When Students Can Do It… But Don’t Understand It
My son recently came home with a multiplication and division practice booklet. He was excited to show me that he knew all his basic facts to 100. Wanting to engage him, I asked, “How are division and multiplication related?” He replied that he didn’t know. I tried a different approach: “Imagine you are playing a game and need to group your 20 friends into 5 groups. Is this multiplication or division?” Again he didn’t know. I tried one more: “You have 6 friends, and each brings 3 board games to a party. How many games do you have altogether? What equation represents this?” He couldn’t say.
This isn’t a story about my son; it’s a story about a pattern.
My son could recite facts quickly and accurately. From a traditional assessment lens, he “understood” the material. But when the numbers were removed from a familiar format, when the task required transfer of learning instead of recall, the understanding vanished.
This is the danger of purely procedural learning. Students learn to follow steps and recognize patterns in question types, often becoming successful at this kind of question. But when the context shifts, even slightly, they struggle to make sense of the situation. The learning doesn’t transfer because it was never grounded in meaning.
If we want to move beyond this, we need to pay close attention to the kinds of questions we ask. As educators, we must be intentional not just about what we ask, but why we ask it. Strong questions aren’t about getting a correct answer; they are about uncovering thinking.
To move from “doing” to “understanding,” we can shift our questioning:
| Instead of… | Try… |
| What is 4 times 4? | Create a word problem that represents a multiplication question. How would you solve your question?
Where did you use multiplication today? |
| Which arrays match these questions? | How could you create a visual that shows multiplication as an array?
How could you create a visual that shows division as sharing and grouping? |
| Telling students that multiplication and division are related | How are multiplication and division connected? Explain your thinking. |
These types of questions do more than check for correct answers, they require students to represent, explain, and connect their understanding. In other words, they make thinking visible. When thinking is visible, we are in a much better position to respond instructionally, whether that means extending, clarifying, or re-teaching.
The goal isn’t to eliminate procedures; it’s to ground them in meaning. When students only learn the how, their knowledge is brittle, it breaks the moment the context changes. When they learn the why, their knowledge becomes flexible and transferable.
My son knew his multiplication facts. That wasn’t the problem. The opportunity, the one in front of all of us, is ensuring that when students can do something, they also understand what it means and when to use it. Because when learning goals are clear and understanding is prioritized, students don’t just get better at answering questions, they get better at making sense of the world.