What role does the Pythagorean theorem play in your curriculum?

According to the Common Core standards, every eighth-grade student should learn that a2 + b2 = c2. It’s fundamental knowledge in geometry.

In our lessons, we teach students the equation. We teach them about right triangles, and what a hypotenuse is. They learn about squared numbers. All of these are facts – useful ones at that. But what does that say about other shapes? What about other subjects entirely?

It turns out, a lot. The theorem teaches us about proportionality, similarities and relationships. It says something about testing theories and proofs. It may even touch on the general mystery and power of mathematics. It’s not just important on a factual level – it’s also important on a conceptual level, and important to developing students’ deeper understanding.

That’s what concept-based curriculum is all about: designing curriculums that don’t just walk through the equations but also guide students through conceptual, big-picture thinking.

Breaking down concept-based curriculum

The point of a curriculum is to teach students new knowledge, gain skills and improve understanding. The problem? Too much rote learning stuck at the factual level, and students get conditioned to that shallow pool, even when we expect them to dive into the deep end. Traditional approaches to design don’t go far past the surface.

They list learning goals and activities in topics, under which is a set of facts. They’re probably paired with a thinking skill, too, like identify, analyze, evaluate and solve. You’ll see a lot of verbs like that in Common Core standards.

What’s missing is a clear way to expand those facts and topics into broad constructs that aren’t limited to the lesson, unit or even subject. After all, what students learn needs to apply to the real world and new situations, where things aren’t so clean-cut or predictable.

A concept-based curriculum teaches broad concepts like change, balance, identity and systems. It recognizes that facts and topics are really important in student learning, but that there are other levels of learning above them that we can define and design. It shows how one level of learning informs the next, and how students can transfer knowledge within a subject, between subjects, between grades, and even between school and the world around them.

You can think of a concept-based curriculum in five elements, sort of like a pyramid that builds from fact to theory:


Facts form the foundation of theory. These are the concrete pieces of knowledge, skills or processes students learn that support everything above them.

Example: If we’re teaching a Civil War unit in a social studies class, we might look at:

  • Specific battles that were fought
  • Secession
  • The Emancipation Proclamation
  • The Civil Rights Act of 1867


Topics bundle facts together into specific, cohesive units that give them context. They’re an umbrella that brings individual lessons together. This level is where most curriculum planning stops.

Example: In that same social studies class, the topic might be Civil War and reconstruction.


Concepts are the big ideas. They connect ideas that have common attributes in ways that are abstract, cross-disciplinary and enduring. They lie at the heart of each topic and answer the question, “what is this really about?”

Example: The topic of the Civil War teaches students about conflict and freedom.

Generalizations and Principles

Generalizations and principles pull those concepts together, as supported by facts, in a sentence that says something about the world we live in. Principles are generalizations that reach the level of law or theorem.

Example: For the concepts of conflict and freedom, a generalization might be, “Definitions of freedom vary by individual, group, and time period, which fuel tension and conflict in society.”


Theories describe the way we explain the world around us. Informed by the facts and with an understanding of the concepts and generalizations, theories help us make sense of our experiences and solve problems in new situations.

Example: After understanding how definitions of freedom can fuel tension, students can better grasp other conflicts like major wars in the Middle East or their own fights with their parents over bedtime.

In the end, concept-based learning addresses one very important key question that’s been absent in other approaches: why students should care about anything we teach.

Building a concept-based curriculum

One reason why concept-based curriculums aren’t actually that common? They’re really hard to build from scratch. After all, if we want to ask students to think deeper about what they’re learning, teachers and administrators need to think just as deeply about what they’re teaching.

But that doesn’t mean it’s impossible. Plus, if you’re thinking about or currently in the process of creating a curriculum map for your school or district, now’s the perfect time to add concept-based learning into the mix.

It just means asking yourselves big, guiding questions and defining as you’re putting together your units. You’ll want to craft generalizations as a statement while you’re planning, too.

So, in a media studies course, your plan might include a few extra columns, like this:

Preparing students for success

Doing this work up front will help you figure out the best facts students should learn to support deeper levels of thinking along with ways teachers can work together within their own disciplines and across subject areas to make that learning more transferable and cohesive – a perfect tie-in with vertical alignment!

Ultimately, concept-based curriculum is all about designing a good curriculum that enhances student learning and helps them navigate the world around them – especially when the future is unpredictable. It equips them with the facts, and also the kinds of critical thinking and problem-solving skills they’ll need in the future. And your curriculum can help them see the bigger picture for themselves.

(Examples are based on Tools for Teaching Conceptual Understanding, Secondary: Designing Lessons and Assessments for Deep Learning by Julie Stern, Krista Ferraro and Juliet Mohnkern, and follow H. Lynn Erickson’s structure of knowledge.)

Check out How to Audit Your Curriculum Map: An 8-Step Guide to help your curriculum map be most effective. Learn why curriculum maps are important with 7 Reasons Why Your Curriculum Matters More Than You Think.

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