What is it to "Know"?
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:
- The meaning has to be true,
- The knower has to believe the meaning is true, and
- The knower's justification for believing the meaning is true has to be valid.
Here are a few examples:
- Derek leaves his shoes at the front door when he enters the house, but when he is planning to leave the house later he goes to the back door looking for his shoes. He does not know his shoes are at the back door because they are not at the back door. It is not true that they are at the back door, so he cannot know that they are there.
- Derek leaves his shoes at the front door when he enters the house. His diligent daughter cleans up around the front door and moves them to the back door. When Derek plans to leave the house his daughter tells him his shoes are at the back door, but he goes to the front door looking for them. He does not know his shows are at the back door because he does not believe they are at the back door - he thinks they are at the front door (because that is where he left them). Even though is true that they are at the back door he does not believe it, so he cannot know they are at the back door.]\
- Derek leaves his shoes at the front door when he enters the house. His diligent daughter moves them to the back door while cleaning up, but moves them back to the front door. When he plans to leave he claims to know they are at the front door. It is true that they are at the front door, and he believes they are at the front door, but as he doesn't know his daughter moved them and then replaced them, his justification (that he left them there when he came in) is false, so he cannot know they are at the front door.
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).