Can I photocopy a textbook if it is for educational purposes?

Educational purposes are an exception to the copyright laws generally. But it does not give you the right to make a copy of the entire textbook. A few pages, however, would be fine, especially for the reason given (making notes on them instead of in the textbook).

However, this does not give you the right to copy word for word from parts of the textbook and use it as your own in the essay. That would be called "plagiarism", and can get you a failing grade on the project. Usually you are allowed to copy very small sections word for word (like a paragraph or two), but you must properly cite the source of it. If you are allowed for this project or not is something you have to discuss with your instructor.

Yes, you can photocopy your own textbook.

You are not allowed to profit from any unauthorized reproductions of a textbook, but copies for personal use are totally fine.

It's normal to need to photocopy a few pages here and there, assuming you're finding the book in the library.

It's not normal to go into a bookstore and start photographing pages from a book.

You're pushing "personal education purposes," but it doesn't sound like you're interfering with a sale, again assuming you're finding this in the library.

Doing it with whole chapters is pushing it.

Don't even think of doing this in a bookstore.

If you need to do whole pages, you should think of checking out (or buying) the book, and just taking notes like a normal person. You don't really need to write on the book itself.

Technically, the "educational" exemption is quite narrow and your unauthorized copy of an entire chapter might cross the line, depending upon the laws of the country where you are doing it, and what you do with your copy once you're finished with it.

It will be fine for you to do so.