It is plausible that it is appropriate to assert a proposition only if one believes or maybe even knows that proposition, and it is a lie to assert a proposition if one disbelieves it. Oddly enough, this plausible claim is false.
Example 1: A friend who is both honest and an expert in ichthyology tells you that a certain sentence in German, which sentence exceeds your own abilities of German comprehension, is a truth about fish. Moreover, she tells you that this truth is widely disbelieved by the general public, and that based on her earlier conversation with you, you also disbelieve it. You memorize the sentence. Later on, while speaking in your (poor) German to a friend, you utter that sentence assertively. The sentence expresses a proposition you disbelieve. Yet, you do nothing wrong in asserting it. Nor is this case uncommon. We may quite often parrot what scientists say without understanding it.
Example 2: You are dying and leave with the executor of your estate two sealed letters for your daughter to be opened when she is 65. Letter A is to be given to her if she has had a successful career in aeronautical engineering--currently, you have no idea whether she will or not. Otherwise, letter B is to be given. Letter A opens: "By now you have had a successful career in aeronautical engineering, as I had always wished for you." Letter B opens: "All of my life I have been pressing you to have a successful career in aeronautical engineering, but things did not go my way." Suppose your daughter in fact gets letter A. Then the assertion that she has had a successful career in aeronautical engineering is not the assertion of a belief you had when writing the letter, and whether it is the assertion of a belief you now have depends on contentious claims about what the afterlife is like, claims independent of the appropriateness of the letter. (Similar examples can be manufactured by computer error messages: "This program has received SIGENV and must be terminated" does not express anybody's belief.)
If this is right, then a correct account of the norm of assertion does not involve the requirement that one believe or know what one is asserting. It is, however, possible that the norm of assertion requires that one know that the assertion, when it is made, is the assertion of something true. (Count a letter to be given later as an assertion made at the time of the giving.) But it might be simpler just to say that an assertion is minimally appropriate iff it is true, and then derive the requirement that one believe that what is asserted will be true not from anything specific to assertions, but from the general requirement to act only in ways that one believes to be appropriate.
Since I believe only in moral normativity in the case of humans, for me the view implies that there is a duty to speak the truth. Thus, people who make mistakes on calculus exams act wrongly--but if they've studied enough, they are not culpable.