When a family changes school systems — a new board, a new country, a new curriculum — one subject breaks more often than the rest, and it is nearly always maths.

Not because maths is harder. Because maths is sequential. History forgives a shuffled order; miss the Tudors, join at the Victorians, and the story still makes sense. Languages forgive it too — vocabulary arrives in whatever order life delivers it. Maths does not forgive. Every skill stands on an earlier one, and a curriculum switch quietly rearranges which bricks were laid when. The new school assumes a staircase the old school built in a different order — the same staircase logic that explains most maths struggles that have nothing to do with moving.

The good news is that this is one of the most fixable problems in all of maths parenting, because the gap has a known cause, a known shape and a known size. This is the checklist for the summer in between.

First, the reassurance the research offers

Studies of children who change schools frequently — including research on military families and expatriate students, some of the most-moved children on earth — consistently find the same pattern: a temporary dip in attainment after a move, which closes when the transition gets targeted support.

Read that again, because both halves matter. The dip is predictable — expect it, and don't read it as a verdict on your child or your decision to move. And it is temporary — provided someone actually maps what's missing instead of waiting for it to surface as failure.

A school switch doesn't create a weak student. It creates a mislabelled one — for exactly as long as nobody maps the gap.

The rest of this article is the mapping.

Step 1 — Map the diff

Start with paper, not panic. Put the old curriculum and the new one side by side and list what the new system expects a child of your child's grade to have already met that the old system hadn't reached yet. Our grade-by-grade comparison of CBSE, ICSE, Cambridge, IB and Common Core includes a divergence table built for exactly this job — it shows, system by system, roughly when each introduces multiplication tables, formal long division, fractions of quantities, decimals, negative numbers and basic algebra.

Two things happen when families actually do this. First, the list turns out to be short: usually three to five topics, not thirty. A child moving into a system that formalises written algorithms early may need the compact long-division layout; a child moving the other way may need practice explaining and representing methods they can already execute. It is nearly never "all of maths".

Second, naming the topics kills the panic. "He's going to be behind" is a fog; "long division and decimal notation are new to him" is a to-do list. Fog spreads. To-do lists shrink.

Step 2 — Diagnose, don't assume

The diff tells you what the new system expects. It does not tell you what your child has. Children carry gaps from their own curriculum too, and they also quietly know things no syllabus gave them credit for. So before spending a single summer hour teaching, test — kindly, briefly, at the kitchen table.

The simplest manual version: take the new system's expectations for the previous grade — the material the new school will assume is secure — and try a handful of questions per topic. You are not looking for a score. You are looking for edges: the exact places where confident turns to hesitant.

The easier version is to let software do it. This is, frankly, the most natural moment on this whole blog to mention what we build: an adaptive placement doesn't care which board printed your child's old textbooks. It simply finds the edges — the skills that are secure, the ones that are shaky, and the prerequisites hiding underneath the shaky ones — in a way no fixed test pitched at one curriculum can.

One mother we heard from did exactly this before an international move into an IB school. She spent the summer not buying the new textbooks — no small feat of restraint — and ran a placement diagnostic instead. It found two genuine gaps: data-handling vocabulary her daughter had simply never met, and fraction–decimal fluency that had gone soft. They fixed those two things and deliberately let everything else wait for school to teach in its own way. Her daughter's first term report said, in full: "settled in immediately."

Notice what she didn't do. She didn't re-teach the whole previous year "to be safe". Diagnosis-first meant the summer stayed mostly a summer.

Step 3 — The six-week summer bridge

With the gaps named and confirmed, six weeks of short daily sessions — fifteen to twenty minutes, not marathon mornings — is usually enough. A shape that works:

Weeks 1–2: prerequisite facts and fluency. Whatever the named topics are, they stand on number facts. Number bonds, tables and division facts, place value. If these are shaky, the new topics won't hold; if they're solid, the new topics go in fast. Boring-sounding, highest payoff.

Weeks 3–4: the named missing topics. Now the three-to-five items from Step 1, one at a time, taught for understanding first and method second. Resist the urge to add "just one more topic to be safe" — scope creep is how a bridge plan becomes a punishment.

Weeks 5–6: the new system's style. Same maths, different dialect. Cambridge wants reasoning in words ("explain how you know"); ICSE serves long, wordy problem sets; Common Core classrooms speak in representations — number lines, area models, bar diagrams; CBSE expects tidy formal layouts produced at working speed. A week or two of rehearsing the dialect means your child's first impression is made by their maths, not their unfamiliarity.

Step 4 — Brief the new teacher

This step takes five minutes and changes the whole year. Send the new teacher two lines: "We've just switched from a Cambridge school; formal long division is new for him as of June and we've been practising it over the summer. Everything else tested solid."

Here is why it matters. A teacher who watches a new student stumble on long division, with no context, has one available explanation: weak student. The same teacher, holding your two-line note, has a better one: transition, supported, in progress. The first explanation becomes a label. The second becomes a plan. Teachers are not the villain here — they are working with the information they have. Give them better information.

The special cases

Moving mid-year. No summer bridge available. Compress the plan: diagnose in week one, tell the teacher immediately, and run the fluency and missing-topics work alongside school rather than before it. Expect the dip to last a little longer; it still closes.

Moving countries, not just boards. Curriculum, language and culture arrive at once, and maths class is where all three intersect — word problems are language, and even the division layout is written differently in different countries. Give it an extra half-term of patience before drawing any conclusions, and weight the bridge plan towards vocabulary-heavy topics like data handling and word problems.

Expat and returning families. The return home is the underestimated move. Families prepare exhaustively to go abroad, then assume coming "home" to a familiar board needs no preparation. The staircase mismatch is exactly as real in this direction — run the same checklist.

Moving "down" in formal difficulty. Sometimes the new system covers less, later, and everyone relaxes. Two traps hide here. The reasoning and explanation demands may be quietly higher even while the content looks easier. And a coasting child is a child not building — ask the new school for depth (harder problems on the same topics), not acceleration.

The summer this buys you

The whole checklist — map, diagnose, bridge, brief — costs a few kitchen-table evenings and fifteen minutes a day for six weeks. What it buys is the difference between a child who spends the first term being quietly re-labelled and a child who walks in merely new, not "behind".

If you'd like the diagnosis and the bridge handled for you, this is precisely what CREST Champs' free daily adaptive practice does: the adaptive placement finds the real edges of your child's maths — whatever curriculum built it — and the daily sessions work at exactly those edges, a few minutes a day, all summer. The map gets drawn automatically; you just get to watch the gap close.