The Explain-It-Backwards Technique: A Powerful Study Hack for Math & Coding

Ever stared at a math problem, followed the steps in the textbook, got the right answer, but had zero clue why it worked? It's like knowing the recipe but having no idea what salt does. This creates problems for exam season.

Most of us study forwards. We start with a concept and work until we hit the solution. But what if I told you the real masterminds flip it and reverse it? They employ working backwards in problem-solving—a classic reverse learning tactic.

Think about solving a maze. You could spend ages hitting dead ends from the start. Or, you could do the smart thing: start at the finish line and trace the one correct path back to the beginning. It works because it eliminates unnecessary paths.

Welcome to the world of the Explain-It-Backwards Technique, and it's about to become your favorite problem-solving study method.

Explain-It-Backwards: Why Reverse Thinking in Learning Drives Real Understanding

So, what is this technique?

The Explain-It-Backwards Technique (also known as reverse learning or backward reasoning) is simple: you start with the final answer or a known conclusion and work your way backward, step-by-step, to the original problem or the core concept.

Instead of just memorizing a procedure (how), you're forced to understand the logic connecting each step (why). This qualifies as a legitimate deep learning technique because it exposes the cause-and-effect chain reaction that holds a concept together. You're not just a student; you're a detective reverse-engineering the scene of the crime.

This method works well for logic-heavy subjects. If you've been wondering how to study math effectively, or trying to level up in physics or coding, this is for you. These subjects aren't about memorizing random facts; they're about understanding systems and rules. And the fastest way to understand a system is to take it apart.

From Result to Rules: A Step-by-Step Backward Derivation

Okay, theory's cool, but let's make it real. How do you actually use this in problem-solving strategies in mathematics?

Math Example: The Quadratic Formula

You've had x = [-b ± sqrt(b² - 4ac)] / 2a drilled into your head since freshman year. But where did it come from? Let's work backward.

1. Start with the answer: The formula itself.
2. Ask "What was the step right before this?": To get x by itself, we probably had something like (x + b/2a)² = (b² - 4ac) / 4a². We just square-rooted both sides.
3. And before that? We were probably completing the square on the standard quadratic equation, ax² + bx + c = 0. We isolated the x terms, divided by a, and added a specific value to create a perfect square.
4. The Foundation: We're now back at basic algebraic rules and definitions.

See? We didn't just recite a formula. We retraced its origin story, connecting it back to the foundational principles of algebra.

Physics Example: Unpacking Equations

Start with a final result, like an equation for projectile motion. Ask why each term exists. Why is gravity g in there? Why is there a t²? Working backward from the solution forces you to connect the math to the physical laws, approximations, and assumptions that created it.

Coding Example: Deconstructing a Function

You see a perfectly working sorting algorithm. Don't just run it—reverse it. Take the final, sorted array. What had to be true for the last two elements to be in the correct place? What about the step before that? By using a backward strategy in education, you can re-derive the entire algorithm, whether it's bubble sort or a complex recursive function.

When you get stuck—when you say, "Wait, I don't know how they got from this step to the one before it"—you've just found the exact gap in your knowledge. Here's what to do: write down the specific concept you're missing, look it up in your textbook or notes, practice similar examples until you understand it, then return to your backward chain. This targeted approach saves time and builds stronger understanding.

Pairing with the Feynman Technique and Active Recall for Mastery

This technique is already powerful, but you can combine it with two other proven study methods.

1. The Feynman Technique: At each backward step, explain the "why" in the simplest terms you can. Pretend you're explaining it to your little cousin. If you're using jargon or complicated phrasing, you don't actually get it. This forces conceptual clarity.
2. Active Recall: Instead of passively looking at the steps, turn them into quiz questions. After you work backward from Step 5 to Step 4, cover your notes and ask: "Given the result at Step 5, what prior rule must be true to get me to Step 4?" This is active recall and it's scientifically proven to build stronger memories than just rereading.

Quick Study Session Template:

• Goal: Understand a key formula for your exam.
• Step 1: Write the final formula at the bottom of a page.
• Step 2: Work backward one step. Write down the previous equation or logical statement.
• Step 3: (Feynman) In a separate color, explain why that step is valid in one simple sentence.
• Step 4: (Active Recall) Hide the explanation and ask yourself the "why" question again.
• Repeat until you're back at the foundational axioms or the original problem statement.

Practicing Explain-It-Backwards with Snitchnotes (Your AI Study Partner)

Doing this on paper is powerful, but let's be real, we don't always have the time or energy to create these materials from scratch. What if you had an AI training partner to do the heavy lifting?

Meet Snitchnotes, your AI-powered assistant specializing in effective math study techniques.

Here's how Snitchnotes puts the Explain-It-Backwards Technique on autopilot:

• Automated Reverse Prompts: Forget trying to come up with questions yourself. Snitchnotes scans your material and auto-generates backward-derivation prompts. It will present you with a conclusion from your notes and ask you to explain the principle or preceding step that led to it. It's like having a tutor whose only job is to make you think in reverse.
• Quizzes That Test for Real Understanding: Snitchnotes creates personalized quizzes that go beyond simple definitions. They use active recall to test the logical connections you just practiced, ensuring you understand the cause-and-effect chain, not just the vocabulary.
• Lock It In with Spaced Repetition: After you've mastered a logical chain, Snitchnotes uses a spaced repetition algorithm to re-test you on it at the perfect time—right before you're about to forget. This locks in that deep understanding for the long term.

The Workflow is simple:

1. Upload: Drop in your lecture slides, notes, or a textbook chapter.
2. Get Notes: Snitchnotes gives you a comprehensive, structured summary.
3. Practice: Use the AI-generated "explain it backwards" prompts to drill the logic.
4. Quiz: Take adaptive quizzes that reinforce your understanding.
5. Reinforce: Let spaced repetition lock in your knowledge for exam day and beyond.

The outcome? You study faster, build a much stronger grasp of why things work, and finally have a repeatable system for how to study math effectively. You're not just preparing to pass a test; you're learning how to think.

Bet.