Beyond Grades: Building Mental Models That Last a Lifetime

One of the core principles to my teaching is recognizing that whatever immediate academic need we're addressing is just one piece of a larger mosaic that makes up the whole student. Grades, while important, are only feedback and high grades should not be an objective of education excellence, but rather a consequence of an excellent education.

I was fortunate to have a mentor who understood the profound difference between understanding and merely knowing. As classically trained engineers, we learn to grasp first principles—the fundamental building blocks of any larger system—so that no matter how complex a problem becomes, we can always work back to these foundations to understand even the absurdly complex.

The Problem with Grade-Centric Education

Our classrooms are filled with students who excel at studying for specific test patterns, who memorize effectively, and who can regurgitate knowledge when prompted just fine. But there's a vast difference between this kind of performance and truly owning knowledge in a way that can be deployed in novel contexts and challenges.

In my education practice, we prioritize building robust mental models over memorization and test performance. This approach isn't so much about dismissing grades—it's about creating the deep understanding that naturally leads to better academic performance while also preparing students for real problems life presents beyond the classroom.

What Are Mental Models?

A mental model is essentially how we organize and connect knowledge in our minds. It's the framework that allows us to relate new information to what we already know, apply concepts across different domains, and adapt our understanding as we encounter new situations.

Mental models help us answer critical questions:

• How does this new knowledge connect to what I already understand?
• How can I apply this concept in different contexts?
• How does this information change or enhance my previous understanding?
• What questions arise from this new perspective?

As a constructivist, I believe that learners must not only own their mental models but must actively participate in creating them. You're constructing your own understanding through the assimilation of new information into your existing knowledge framework.

The Difference Between Memorization and Understanding

Consider this: You spend an entire evening memorizing 100 random digits and perhaps recite them perfectly the next day. But I ask: In what way has this moved your understanding of the world forward?

It hasn't. Yet this is precisely what many students do. They're not memorizing random numbers, but they are memorizing isolated facts without creating meaningful connections. The information remains compartmentalized, ready to be regurgitated for a test but not integrated into a framework that allows for deeper understanding or practical application.

Mental Model Building in Action

The Quadratic Formula

Recently, I worked with a pre-algebra student on the quadratic formula. She was already competent with the procedure—identifying coefficients and plugging them into the formula she had memorized. We could have simply practiced this skill, but that would have added little value.

Instead, I asked her to explain the significance of the numbers we were finding. She correctly identified them as solutions to the quadratic. I then asked where we might find these solutions on a graph—where would they be located? We explored how different discriminant values would affect these solutions.

We plotted several quadratics to connect her understanding of the computed roots with their visual representation as points where the parabola crosses the x-axis. Finally, we derived the quadratic formula through completing the square.

I shared with her that I don't have the formula memorized—if someone asked me to recite it cold, I'd need a moment. And that's perfectly fine, because I can derive it from first principles even if my memory fails me. That's the power of understanding versus memorizing.

Assembly Programming

In my assembly programming class for high school students, we focus on a specific implementation of an assembly language, but we consistently tie these to broad computing principles that build foundational understanding for any future in computer science.

The class emphasizes problem-solving, critical thinking, and developing platform-independent approaches before distilling solutions into specifics. Beyond the technical content, we develop the professional mindset needed to approach complex problems and the personal qualities—tenacity, focus, determination, resilience—that are essential to success but never show up directly in a grade.

Recognizing Developing Mental Models

The most telling sign that a student is developing mental models is the number and quality of questions they ask. This is why young children ask seemingly endless questions—they're establishing their most basic models of how the world works.

To create models, we need information from our environment, but we fill the gaps by asking questions. The more questions someone asks, the more actively they're creating and refining their mental models.

If a student isn't asking questions during our sessions, it's likely they're not engaged in model creation. They may be passively receiving information, but not actively processing it. Building mental models requires engaged thought and active participation. Models cannot be given; they must be created by the learner themselves.

The Role of Metacognition

What we're really talking about is metacognition—thinking about thinking. In an age of AI and instant information access, the mere knowledge of facts has diminishing value. What matters is how we organize knowledge, how we think about that organization, and whether we're even aware there's information to be managed.

As the saying goes, "You can't manage what you can't measure"—or more accurately, you can't manage what you're not even aware of. Developing metacognitive skills helps students recognize not just what they know, but how they know it and how to apply it.

But What About Grades?

In reality, strong mental models lead to better grades naturally, as understanding makes performance more consistent across different types of assessments.

While memorization might help a student perform well on a specific test format, true understanding allows them to adapt to any assessment approach. More importantly, as students progress to higher-level coursework where critical thinking becomes central and mere regurgitation diminishes in value, those with strong mental models have a significant advantage.

Moving Forward

As an educator, I encourage parents to shift their primary concern from "What grade did you get?" to the more important questions: "What did you learn? What did you understand? What questions do you still have?"

This process is often messier than focusing solely on grades. It requires students to take greater ownership of their learning and demands patience from teachers and mentors as we allow students to struggle, articulate their thoughts, and develop their own understanding.

But this mess is worth it. It gives students agency in creating their own mental environment and makes them aware that they are not just passengers on their educational journey—they can determine their destination, and route too.