Attempt the question on paper first, then check your answer with a method that does not depend on the explanation you are testing. If the two disagree, pause and find out why. This routine works whether the explanation came from a chatbot, a video, a classmate or an answer key.
The aim is to keep your own reasoning in charge. An explanation should correct your thinking, not replace it.
The six-step routine
- Attempt first. Give the question a fixed time, such as ten minutes. Write working, even if you are unsure.
- Mark your confidence. Write “sure”, “unsure” or “guess” beside your answer before checking.
- Get an explanation if you need one, from a textbook, teacher, answer key or tool.
- Check it independently. Use at least one method from the table below.
- Close everything and redo a fresh, similar question without looking.
- Record it. Note the result and what you learned in a mistake log.
Independent checks to choose from
| Check | How it works | Good for |
|---|---|---|
| Substitute back | Put your answer into the original question and see if it holds | Equations, algebra |
| Estimate | Round the numbers and see if the answer is the right size | Calculations |
| Second method | Solve a different way and compare | Maths, physics |
| Units and sense | Check units, sign and realistic size | Science calculations |
| Syllabus or notes | Compare with the listed content and the exact wording | Theory, definitions |
| Teacher or class | Ask, with both answers written down | Anything still unclear |
Filled example: a confident wrong explanation
Question: A price of RM80 is increased by 15%, then the new price is decreased by 15%. What is the final price?
Student’s attempt (10 minutes): “15% up then 15% down, so it is back to RM80.” Confidence: guess.
An explanation the student reads: “Increasing and decreasing by the same percentage cancels out, so the final price is RM80.”
It sounds tidy and clear. Now the independent check.
| Step | Working |
|---|---|
| Increase by 15% | 80 × 1.15 = 92 |
| Decrease the new price by 15% | 92 × 0.85 = 78.2 |
| Compare | 78.2 ≠ 80 |
| Second method | 15% of 92 = 13.8, and 92 − 13.8 = 78.2 |
| Sense check | The 15% is taken from a larger number in the second step, so more is removed than was added |
Final price: RM78.20. The explanation was wrong because the second 15% is calculated on RM92, not RM80. The overall change is 78.2 ÷ 80 = 0.9775, a decrease of 2.25%.
Check the arithmetic: 80 × 1.15 = 92, 92 × 0.85 = 78.2, and 92 × 0.15 = 13.8.
What the student does next: writes the error in a log as “Incomplete reasoning: changed the base without noticing”, then attempts a fresh question: “RM200 is decreased by 20% and then increased by 20%.” Working: 200 × 0.8 = 160, 160 × 1.2 = 192. The final price is RM192, not RM200.
Warning signs in any explanation
- It states a rule but never checks it against a number.
- It skips the step that feels hardest.
- The answer changes when you ask the same question in different words.
- It uses a method your syllabus or class has not taught, without saying why.
- You can follow it but could not reproduce it tomorrow.
The last one matters most. Understanding is being able to start from a blank page.
Tracking honestly
Keep your attempt, check and redo together.
Over several weeks, compare like with like: similar questions under similar conditions. The evidence-of-progress tracker helps you do that without turning one easy set into a claim of improvement. More routines are on the resources page, including how to move from a worked example to independent practice.
A teacher can give you a reliable second opinion because they watch you work, not just read your final line. That is what online one-to-one tuition adds to your own checking.