Why Students Struggle to Explain Their Thinking, and What You Can Do About It

Picture this: You ask your students to justify their answer, and suddenly the room goes silent. Sound familiar?

An 8th-grade teacher recently shared this frustration with me: "It doesn't matter if I tell my students to 'explain' or 'justify,' they freeze. And the ones who do speak just state the steps they followed to solve the problem."

If you've experienced this, you're not alone. Her observation reveals something crucial that's missing from most math classrooms. Here's what's happening: We teach content standards thoroughly, but we rarely teach the type of thinking required to reason within that content. Students struggle not because they don't understand the math, but because they don't know what we're asking them to do with the math.

Let me show you what I mean by examining the responses of two students. When asked to "justify" their solution to a multi-step equation, here's what they said:

Student A: "First, I added 3 to both sides, then I divided by 2, then I got x = 5."

Student B: "To find the solution, I knew I needed to isolate the variable. I chose to add 3 on both sides first because it would eliminate the constant, making the coefficient easier to work with. Then I divided by 2, which was the inverse of multiplying by 2. I verified that my solution was correct by substituting back into the original equation."

The difference here isn't mathematical ability. It's that Student B understands that "justify" means to support a position with reasons and evidence.

This matters more than you think. Why? Because for most secondary math and science curricula, "analyze" appears in 40–60% of state standards. That means nearly half the time, students aren't just expected to memorize content, they are expected to show mastery by thinking critically about it. But if we never teach them what these thinking verbs actually mean, how can we expect them to succeed?

When you explicitly teach cognitive verbs, four powerful things happen:

1. Academic Language Becomes Second Nature. Students can articulate their thinking using precise vocabulary that demonstrates higher-order reasoning, not just step-by-step recall.

2. Assessment Scores Improve. When students understand what "justify," "describe," or "analyze" actually mean, they can show their mathematical knowledge more effectively on every type of assessment.

3. Class Discussions Get Deeper. Conversations move beyond sharing answers to exploring reasoning, making connections, and building on each other's ideas.

4. Skills Transfer Everywhere. Students who learn to analyze in mathematics can apply that same thinking in science, social studies, and language arts.

Ready to transform how your students engage with mathematical thinking? Here's your roadmap:

• Strategy 1: Make It Visual
  Display common cognitive verbs prominently where students can see them during instruction and independent work. This constant visual support helps students internalize the language over time.

• Strategy 2: Show, Don't Just Tell
  Model the thinking behind each verb during your instruction. When you say "Let's analyze this graph," actually show students what analysis looks like in action.

• Strategy 3: Build It Into Success Criteria
  Instead of "Students will solve multi-step equations," try "Students will justify their solutions to multi-step equations by describing their solution path." Make the thinking visible from the start.

• Strategy 4: Practice in Safe Spaces
  Give students opportunities to "explain" or "compare" during daily warm-ups or exit tickets before using these verbs in high-stakes assessments.

Multiply Your Impact With A Department-Wide Approach

This strategy becomes exponentially more powerful when your entire math team gets on board. When all teachers use consistent language for cognitive functions, students develop deeper fluency and confidence. They start seeing these thinking skills as transferable tools rather than mysterious, teacher-specific requirements. Here's how to make it happen:

• Collaborate with your team to identify the cognitive verbs that appear most frequently in your state standards.

• Create common definitions everyone uses.

• Share modeling strategies that work.

• Develop consistent ways to scaffold these skills across grade levels.

Your Turn: Small Steps, Big Impact

Teaching cognitive verbs is one of the most powerful tools for shifting students from learned helplessness to academic confidence. Instead of freezing when they encounter unfamiliar language, they become equipped with a toolkit for engaging with complex thinking tasks. Start small. Pick one cognitive verb that appears frequently in your curriculum. Make it visible, model it consistently, and give students safe spaces to practice. Watch how quickly your students transform from deer in headlights to confident mathematical thinkers.

What cognitive verbs appear most frequently in your curriculum? How might explicit instruction in these thinking processes transform your students' mathematical discussions and assessment?