Ever feel like you’re just constantly answering questions in your math class? Like you turn around, and there’s a million hands in the air? It’s a familiar feeling, right? Today, I want to dive into chapter five of Building Thinking Classrooms in Mathematics by Peter Liljedahl. This chapter asks a thought-provoking question: Could answering too many questions actually be bad for students?
It’s an interesting idea, because so much of teaching often feels like just answering questions. But Liljedahl suggests it really depends on the types of questions we’re choosing to answer. He breaks them down into three categories: proximity questions, stop thinking questions, and keep thinking questions.
Let’s start with proximity questions. Imagine you’re walking around the classroom, and a student asks a question about something they were just working on—something they could totally figure out on their own. But they ask because you’re nearby. It’s not really about the math; it’s about your presence. Liljedahl even shares an anecdote about a student using a calculator app but asking a simple arithmetic question as soon as the teacher walked by. Proximity questions are triggered by your presence, not by genuine need.
Then there are stop thinking questions. These are the ones that shut down a student’s thinking process. For example, a student might ask, “Is this the right way to do it?” before they’ve really tried anything. They’re looking for you to validate their approach or just give them the answer. It’s tempting to respond, but when we answer these questions too often, we train students to become dependent learners. They don’t develop the problem-solving skills they need to tackle challenges independently.
Finally, we have keep thinking questions—the ones we want to encourage. These questions show that students are genuinely engaged and curious. Instead of asking, “Is this right?” they might ask, “Why does this rule work?” or “Can you help me understand the connection between these two ideas?” These questions lead to deeper understanding and those wonderful “aha” moments.
Reflecting on these types of questions, it’s clear that proximity and stop thinking questions can prevent students from truly engaging with the material. We often think we’re helping by giving quick answers, but it creates a classroom culture where students look to the teacher for validation rather than trusting their own thinking.
So how do we shift this dynamic? Liljedahl suggests we prioritize keep thinking questions and find ways to redirect proximity and stop thinking questions. One strategy is to simply smile and walk away. It might sound harsh, but it’s a subtle way of saying, “I trust you. You can figure this out.” Another approach is to redirect the question to the whole group, turning it into a class discussion. This encourages collaboration and exposes students to different perspectives.
Of course, there are times when a student is genuinely stuck and needs support. In those moments, it’s important to acknowledge their feelings first. Say something like, “I see you’re feeling frustrated, and that’s okay. Math can be tough, and it’s normal to feel stuck sometimes.” This validates their experience and creates a safe space for them to keep trying. From there, guide their thinking with questions like, “What part is confusing you the most?” or “What have you already tried?” This approach keeps them in the driver’s seat.
Sometimes, though, even with support, a student might still struggle with a concept. That’s when creativity comes into play. Use visuals, analogies, real-world examples, or hands-on activities to make abstract concepts more concrete. For example, if you’re teaching fractions, you might use manipulatives, draw pictures, or even bake a cake and divide it into parts.
What about parents? Some might be hesitant about this thinking classroom approach, especially if they’re used to more traditional methods. Communication is key. Explain that this approach isn’t about making things harder or being lazy—it’s about teaching skills like critical thinking, problem-solving, and perseverance. Share specific examples of their child’s progress, like taking risks in math or helping classmates when they’re stuck. Let parents see the growth for themselves.
Building a thinking classroom is a journey. It won’t happen overnight, and there will be bumps along the way. But the rewards are worth it. By shifting our focus from answering every question to guiding students toward their own discoveries, we can create classrooms where curiosity thrives and understanding takes root.
I encourage you to check out chapter five of Building Thinking Classrooms in Mathematics and start experimenting with these strategies in your own teaching. You might be surprised by the results. Keep thinking, keep questioning, and keep learning!