I teach in the Universidad Politécnica de Madrid, which is a fairly large public engineering school with research objectives. The students are comparable to those I have taught in engineering degrees at places like Georgia Tech or the University of Washington, although they enter the univesity with better preparation. The teaching of calculus in the UPM varies somewhat from school to school (the UPM is divided into many different schools) but is in broad strokes similar to what is standard in Spanish universities, which are more uniform in their practices than are their counterparts in the US (although of course there are lots of variations in details). It is strongly conditioned by the structure of Spanish degree programs and by the comparativaley poor financing of Spanish universities (when compared with other countries having a comparable ecomonic level professors and administrative staff are few and poorly paid).
Classes typically meet in large lectures, somewhere in the 50-150 students range. There is plenty of willingness to teach in smaller groups, but there are usually not enough professors available to do so. A typical class meets 4 or 5 hours a week, perhaps 1 or 2 of which are formally or nominally dedicated to working problems (this depends on local practices), although this would often be done in the usual classroom, by the usual instructor. For example, in my school we have 4 hours of instruction in a large lecture hall, and 1 hour in a room with movable tables so students can work problems in small groups or in the computer lab to use Matlab, R, or whatnot (with the one professor circulating to help them - I have only about 70 students so this is viable). Sometimes these problem sessions, computer lab session are broken into smaller groups but not for educaitonal reasons, simply because they don't fit in the rooms used (this requires assigning additional professors). Semesters are 15 weeks by law.
There are no teaching assistants or graders in the US sense, so it is generally not viable to assign homework in calculus classes. Often one gives some sort of quiz or weekly in class assignment or computer exercise, that might be evaluated automatically via some cell phone app, or something of this sort, or might be done in groups, so as to make grading viable, but this is often left up to individual professors, and is not universal. The main components of grading typically are one or two tests and a final exam.
Whether instructors have broad autonomy to teach however they want, or
whether instruction is coordinated across sections to ensure some kind
of consistency and anything else that seems relevant for a specific institution.
Such autonomy is basically inconceivable in the Spanish system. Each degree program has an official plan of study approved by a national accreditation agency. Modifying the study plan requires substantial bureaucratic movement at the level of a dean's office, so principally occurs in response to flagrant problems, or at regular 5 year intervals when these plans are obligatorialy revised. The study plan stipulates course contens, and for something like calculus it sometimes essentially establishes the curriculum. In engineering degrees the contents of even calculus courses are in any case basically obligated by law and professional accreditation requirements.
Every year the department responsible for teaching a course approves a "study guide" for the course (later approved by the large faculty - this all occurs many months before the semester starts). This is written by the official course coordinator in conjunction with the other professors assigned to teach the class. It is a document of some pages that stipulates course objectives and learning goals, and details the syllabus (in my school to the point of indicating what contents will be covered in what lecture). It describes the evaluation scheme to be used (and the description is supposed to be obligatory for the professor). It contains recommended books and other information about learning resources. The professor is expected to adhere to it more or less rigidly. Of course there are professors that don't, and not much can be done about this, but the general spirit is to do what has been stipulated in advance.
This sort of planning guarantees considerable uniformity, at least where such uniformity is desired. I teach one class where the study guide intentionally leaves 20% of the grading, as well as the structuring of problem sessions, at the discretion of the individual professor (there are 9 professors). In other classes all grading is done in common. Certainly there is no grading on a curve, or a posteriori changing of grading schemes, etc. Such practices, common in the US, are generally viewed as unprofessional, unfair to the student, and potentially unethical.
Generally speaking books are only recommended, not assigned. It is economically impossible to do anything else. Many families can't afford to shell out euros for books and no one thinks it reasonable to force them to do so. In any case everything can be downloaded from the web, and everyone knows this. Books are formally recommended, but it is essentially unheard of to assign problems from a book. Typically professors prepare weekly problem sheets (voluntary) and provide lecture notes that constitute unedited books. When several professors teach together this effort is often coordinated. There might be an official course problem list accompanied by official lecture notes, often distributed through the university's internal publication service.
At the university level there is no precalculus as this is not considered (essentially in a legal sense) a university level subject and could not count towards an official university degree. The high school courses required to enter the university in a degree program that involves calculus include calculus and linear algebra. Typical first year calculus courses assume knowledge of basis differentiation and integration, and typical first year linear algebra courses assume ability to analyze and solve systems of linear equations. A typical first year program in mathematics includes calculus, one variable and multivariable, linear algebra, and often gets to more advanced topics such as Laplace and Fourier transforms, ODEs, a bit of numerical methods.
In the old days (a decade ago, before the Bologna treaty), pass rates were in the 10-30 percent range, at least in engineering programs. Now they are typically more in the 30-70 percent range. (I'm guessing a bit at the numbers, but the upwards shift has been undoubtedly pronounced, a response to changing administrative exigencies).
Professors are obligated to hold office hours, in my institution 6 hours a week, and in my experience this obligation is taken more seriously than it is in the US, although students come to office hours just as infrequently as they do in the US.
The bureaucratic overhead associated with teaching a calculus course is substantial in Spain, in my experience more onerous than in the US and with substantially less administrative support and fewer instructors per student. This involves things like the annual preparation of the aforementioned study guide, various offical reports on class outcomes, etc., in addition to the day to day handling of matters related to enrolment and the like. Teaching a course of 150 in the US I would have 4 TAs and several graders at my disposition, also some departamental administrative personel to attend to purely administrative matters. In Spain there is one administrative person serving three departments with a total of 50 professors, and there are no TAs or graders.
Teaching style is generally a professor's prerogative. When teaching calculus I mainly use a blackboard (when I teach programming this is done entirely in a computer lab). Some professors teach entirely using a computer/projector. Most instruction is classic lecture format, but there are people trying other approaches and this is encouraged administratively.
