Try to analyse some buildings that fascinate you in some way or the other and try to find out what the parti is and how that informed the entire project and why you think it is a good building.

The most important thing about a design is knowing how to value it - what ideas drove the process - and why those particular ones; how do you see the end result and if you can call it a success, why?

and yes,
there's nothing inherently good about a building as a letter.

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I don't think its bad at all that you have taken the path of "getting something done" instead of having your first ideas killing you - it's not always the designers that have to "kill their darlings", it can go the other way too.

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But try this: in the example you gave, about having a particular piece of a complex building look and functon in a particular way -

"My first idea was: I want to make this sports hall a modernistic glazed box, supported by columns, with a terrace overlooking the nearby river. "

- there's an awful amount of formal "requirements" you restrain yourself with - think about why you want to make this hall in especially this way and distill the important elements - not as formal requirements (glazed box, columns, terrace) but as possibilities and conditions (a view, a position in the landscape, a connection with the outdoors, ...)

Then when you unravel the program, it's functional and spatial order - you can start to play these things against each other - the optimal functioning of the program and the conditions you want to achieve.

Then the design starts to form itself, as a push and pull between these two realms.

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When going all out in favor of one approach - certain wants about a spatial/formal condition, or the optimal functioning of a program - you often just crash and burn when hitting the first obstacles. And have to adopt a plan B that "gets the job done" but does not help to realize materially the things that you value.

Helsinki: thanks for a thoughtful reply.
That leaves a question of the parti open, though. In my example you mentioned, yes, I could relax the constraints - lets say, to "I want a specific view". And then let the design proceed "as a push and pull" between this condition and the program.

But "a specific view" is not an example of a good parti, I guess a parti is something more, something that should inform and shed light on the whole of design, so that is not a mere "push and pull", but rather a winding road, but with a direction.

So what is a good parti? "glazed modernistic box on columns" is not. Abstract parti is not. What is?

I don't know about other schools, but in our university, I guess the notion of parti was not made clear enough. The teachers were usually speaking of parti as "image"", and most students came up with images like "a boat turned upside-down" or "a sail" or "a stylization of a rural shed" etc. That was at least during the first 2 years of studies.

But now in the 3d year we have to design a school, this is a more complex project. I don't think a parti like "a sail" or "a something" would do here. And I don't think I've learned to formulate this "more complex kind of" a parti.

identify a set of particular spatial, formal, site, experiential, or what-have-you forces, and have them shape your design

First, why are you asking the internet and not your teachers? To me that’s very strange – this kind of question is kinda what the whole process of education is about. But I suppose that’s just my particular problem.

The best things I found to get my head around the idea of parti were:

Rowe’s Mathematics essay where he juxtaposes the plans of Shinkel’s Altes musuem and Corb’s Palace of assembly. So what’s an example of a general, abstract analytic parti? What those two plans have in common. An example of a particular parti? The differences.

The other is the book for the big MOMA Beaux-Arts show from the 70s, edited by Arthur Drexler, because it has a long history of the French Academy and the thematic ideas which shaped the pedagogy of the place over time: distribution, parti, poche, etc. These are all ideas from the French Academy that we still use.

Like the phrase parti pris, it basically means something you bring to the table or a decision you’ve already made. In the architectural case it’s a decision regarding massing and organization, around which your structure and circulation, all your decisions, will conform, congeal, or reinforce, unless you work some counter-motifs in there.
For example, will I use a small cluster of volumes, or a large volume? Will they be in a line or random? Etc. Etc. This isn’t about a particular interior, because an idea for a particular interior doesn’t necessarily help you make decisions about the rest of your project. A glazed box supported by columns can be a parti if you ask how how all the other parts of the program and organization must be reworked to maintain the clarity of a box. Notice that your examples of succesful partis all have to do with how masses can be broken down and arranged in a way that will help establish the general organization of the whole of the project. Also notice that these aren’t ‘images.’ Having something ‘look like x’ is not a parti. And yes, a parti is random. What make it better or worse is how it’s developed into a project and the possibilities its creates for organization and form (if only in a general sense regarding form).

This is probably old school, but a parti by definition is a diagram of the thought behind the design. In order to express that thought there probably should address the organization, the hierarchy, the adjacencies, and the functionalities of the spaces in plan, section or 3 dimensionally.

"sports hall a modernistic glazed box, supported by columns, with a terrace overlooking the nearby river." or "a steps-like succession of 3 different volumes with 3 different heights, interrupted by cuttings for loggias." can both be rationalized as the main plot of the story but it is just the cover or title of the story. The individually less important spaces that lead to this grandiose concept is equally if not more important than the main space itself.

anyway, the point is, a well thought out parti should tell the whole story; how the important parts fit with in the not so important parts of the story; or vise versa. A simple example would be how Kahn described as spaces that serves and the spaces that is served. So, a good parti is probably something that was approached holistically rather than simply the beginning of an idea.

I think maybe you are starting at the end in a weird way. You don't start with a "modernistic glazed box". You start with a concept, like a simple box that opens to the environment around. This was probably the real basis for choosing a modern glass box? Maybe I'm inferring too much here.

You are trying to accomplish something with the materials and organization of these materials. "Glazing" is merely a way to accomplish "open" The terrace is accomplishing an area to have views and or congregate outside. Its another version of open really.

Sounds like your parti is to create an environment that's blurring interior and exterior, maybe it revolves around the ability to be in constant contact with nature. I'm not sure, you'll have to determine what made you choose the glass box.
The glass box is merely the method of expressing the concept. Look at why you chose it.

Second Orhans post - first things first and think about what you are doing in architecture: - designing an environment, not a form.

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You will not come up with a shape that explains everything - the idea of a parti in design should be to either help organize your functions and get started [working as a diagram], or stave off the disintegration of overall forms once you have proceeded along [working as an image] - it's not an end in itself, by any means, but a tool.

You can question the way your professors present a problem - if they insist on being presented an "image", a metafor or something similar, when what you should be doing, is presenting an architectural design.

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Anyway, an idea for a parti does not present itself before you have started tackling the particulars of the program, the site and your own inclinations - maybe later, after a while working with architecture you will recognize certain problems and can a test previously explored spatial configurations, formal solutions, and modify them according to a situation, but for now you have to dig in to get a hold of the possibilities.