Maths in Italian primary and middle school, class by class, against CBSE: where an Indian child is ahead, where the Italian method differs, and the terza media algebra

Italian school maths class by class is the comparison every Indian parent wants in the first term, when a child who knew all the tables at 7 comes home with discreto and a page of problemi with the wrong operation on every line. The short version: the Italian primaria and scuola media teach maths carefully, slowly and in a particular style. In algebra an Italian child is about two years behind a CBSE child. In geometry with formulas, long arithmetic expressions and unit conversions the Italian school asks more, and earlier. And the problemi, the word problems, are in Italian, which hides the maths the child has until the words are learned. This post walks the years, the methods, the words and the exam.

Class by class, with CBSE beside it

Read down the last column and the pattern is clear. An Indian child arrives ahead in raw number work and in algebra, is level for most of the middle years, and is asked things the Indian school did not ask: geometry driven by formulas and their inverses from classe 4, long expressions with nested brackets from classe 5, and a heavy diet of unit conversions. A child who comes to Italy in classe 4 or 5 and is not supported in exactly those three things will look average in a subject they are good at.

The Italian methods the teacher grades

Italian teachers grade the working, and the working has a house style. Five things to learn early.

The column layouts (in colonna). Addition and subtraction with the riporto (carry) and the prestito (borrow) written small above the columns, much as in India. Multiplication by two digits with the second partial product shifted and a dash or zero in the units place.

Division without written subtraction. The standard Italian long division writes the divisor to the right of the dividend, works one digit at a time, and does not write the subtractions; the child multiplies, subtracts in their head and writes only the remainder before pulling down the next digit. Indian children who write the full subtraction are not wrong, but they are slow and their page looks unfamiliar to the maestra. Some schools now allow the divisione canadese, which writes the subtractions, so ask.

Espressioni. From classe 5 and through the media, a large part of the maths is evaluating long expressions with round, square and curly brackets in a strict order, first with whole numbers, then fractions, then powers, then relative numbers. A single slipped sign fails the whole exercise. This is drill, and Indian children are good at drill once they know that the brackets go round, square, curly and that the Italian writes the steps one under the other, copying the whole expression each line.

Equivalenze. Converting between metric units with the table of prefixes, km hm dam m dm cm mm, and the same for weight and capacity, and for area and volume where each step is a hundred or a thousand. Italian children do hundreds of these. Indian children do a few. It is a week's work to learn the table and it removes a whole category of lost marks.

Formule inverse. Geometry in Italy runs on formulas and their inverses: given the area and the base of a triangle, find the height; given the volume and two edges, find the third. The formulas are learned by heart, the inverse is derived, and the working shows both. Indian children usually reach this only in Class 8 and 9.

The thirty words of maths Italian

Most problemi use a small vocabulary. Put this on the fridge.

Question words: quanto, quanti (how much, how many), calcola (calculate), quanto costa (how much does it cost), quanto resta (how much is left), quanto manca (how much is missing), trova (find).

Operations in disguise: in tutto, in totale (altogether), ciascuno, ognuno, per ogni (each), il doppio, il triplo (double, triple), la metà, un terzo (half, a third), in più, in meno (more than, fewer than), la differenza (the difference), il resto (the change, or the remainder), diviso (divided), ripartire, distribuire (share out), volte (times).

Money and shopping: costa (costs), paga (pays), spende (spends), guadagna (earns), lo sconto (the discount), il prezzo (the price), il ricavo (the takings), la spesa (the outlay).

Measure and time: la lunghezza (length), la larghezza (width), l'altezza (height), il perimetro, l'area, il volume, il peso (weight), la capacità, la distanza, dura (lasts), parte, arriva (leaves, arrives), la velocità (speed).

Data and ratio: la media (average), il rapporto (ratio), la proporzione, la percentuale, la scala (scale), la tabella, il grafico, circa (about), stima (estimate).

The Italian problema also follows a written ritual the teacher expects: dati (the data, listed), domanda (the question, written out), and then the operations in colonna, each with a short label of what it finds, and a sentence with the answer. A child who skips the dati and the domanda loses marks with the right answer; a child who writes them finds the operation more often, because the ritual does the thinking.

Marks and what they mean

The primaria gives giudizi, ottimo down to non sufficiente, and no marks, so a parent cannot see where in buono a child sits. The media gives marks out of 10 on every test and interrogazione, visible in the registro elettronico, with 6 as the pass. Ottimo and 9 or 10 are rarer than an Indian parent expects; Italian teachers keep the top of the scale for work that is complete, correct and neatly laid out in the house style, and an Indian child with the right answers and Indian working will sit on 7. The layout is worth two marks. How to read the Italian report and the register is in the Italian school system explained.

The terza media and what it tests

The written maths paper of the esame di terza media in June is usually four problems in about three hours, and the four are predictable: a geometry problem on a solid or a plane figure using formulas and their inverses; an algebra problem, an equation to solve or expressions to simplify, sometimes with a check; a probability or statistics problem from a table or a graph; and a problem tied to science, a formula or a graph to read. The INVALSI in April, on computer, is different in style, shorter questions across the whole syllabus, and its result does not count towards the mark but is certified. The school's consiglio orientativo in December, which points the child at liceo, tecnico or professionale, is largely built on seconda media marks, so the preparation that matters for a liceo scientifico recommendation happens in seconda media, not in the last spring.

What to do at home, and what we do

Three things, in order. First, the words: the list above, read aloud with the child, and every problema translated before it is solved, for the first term. Second, the house style: dati, domanda, the column layouts, the espressioni written one step under the other, the equivalenze table. Third, keep the algebra that the Indian school gave the child alive, because it will be two years before the Italian school asks for it and it is the thing that makes terza media and the liceo easy.

We teach maths to children in Italian schools in English, Hindi or Punjabi, in the Italian class order and a term ahead, with the working in the Italian layout and the words alongside, and from seconda media with the four terza media problems as the target. Bring the last verifica or the pagella to the free demo, and we will tell you within thirty minutes whether the marks reflect the maths, the Italian or the layout.

Questions parents ask

See how we teach this, 1-on-1 online →