Why Watching Solutions Isn't the Same as Solving Problems

When you watch a solution, the hard parts are removed:

• you don’t have to decide what method to use
• you don’t have to manage your own algebra
• you don’t have to deal with uncertainty

In other words, watching skips the exact mental work that causes struggle on exams. It’s like watching someone swim and expecting your body to learn it.

That doesn’t mean solutions are useless. It means they’re a tool that must be used actively, not passively.

Mistake 1: Watching immediately when stuck. If you look at the solution at the first sign of difficulty, you never develop the ability to push through the early confusion.

Mistake 2: Not reattempting after watching. Students watch, feel relief, and move on. The brain stores “the solution exists,” not “I can produce it.”

Mistake 3: Copying steps without understanding choices. The most important part of a solution is not the algebra. It’s the decisions: why this rule, why that substitution, why that setup.

Mistake 4: Using solutions to avoid discomfort. Struggle is uncomfortable. But in math, controlled struggle is the training.

Successful students still use solutions—but they use them with a plan:

• they attempt first
• they identify the exact point of failure
• they watch/read only enough to repair that point
• they redo the problem later without help

They also practice “solution reading” like a detective. They ask:

• What was the first key decision?
• What clue in the problem pointed to that decision?
• What could I check to catch errors?

Strategy 1: The 5–10 minute struggle rule When you get stuck, set a timer for 5–10 minutes. Use that time to:

• write what you know
• identify the topic
• try a simpler version
• attempt the first step

If you’re still stuck after that, then look at a hint or solution.

Strategy 2: Cover-and-rebuild After you view the solution, close it and rebuild from memory:

• write the method in your own words
• solve the problem again without looking

This is where learning actually happens.

Strategy 3: The “next-day redo” The best test is tomorrow. Redo the same problem (or a close cousin) the next day with no notes. If you can’t, the skill isn’t stable yet.

Concrete example (a common WeBWorK pattern): Evaluate ∫ 2xcos(x^2) dx.

Many students watch someone do substitution and think “easy.” But the skill is recognizing the pattern: derivative of the inside appears outside.

• Inside: x^2
• Derivative: 2x, which is present
• Let u=x^2, then du=2x dx

So the integral becomes ∫ cos(u) du = sin(u)+C = sin(x^2)+C.

If you watched this and moved on, you might miss the deeper lesson: substitution is “reverse chain rule.” You want to practice spotting that relationship across different problems, not just copying steps once.

WeBWorK is a perfect place to build skill *if* you don’t treat it like a guessing game. Here’s a method I teach students who feel stuck in the “I watched it but I can’t do it” loop.

Step 1: Write a plan line before you look at anything Even if you’re not sure, write the best plan you can:

• “This looks like chain rule because…”
• “This looks like substitution because…”
• “This looks like an optimization setup because…”

If your plan line is wrong, that’s valuable information”you’re training recognition.

Step 2: When you look at a solution, focus on the first decision The most important part of a solution is usually the first 1–2 lines. Ask:

• What clue in the question told them to choose this method?
• What alternative method might a student mistakenly try?

Step 3: Do a ‘near twin’ problem immediately Don’t redo the exact same numbers. Change one detail so you have to think:

• If the solution used u=x^2, try a problem where u=1+x^2 or u=3x^2-1.
• If the solution used product rule, try a problem with a similar product but different inner functions.

Example of a near-twin substitution problem: After solving ∫ 2xcos(x^2) dx, try ∫ 6xcos(3x^2) dx.

• Inside is 3x^2, derivative is 6x.
• Substitution works the same way, but you have to recognize the structure again.

That’s what builds exam-ready skill: repeated recognition, not repeated watching.

• Watching builds recognition; exams require recall and decision-making.
• Solutions are useful only if you attempt first and redo afterward.
• Use timers to force productive struggle before viewing help.
• Always do a next-day redo to lock in the skill.

If you want structured, concept-focused help, Learn4Less offers tutoring sessions designed specifically for first-year university math.