A professora ensina matemática aos filhos da vizinha.

Questions & Answers about A professora ensina matemática aos filhos da vizinha.

Why is there no definite article before matemática, since Portuguese usually requires articles for general nouns?
While Portuguese generally uses definite articles for broad concepts (like A matemática é útil), academic disciplines often drop the article when they are the direct object of verbs related to education, such as ensinar, aprender, and estudar.
Why use filhos for "children" here instead of crianças?
The word crianças refers to children in terms of age (kids), whereas filhos refers to children in terms of kinship (offspring). Because the sentence specifically talks about the neighbour's offspring, filhos is the accurate choice regardless of how old they are.
Could I use the preposition para instead of a, saying para os filhos?
While using para is very common in Brazilian Portuguese, European Portuguese strongly prefers the preposition a for the indirect object of the verb ensinar (to teach something to someone). Therefore, the contraction aos (a + os) is the most natural choice here.
Is it possible to place the indirect object before the direct object, like ensina aos filhos da vizinha matemática?
It is grammatically possible, but placing the shorter, direct object (matemática) before the longer indirect phrase (aos filhos da vizinha) is the standard, most natural word order in Portuguese. Reversing them can sound clunky unless you are specifically emphasizing the subject being taught.

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