Most GCSE Maths textbooks follow the same structure: a brief explanation of the topic, two or three worked examples, then a set of practice questions.
Most students do the following: read the explanation quickly, glance at the worked examples, then go straight to the practice questions.
This is understandable. The questions feel like the work. The examples look like the preamble.
They aren’t.
What a worked example is actually for
A well-written worked example isn’t showing you an answer. It’s demonstrating a chain of reasoning — the decisions made at each step, in sequence, with the justification visible.
When you read a worked example carefully, you’re not just seeing the method. You’re seeing:
- Which information from the question is relevant
- What form to set up the working in
- Where a shortcut is legitimate and where it isn’t
- What to do when the working gets messy partway through
This is the tacit knowledge that experienced Maths students have and less experienced students don’t — and it’s genuinely hard to extract from practice questions alone, because practice questions show you the problem and the answer but not the decisions in between.
How to actually use a worked example
The approach that works is annoying. It takes longer. It works.
Step 1: Read the problem statement only. Close the solution. Try the problem yourself, on paper, without looking at the worked example. Even if you get stuck — especially if you get stuck — spend a few minutes on it first.
Step 2: Look at where you got stuck. Before you read on, notice exactly where your working stopped. Was it the setup? A specific algebraic step? A decision you didn’t know how to make?
Step 3: Read the worked example, step by step. Don’t skim to the answer. Work through each line. At each step, ask: why did they do this here? Could they have done something else?
Step 4: Cover the solution again and attempt a similar problem. Most textbooks have at least one more example after the main worked one, or you can modify the numbers slightly. Do it without reference.
This process is slow compared to reading the examples as warm-up and doing ten questions in a row. But each iteration is doing genuine work — it’s building the decision-making intuition, not just the answer-getting reflex.
Why students skip this
The honest answer: because practice questions feel like progress, and reading a worked example carefully feels like studying, which feels like it should be harder.
There’s also a difficulty curve issue. If you go straight to ten practice questions and get seven right, you feel competent. If you read a worked example carefully and discover you couldn’t have explained step 3 without it, that’s uncomfortable — even though the second experience is more useful.
The discomfort of discovering a gap is how you find out where to do the work.
A note on the bundles
The context bundles James is building follow this principle: every topic has a worked example with the reasoning explained at each step, not just the algebra. When the GCSE Maths bundle is available, that’s how it’s structured.
Written by James MacKellar — University of Bristol EEE undergraduate.