Fix the gap that other gaps stand on first. If you catch up in school order, you may spend weeks on topics that keep failing because of one weak skill underneath them.
This page shows how to find that skill by counting dependencies. It follows on from mapping missed learning without explaining circumstances.
Why is catching up on everything the wrong plan?
Topics in IGCSE are layers. A later topic uses earlier ones as tools. When a tool is missing, every topic that uses it breaks, and the breaks look like separate problems.
Fixing the tool once can repair several topics at the same time. Catching up topic by topic misses this, and costs more hours.
How to rank the gaps
- List your gaps from your topic map.
- For each, ask which other gap topics depend on it. Count them.
- Rank by count, highest first. Break ties by which topic you need sooner for school work.
- Start with the highest-ranked gap. Retest the topics that depended on it before doing any teaching for them.
Worked example
A student has six gap topics in Mathematics.
| Gap topic | Depends on | Gap topics that depend on this one |
|---|---|---|
| Negative numbers | none | Linear equations, Simultaneous equations, Straight-line graphs, Expanding brackets, Factorising, Quadratic equations |
| Expanding brackets | Negative numbers | Factorising, Quadratic equations |
| Linear equations | Negative numbers | Simultaneous equations, Straight-line graphs |
| Factorising | Expanding brackets | Quadratic equations |
| Simultaneous equations | Linear equations | none |
| Quadratic equations | Factorising | none |
Count the dependents for each gap topic (how many other gaps in the list use it directly or indirectly).
Negative numbers: six other gap topics all lean on it, so that is 6.
Expanding brackets: factorising and quadratic equations, so 2. Linear equations: simultaneous equations and straight-line graphs, so 2.
Factorising: quadratic equations, so 1. The last two have 0.
The plan therefore starts with negative numbers, then linear equations and expanding brackets, then factorising, then the topics that nothing else depends on.
The surprise is that the student’s most urgent school topic, quadratic equations, comes last. It fails because it sits on factorising, which sits on expanding, which sits on signs.
The mistake to watch for
The common slip is starting with the topic currently being taught, because it is the one that feels urgent. The student spends a week on quadratic equations, still gets signs wrong, and concludes that they cannot do quadratics.
The correction is to follow the failure downward. Find the wrong answer, find the step that went wrong, and ask which earlier skill that step needs. Repair that one first, then return.
A short protocol
- Choose one question you cannot do.
- Ask: what is the first step? Can I do it?
- If not, what would I need for that step? Repeat until you can.
- The skill at the bottom is where to begin.
Check yourself
1. In the example above, why is negative numbers ranked above linear equations?
Show answer
Six gap topics depend on negative numbers, but only two depend on linear equations. Fixing negatives repairs more topics at once.
2. A student cannot solve 2x + 6 = 0 and gets x = 3. Which earlier skill should they check first?
Show answer
Handling negatives when moving terms across the equals sign. The correct answer is x = −3, and the slip is a sign. Check: 2(−3) + 6 = 0 ✓.
3. A topic has 0 dependents and is not needed for school next month. Where should it go in the plan?
Show answer
Near the end, or on a later list. It can wait because nothing else relies on it yet.
Where this leads next
The prerequisite gap explorer is built to trace a wrong answer back to the skill beneath it, without labelling you as weak. After ranking, see keeping a return-to-study plan manageable for how to pace the catch-up.
Self-study may be enough when your gaps are few and one skill clearly sits under them. If several gaps overlap and you cannot find the bottom one, how our online one-to-one tuition works explains the paid trial, and our teachers can test the chain with you in the trial class.