“I don’t know what to do.”

It’s a phrase you’ll hear many students say at the kitchen table while doing homework. And often, it’s not that they’ve never seen the math before or don’t know how to carry out the individual steps. It’s that they don’t know which strategy to use.

Many students experience math as a collection of disconnected facts. To them it can feel like a new idea is being introduced everyday, simply because they aren’t seeing how it connects to what they’ve already learned. Each idea might make sense on its own, but when several strategies are available, they struggle to decide which one fits the problem in front of them.

Without some kind of structure for making that decision, every new problem can feel like a guessing game.

At Inquisia, one way we make that structure visible is through a simple metaphor: math is a toolbox. Students collect “tools”—formulas, strategies and processes—but knowing how to use a tool isn’t enough. They also need to recognize when and why it fits.

Here’s what that looked like in a Grade 10 trigonometry lesson.

Step 1: Make the Toolbox Visible

Students often don’t realize how much they already know. So before solving problems, we start by making that knowledge visible.

At the start of this lesson, I gave this student a table (as shown below) and asked them to fill in as much as they could remember about sine law, cosine law, and trigonometric ratios. My goal wasn’t for them to fill it in perfectly. In fact, I expected that there would be empty boxes, missing information and even ideas in the wrong places. I simply wanted to get the student’s existing thinking onto the page so we had something to work with.

	Sine Law	Cosine Law	Trigonometric Ratios
Formula
When do you use it?			N

This does two important things. First, the student has to retrieve what they already know rather than simply rereading it. Second, we begin to organize that knowledge so that instead of seeing three unrelated formulas, the student starts to see three tools with different purposes.

Just as importantly, the student can see that they aren’t starting from zero. There’s already knowledge there and we’re simply building on top something they already understand. That small realization can provide an important confidence boost going into the rest of the lesson.

Step 2: Let Them Test Their Tools

Once the tools are visible, they’re ready to use them.

Next, I gave this student three triangle problems that looked similar, but each required a different strategy: sine law, cosine law or trigonometric ratios. And rather than telling them which formula to apply, I asked them to decide.

Find the length of side b.

Find the length of side f.

Find the length of side i.

The student chose a method and began substituting the information from the problem. If the strategy fit, they had what they needed to continue. If it didn’t, they eventually reached a point where something was missing. When that happened, I didn’t immediately correct them. Instead, we stopped and examined what had happened:What information is missing? What does that tell us about the strategy we chose? What else could we try? And why might that be a better fit?

Now the student isn’t simply practising how to carry out three different procedures. They’re learning to evaluate a problem, choose a strategy, notice when that strategy isn’t working, and adjust.

But there’s another reason we want students to experience getting stuck: we want them to learn that a wrong turn isn’t evidence that they can’t do the math. It’s information. A strategy that doesn’t work gives us an opportunity to examine why it doesn’t fit. And that information helps us choose the right strategy next time.

Step 3: Put The Model Together

After working through the problems, we returned to the original table. This time, we revised it with clear criteria for when to use each strategy, based on what we had discovered earlier in the lesson.

Now the table wasn’t simply a place to store formulas. It had become a decision-making guide the student could return to when studying or working independently.

This is an important part of how we design learning at Inquisia. We don’t just want students to complete an activity and move on. We want them to recognize what they learned from it.

By returning to the original table, the student could see how their understanding had changed over the course of the lesson. What started as a collection of incomplete facts had become something more organized, connected and useful.

Step 4: Test their Understanding

To close the lesson, I gave the student several more triangle problems. But this time, I didn’t ask them to solve anything. Their only job was to identify which tool they would use and explain why.

By removing the calculations, we can focus entirely on the skill we’ve actually been developing: strategy selection. Can the student look at the information given, recognize the structure of the problem, choose an appropriate method and justify that choice?

If they can, that gives us much stronger evidence that the lesson accomplished its goal than simply watching them complete another calculation correctly. It also gives the student evidence of their own learning. They leave knowing they can approach a new problem and make a reasoned decision about what to do next.

Moving Beyond Explanations

This lesson wasn’t really about teaching sine law, cosine law or trigonometric ratios. The student had already encountered those ideas in class. The learning problem was one step earlier: How do I know which one to use?

So instead of simply explaining the three methods again, we designed the learning around that decision. We retrieved what the student already knew. We organized those ideas into a useful structure. I gave the student opportunities to choose and test different strategies. We used wrong turns as information. And eventually, I asked the student to make the decision independently.

That’s what we mean when we say good teaching is more than a good explanation. Oftentimes, students don’t need another explanation. They need help organizing their thinking in a way they can actually use.

When students understand what tools they have, what each one is useful for, and how to decide which one fits, “I don’t know what to do” can become a much more productive question: “Which of my tools fits this problem?”

In this way, the math doesn’t necessarily become easier. The student just becomes better equipped to approach it.