Self-explanation is a powerful metacognitive learning strategy where learners actively articulate their understanding and reasoning processes while engaging with new material. This page provides concrete examples of self-explanation across different disciplines and learning contexts.
Mathematics Examples
Problem: Solve for x in the equation 3(x + 2) = 18
Self-Explanation: "First, I need to distribute the 3 to everything inside the parentheses. So 3 times x is 3x, and 3 times 2 is 6. That gives me 3x + 6 = 18. Now I need to isolate x by subtracting 6 from both sides. 3x + 6 - 6 = 18 - 6, which simplifies to 3x = 12. Finally, I divide both sides by 3 to get x by itself: x = 12/3 = 4. I can verify this is correct by plugging 4 back into the original equation: 3(4 + 2) = 3(6) = 18. Yes, that works!"
Concept: The Chain Rule in differentiation
Self-Explanation: "The chain rule allows me to find the derivative of a composite function. If I have a function like f(g(x)), the chain rule says I multiply the derivative of the outer function f'(g(x)) by the derivative of the inner function g'(x). So if y = sin(x²), I can think of this as sin(u) where u = x². The derivative of sin(u) with respect to u is cos(u), and the derivative of u = x² with respect to x is 2x. So applying the chain rule, dy/dx = cos(x²) · 2x = 2x·cos(x²). This makes sense because the chain rule is accounting for how quickly the inner function is changing in addition to how the outer function changes."
Science Examples
Process: Cellular Respiration
Self-Explanation: "Cellular respiration is how cells convert glucose into energy in the form of ATP. It starts with glycolysis in the cytoplasm, where glucose is split into two pyruvate molecules, producing a small amount of ATP and NADH. I understand that this doesn't require oxygen, which is why it's considered anaerobic. If oxygen is present, the pyruvate enters the mitochondria and gets converted to acetyl-CoA, which enters the Krebs cycle. The Krebs cycle produces more NADH and FADH2, which carry electrons to the electron transport chain. As electrons move down the chain, their energy pumps protons across the membrane, creating a gradient. ATP synthase uses this gradient to produce ATP through chemiosmosis. This explains why we need oxygen - it serves as the final electron acceptor at the end of the chain. Without it, the entire process would back up and stop."
Concept: Newton's Second Law of Motion
Self-Explanation: "Newton's Second Law states that force equals mass times acceleration (F = ma). This means that the force applied to an object is directly proportional to the mass of the object and the resulting acceleration. If I double the force on an object, the acceleration will double. If I double the mass while keeping the force constant, the acceleration will be halved. This explains why it's harder to push a heavy shopping cart than an empty one with the same force - the heavier cart has more mass, so it accelerates less for the same applied force. It also explains why the same object would weigh different amounts on different planets - the mass stays the same, but the gravitational force changes, resulting in different weight (which is a force)."
Problem-Solving Examples
Concept: Recursive Functions
Self-Explanation: "A recursive function is one that calls itself to solve smaller instances of the same problem. For example, a factorial function: factorial(5) = 5 × factorial(4). The key insight is that each recursive call must work on a simpler version of the problem, and there must be a base case to prevent infinite recursion. In the factorial example, factorial(1) = 1 is the base case. I visualize this as a stack of function calls: factorial(5) waits for factorial(4), which waits for factorial(3), and so on until we hit factorial(1), then the results propagate back up the stack. This is different from iteration because the computer actually maintains this call stack in memory, whereas an iterative solution would just use a loop and a single variable. Recursion can make code more elegant for certain problems like tree traversal, but it's less efficient for simple calculations like factorial because of the overhead of multiple function calls."
Applying Self-Explanation to Different Learning Materials
After reading a paragraph: "This paragraph is explaining how monetary policy affects inflation. The central bank can raise interest rates to reduce borrowing, which decreases consumer spending and business investment. With less money chasing the same goods, prices tend to rise more slowly or even fall. This makes sense because it's connecting to the supply and demand concept we learned earlier - if demand decreases while supply remains constant, prices should drop. I'm wondering how quickly these effects are felt in the economy, though. The text doesn't mention timing, so I'll need to look for that information later."
After a lecture: "Today's lecture covered photosynthesis. The professor emphasized that it's essentially the reverse of cellular respiration - plants take in CO₂ and water and use light energy to produce glucose and oxygen. The light-dependent reactions create ATP and NADPH, which power the Calvin cycle where actual glucose is made. I think I understand the connection now - the products of respiration (CO₂ and H₂O) are the reactants for photosynthesis, and the products of photosynthesis (glucose and O₂) are the reactants for respiration. This creates a beautiful cycle between plants and animals. What's still unclear to me is exactly how the chlorophyll captures light energy and converts it to chemical energy. I need to review that section again."
Self-Explanation in Practice
- Speak aloud while studying to externalize your thinking process
- Write explanations in your own words in the margins of textbooks or notes
- Record audio of your explanations for later review
- Explain to someone else (or pretend to) to test your understanding
- Use self-questioning: "Why does this make sense?" "How does this connect to what I already know?"
- Draw diagrams to visualize relationships between concepts
Benefits of Self-Explanation
Identifies knowledge gaps - When you can't explain something clearly, you've identified exactly what you need to study more
Creates meaningful connections - Explicitly linking new information to prior knowledge strengthens neural pathways
Improves retention - The additional cognitive processing helps move information from short-term to long-term memory
Enhances transfer - Understanding underlying principles makes it easier to apply knowledge to new situations
Promotes active learning - Prevents passive reading or listening where information isn't properly processed