If I divide development of a particular feature into multiple stories:
- First one for a high level design of the feature,
- Based on first story I create other stories to develop the different stand-alone pieces that compose the feature,
Does it mean I’m doing waterfall?
Furthermore – if I divide development of the previously identified stand-alone pieces into design and implementation.
Would that mean that I’m doing waterfall?
Note: I am big time Scrum novice.
There is no such thing as design and implementation stories, User Stories should provide some level of end-to-end functionality to the user (i.e. delivering customer value).
The fact that you are mixing the terms stories and features doesn’t help to communicate but what you’re describing sounds actually like tasks (Sprint Backlog level), not user stories (Product Backlog level).
And if they are not tasks, then they are very bad stories. Maybe the “functionality” is too big and you should put the story on diet but what I see here is a typical story smell.
If you are new to User Stories, I strongly recommend to use the regular template (As a <type of user>, I want <some goal> so that <some reason>) and also to follow the INVEST model. This will really help you to avoid pitfalls like the one of your question.
Back to the real question (Am I doing waterfall?): there is nothing wrong with doing so design inside a Sprint (as a task of a story). But if your whole story is about design, you’re not really doing Scrum, you are supposed to deliver a demonstrable end-to-end increment at the end of the Sprint.