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Author: Shraddha Rajpal
Early in my teaching, I started noticing the same thing happening in almost every class. I’d finish working through an example, turn to my students, and ask, “Does that make sense?”
Most of the time, I’d get a room full of nods. Great, I thought. We’re ready to move on. Then I’d give them a similar problem to work on by themselves. Almost immediately, someone would raise a hand.
“Where do I start?”
“I don’t know what to do next.”
I remember thinking, We just worked through a problem like this together. What changed?
At first, I assumed I needed to explain things better. I slowed down, added more examples, and talked through every step in greater detail. I wanted to make sure I wasn’t skipping over anything important. It helped a little, but not as much as I expected.
After a while, I realized the problem wasn’t that students couldn’t follow my examples. They could. The challenge came when they had to make the next decision on their own. Watching someone solve a problem and solving one yourself are completely different experiences.
That realization led me to make one small change.
Now, every so often, I’ll stop in the middle of an example and say,
“I’m going to leave the next step to you.”
Then I wait.
Sometimes students work quietly for a minute. Sometimes they compare ideas with a classmate. Sometimes the room is silent long enough that I have to resist the urge to jump back in. I’ll be honest—that silence felt uncomfortable when I first started doing this. As instructors, we often feel responsible for keeping the class moving. When nobody says anything, it’s easy to assume they’re confused or that we’ve lost them. But I’ve learned that silence doesn’t always mean students are stuck. Sometimes it means they’re thinking. Usually, after a minute or two, someone offers an idea. Another student suggests a different approach. Someone points out why one method won’t work, and before long the class is having a conversation instead of listening to another explanation from me.
One student said something after class that has stayed with me.
“I thought I understood it while you were doing the example,” she said. “I didn’t realize what I didn’t know until I had to try it myself.”
That comment made me rethink what understanding really looks like.
As math instructors, we spend a lot of time making complicated ideas look organized and logical. We practice examples beforehand, anticipate common mistakes, and present solutions in a clean, step-by-step way. Students don’t experience mathematics that way. For them, solving a problem means deciding where to start, choosing between different approaches, making mistakes, and figuring out how to recover. That’s a very different skill from recognizing the steps while someone else is doing the work.
I’m still early in my teaching career, so I’m constantly trying small changes to see what helps students learn more effectively. This has been one of the simplest changes I’ve made, but it’s also one of the most meaningful. Those brief pauses tell me far more about what students understand than another perfectly explained example ever could. They also give students permission to think, make mistakes, and learn from each other. If there’s one idea I’d encourage another instructor to try, it’s this: don’t feel like you have to finish every example yourself. Leave a small gap. Ask students what they think should happen next. Then give them a minute or two before you step in.
It doesn’t require changing your course or redesigning your lesson. It’s simply a small pause that invites students to become active participants instead of careful observers.
I’m still learning every semester, and I suspect I always will be. But if these first few semesters have taught me anything, it’s that some of the best learning happens when I stop talking and give students a chance to think.
About the Author: Shraddha Rajpal
I am a Lecturer in the Department of Mathematical Sciences at Clemson University, where I teach undergraduate mathematics courses. As a newer instructor, I enjoy experimenting with practical teaching strategies that help students become more confident and independent problem solvers. I’m particularly interested in finding simple classroom practices that encourage students to engage more actively with mathematics.
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Blog Post Created by: S. Otterbeck, Ph.D.
