The Spanish here is pitched at the IB Spanish A and B syllabus, not just conversation practice — which is the thing your child is actually graded on if they are at an international school. And because AE Teaching already has arrangements to teach on several Barcelona campuses, a tutor can sometimes meet your child at school straight after the bell rather than at home.
AE Teaching is a Barcelona tutoring agency that has worked with international-school families since 2011. Its main business is IB and academic subjects taught in English, but Spanish is one of the languages it tutors, and its published tutor roster includes several specialist Spanish teachers with philology or Spanish-as-a-foreign-language degrees — covering IB Spanish A and B as well as everyday Spanish. Lessons are one-to-one on a fixed weekly slot: at your home anywhere in the city of Barcelona, at your child's school, at a tutor's home office, or online. You tell them the subject, the hours you want and when your child is free; they take two or three days to match a tutor, then send you that tutor's CV, a proposed schedule and a price to approve before anything starts.