Analysis is a Process, Not an Answer. Can AI Help Students Reflect On It?

Y’know those days? The ones where you’re trying to work through a complex set of logistics, juggling work, relationships, and a dozen other mental tabs, and you just need to talk it through with a friend?

I was having one of those days. I was excitedly laying out a problem for a brilliant friend of mine who nodded along, paused for the occasional "Hmmm," and gave those reassuring nods of understanding. She didn't give me the answer. She just gave me the space to hear my own thinking. By the end of our chat, the fog had lifted. I wasn't thinking about it in academic terms; I was just relieved I knew how to solve my problem.

It wasn't until later that I realized what had happened. My friend had acted as a mirror for my own metacognition—my ability to be aware of, reflect on, and direct my own thinking.

This experience threw me back to years I spent in a Professional Learning Community with fabulous educators, diving deep into this very topic. We poured through research from the Education Endowment Foundation (EEF) and explored Visible Thinking routines from Harvard's Project Zero. We were on a mission to embed these skills in our students.

And as I stood there, fresh from my own "mental logjam," I realized the process I used with my friend is the exact process our students desperately need when they hit a wall in mathematics and declare, "I'm stuck."

We can’t be there for every single student's moment of frustration. But we can equip them with a map and a toolkit to navigate their own way out.

The Map: The EEF's Three-Stage Metacognitive Cycle

The EEF provides the evidence-based "why" and "what." Their research shows that explicitly teaching metacognitive strategies is one of the highest-impact, lowest-cost things we can do for our students. Their framework is a beautifully simple cycle that acts as an internal GPS for any learning task.

• PLAN: Before you start, what do you already know? What is your goal? What strategy will you choose?

• MONITOR: As you work, is this strategy working? Do you understand what you're doing? Do you need to change course?

• EVALUATE: After you've finished, what went well? What did you learn from the process? What would you do differently next time?

  
  

This is the theoretical backbone. But theory on its own can be abstract. To bring it to life in a busy classroom, we need practical tools.

The Toolkit: Making Thinking Visible

This is the "how." Ron Ritchhart's Visible Thinking routines are the classroom-ready tools that make the EEF’s abstract cycle tangible. They are structured questions and frameworks that guide students through the process of planning, monitoring, and evaluating.

Let's apply this to a classic mathematical roadblock: a problem where a 3D Pythagoras question unexpectedly turns into a simultaneous equation, which then becomes a quadratic. I see this with my own students. They master the individual skills but freeze when they need to chain them together. Here's how the map and toolkit guide them through.

Stage 1: PLAN with "See, Think, Wonder"

Before students even attempt to solve it, we can use this routine to activate their prior knowledge and choose a strategy.

• See: "What do you literally see in the diagram? What information is given?"

  
  

  Student Response: "I see a cuboid. I see a few right-angled triangles. I see some known lengths and two variables, x and y."

  
  

• Think: "Based on what you see, what do you think this problem is about?"

  
  

  Student Response: "I think I'll need to use the Pythagorean theorem, probably more than once because it's 3D."

  
  

• Wonder: "What does this make you wonder? What questions do you have?"

  
  

  Student Response: "I wonder how I can connect the different triangles. I wonder why there are two variables—that usually means I need two equations."

  
  

Right away, the student has a plan. They've identified the core concept (Pythagoras) and anticipated the need for a system of equations. The problem is no longer a terrifying monolith but a series of steps.

Stage 2: MONITOR with "What Makes You Say That?"

As a student works through the problem, this routine is the perfect tool for self-questioning and checking their progress.

Imagine a student decides to set up their first equation. You, or they themselves, can ask: "What makes you say that is the right equation?"

This simple question pushes them to pause and justify their reasoning: "Well, this length is the hypotenuse of the triangle on the base, so its square must be the sum of the squares of the other two sides. This is the first step to finding the main diagonal."

This act of verbalizing their logic is a powerful monitoring tool. It stops them from just "doing" and pushes them to "understand."

Stage 3: EVALUATE with "I Used to Think... Now I Think..."

This is where the deepest learning happens, and it's the stage most often skipped. After the answer is found, the real work begins.

• I used to think... "this was just a hard Pythagoras problem."

  
  

• Now I think... "it was a problem about how different areas of math—geometry, algebra, and quadratics—are really just tools you can chain together to solve one bigger puzzle. The trick wasn't the math, it was spotting the chain."

  
  

This reflection solidifies the learning and reframes their understanding of what it means to be a mathematician.

The Amplifier: Supercharging Metacognition with AI

So where does modern technology fit in? As I discovered when building my own AI chatbot, technology can be a phenomenal coach for the Plan and Monitor stages. It can ask questions, provide hints, and guide students.

But its greatest potential lies in amplifying the Evaluate stage, the part my early bot struggled with. A student can’t just close the tab. We can teach them to use AI as a Socratic partner to go deeper.

Once a student has done their own "I Used to Think... Now I Think..." reflection, they can turn to an AI like Gemini and prompt it:

"I've just solved a complex problem that connected 3D geometry with simultaneous equations. I've realized the key was spotting the chain of connections. Can you ask me some challenging questions to test if I can apply this 'chain-spotting' skill to other types of math problems?"

This carves a new path for learners. The student is no longer a passive recipient of help but an active director of their own learning, using the AI to deepen their reflection and prepare for future, unfamiliar problems.

From a Simple Conversation to a Classroom Culture

That conversation with my friend was a powerful reminder that solving complex problems isn't about having all the answers. It’s about having a process to find them.

By explicitly teaching the EEF metacognition cycle as our map, equipping students with Visible Thinking routines as their toolkit, and showing them how to use AI as an amplifier, we can move them beyond "I'm stuck." We can help them become confident, self-regulated learners who, when faced with a challenge, know exactly how to begin puzzling it out.

Ideogram: Working through the process and puzzling it out.