assert
To state something firmly and confidently as true or important.
To assert means to state something firmly and confidently, especially when you believe it's true or important. When you assert an idea in a class discussion, you're declaring it with conviction and strength. A scientist might assert that her hypothesis is correct based on experimental evidence. A character in a story might assert his innocence when falsely accused.
The word carries a sense of strength and certainty. There's a difference between timidly suggesting “maybe we could try this?” and asserting “this is the right approach.” When you assert something, you're standing behind your words.
You can also assert your rights or authority. When a new teacher asserts control over a rowdy classroom, she's making it clear that she's in charge. When citizens assert their rights, they're insisting those rights be respected.
An assertion is the statement itself: “The student made the assertion that homework helps learning.” People sometimes talk about being assertive, which means expressing your thoughts and needs clearly and confidently without being aggressive or rude. Being assertive is speaking up for yourself while still respecting others.