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In this article, I’ll show you how using worked examples in your maths tutoring sessions can dramatically improve your students’ performance. I’ll explain exactly what worked examples are, highlight their main benefits, and give practical tips on how you can effectively incorporate them into your online tutoring.
What are worked examples?
Worked examples are step-by-step demonstrations of how to solve a particular problem. Unlike standard solutions such as exam paper mark schemes that only show correct answers or methods, worked examples detail every logical step taken during problem-solving, explaining the rationale behind each.
An excellent worked example:
- Breaks down each step of a mathematical process in simple terms.
- Clearly illustrates both what was done and why it was done.
- Uses the principle of transparency during explanations to help students follow the tutor’s thought process from start to finish.
If you’re familiar with the ‘I Do, We Do, You Do’ approach, you’ll notice a clear similarity—both methods guide students from seeing an example to working through it together, and finally, attempting it independently.
Why are worked examples useful?
Here’s what makes using worked examples so effective:
- Ensures understanding: Instead of just memorising methods, students understand the reasoning behind each step, which greatly enhances their ability to tackle similar problems in exams.
- Identifies and addresses knowledge gaps: Detailed step-by-step explanations quickly reveal exactly where a student’s understanding needs improvement.
- Encourages active learning: Having your students explain the worked example back to you means they have to actively engage with the material, significantly boosting their understanding and retention.
- Builds student confidence: Breaking complex problems into clear, manageable steps means students are less overwhelmed and become more confident in tackling similar challenges.
As the renowned physicist Richard Feynman once said: “If you want to master something, teach it.”
This captures perfectly why worked examples work so well—they encourage students to explain concepts back to you, effectively turning them into tutors themselves. From my own experience, this approach has been particularly successful.
How to integrate worked examples into tutoring sessions
Integrating worked examples into your online tutoring is straightforward, practical, and highly effective. Here’s a suggestion on how to do it:
- Choose the right problems: Select problems appropriately matched to your student’s skill level, and gradually increase the difficulty as they progress.
- Clearly write out every step: Initially, assume your student knows very little. This means stating what you may think is obvious—you never know what might be your student’s “lightbulb” moment!
- Annotate each step: After solving the problem, go back and annotate each step in a different colour, such as “expand brackets,” “collect like terms,” or “complete the square.” This makes it clear what each step involves.
- Reverse roles (my favourite part!): Students become the tutor by explaining the solution back to you. Interrupt constructively when misunderstandings occur, guiding them towards clarity and accuracy.
- Use open-ended questions: Instead of asking yes-or-no questions (e.g., “Does this make sense?”), ask probing questions to gauge their understanding:
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- “Why did we choose this approach?”
- “What would have happened if we’d used a different method?”
- “How do we know this step is correct?”
- Scaffold practice problems: After demonstrating, present students with a similar problem. Offer partial scaffolding (some help without giving them the whole answer), if necessary, such as outlining the initial steps to get them started confidently.
Important tip: Keep explanations concise and clear. Overloading students with too much information can lead to confusion, so aim to use simple, everyday language and brief explanations.
Common pitfalls to avoid
- Overly detailed explanations: Too many words or redundant steps clutter the example and confuse students. Aim for clarity, brevity, and precision.
- Assuming comprehension from closed questions: Questions like “Does this make sense?” don’t reliably confirm understanding. Use open-ended questions instead.
- Neglecting the ‘why’: Don’t let students mindlessly follow methods without understanding the reason behind them. Constantly reinforce why each step is important.
When used correctly, worked examples are one of the most effective tools in mathematics tutoring. They help students develop a deep understanding of concepts, build confidence, and become more independent problem-solvers.
By incorporating these structured examples into your online lessons, you’ll help students move beyond memorisation and towards true mastery. Ultimately, it’s this level of mastery that separates A and A* students from the rest—the ability to choose the right mathematical tools and apply them confidently to an unfamiliar exam question.
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