Guide

Catching up in maths: finding the real gap, and repairing it

He does not understand anything in maths any more. Almost always, what blocks a student is not the current lesson but an older chapter that was never fully set. Here is how to find which one, why it is repairable in a few weeks, and what makes families lose a whole year on it.

In short

Falling behind in maths is a stacking problem, almost never a question of ability.
The chapter that actually blocks a student usually sits one to three years upstream of the one being worked on.
Three signs tell a genuine gap apart from a passing difficulty — and they are easy to check at home.
Repairing two or three foundation blocks takes weeks. Redoing a whole year repairs nothing if the gap has not been identified.

Why maths breaks down differently from other subjects

In history or biology, a chapter missed is a chapter missed: the next one starts again from a clean slate. Maths does not work that way. Every chapter is built out of the previous ones, and uses them as tools rather than as knowledge to be recited.

The consequence is brutal and very well hidden: a student can lose the thread in Quatrième and only feel it two years later, on a chapter that has nothing to do with it. What is missing is not the lesson — it is the tool the lesson assumes you already hold.

This is also why the marks fall suddenly rather than gradually. For a long time the student compensates by imitating the model exercise. The day the exercises stop looking like the model, the compensation collapses all at once.

The real gap is almost never where it hurts

A student stuck on derivatives is very rarely stuck on derivatives. He is stuck on algebraic manipulation — expanding, factorising, handling fractions — which the chapter uses at every line without ever teaching it again.

The same handful of foundations comes back again and again, whatever the level:

Fractions and algebraic manipulation. The single most common cause, all levels combined. It blocks equations, derivatives, probability and physics at the same time.
Proportionality and percentages. Invisible at first, then everywhere: scales, statistics, rates of change, chemistry.
Reading a function from its graph. A student who cannot say what the curve means will learn the analysis chapter by heart and understand none of it.
The meaning of the equals sign. It sounds trivial. It is not: many students read it as here comes the result rather than as these two things are the same, and every transformation of an expression becomes guesswork.

What I observe

A student who says I am hopeless at maths almost always has a date in mind — the moment the stack gave way. Finding that moment changes the whole conversation: the problem stops being who he is and becomes something he did not get, which is a completely different thing to repair.

Three signs that tell a gap from a passing difficulty

1. He follows in class and cannot start alone

This is the clearest sign of all. Following a demonstration only requires understanding each step as it comes. Starting alone requires holding the tools. When the second fails while the first works, the lesson is not the problem — the toolbox is.

2. The same mistakes come back, whatever the chapter

A sign error, a fraction added wrongly, a minus sign lost in front of a bracket — appearing in geometry, in analysis and in physics alike. Mistakes that travel across chapters do not belong to any of them: they point straight at the foundation.

3. Working time goes up and the marks do not move

This is the most discouraging one, and the most informative. It means the work is landing above the hole rather than in it. More hours spent in the same place cannot fix what is missing underneath — and the student concludes, wrongly, that effort does not pay.

How the guilty chapter is actually found

Not by starting the year again from page one. That is the reflex, it costs months, and it mostly re-teaches what was already solid.

The method is the opposite, and it takes about an hour:

Take one exercise he cannot do, and watch him try — without helping. The exact line where he stops is the information.
Ask what that line needs, and test that alone. Then what that needs, and test that. Going back down the chain of prerequisites, one step at a time.
Stop at the first level he handles alone and without hesitation. The gap is the step just above it.

The point of the whole method

One does not catch up on maths. One repairs two or three specific blocks. In practice the chain almost always stops after one or two steps — which is why the repair is a matter of weeks and not of years, and why a diagnosis is worth more than ten extra hours of lessons.

What does not work, and why it is tempting

Redoing every exercise in the current chapter. It trains imitation of the model, which is exactly the compensation that has just failed.
Adding hours without changing the target. Three hours a week aimed at the wrong level produce fatigue and nothing else. The number of hours is not what decides; where they are aimed is.
Copying out summary sheets. The most reassuring activity there is, and the emptiest: it produces the feeling of having worked without ever putting the student in front of a problem he has to start alone.
Changing method every month. Each change restarts the clock. What repairs a foundation is repetition on the same point, over several weeks — not variety.

How long it takes, honestly

One foundation block: two to four sessions, provided it is worked on between them. The full set for a student in High School: roughly a term. What takes the longest is not the content — it is rebuilding the belief that effort pays, and that only comes back after the first exercise solved alone.

One warning, and it is the reason not to wait: the stack keeps growing. A gap left alone in Seconde is repaired during that year; the same gap discovered in Terminale has to be repaired while the hardest syllabus of the whole schooling is running at full speed. The cost of waiting is not linear.

When a private tutor genuinely helps, and when he does not

It helps when it does three things the classroom structurally cannot: identify the exact gap, work on that level rather than on the current one, and hold the same point week after week until it is solid.

It is useless when it doubles the teacher, when it turns into doing the homework, or when the student has not agreed to any of it. That last one is worth saying plainly: with a student who refuses, no method works, and paying for hours changes nothing. That conversation has to happen first, at home.

Finding the gap is the first session

Twenty minutes, free and without commitment, to work out where the gap actually sits — and to tell you honestly whether regular lessons are what your child needs.

Book a free first contact

See also: lessons · rates · all the guides