Since Plato, the idea that knowledge is only justified true belief (JTB) has been articulated, discussed, critiqued, and re-articulated. For some, JTB is a fun exercise in philosophy, and for others it functions as a definition of knowledge and a barometer for judging mastery.
The idea of JTB is this: to count as knowing, the meaning in question has to satisfy three criteria:
Here are a few examples:
When it comes to assessment, believing your meaning is true, and it is true, is not enough. The justification of the belief has to be valid. Consider the student taking a multiple-choice test and choosing her neighbour's answer. It happens to be the correct answer, and she believes it is correct because the person from whom she borrowed the answer is very smart, but her justification for knowing it is true is invalid, and thus she does not know the answer.
In the end, to assert that you know something requires valid justification. In math this, most times, valid justification requires that you "show your work" so that the assessor can see that you are using the correct formula or equations, that you understand which variables to use and what values should be used, that your technique in working through the problem is correct, and that your answer is the right answer. You need the right answer, and valid justification.
The "Believing you answer is correct" piece takes the process up a notch, to student-centered learning. When you believe, as a learner, that your knowledge is valid, and you have used the appropriate justification, your knowledge is real, and you know it. Part of being an effective self-directed learner is knowing that you know something (rather than needing your assessor to tell you that you know it).