than one.

And maybe, they won't be the adults who hates math because it makes little sense.

Have you taught addition and subtraction this way? I'd love to hear your stories.