Knowledge of Results is information about achieving the goal or performing of a skill but does not describe the outcome-it only tells the student if they achieved their goal or not. However, Knowledge of Performance is specific information about characteristics that led to the performance outcome.
I can see how this distinction can be important in Math class. Getting the correct answer in Math is important but it is also important to be able to demonstrate how you arrived at the correct answer. Did the student perform the needed operations accurately to get the correct result or did they guess? Being right would imply that they succeeded according to Knowledge of Results. However, if they can not demonstrate how they got to the correct answer then Knowledge of Performance tells us that they have still not mastered the skill. When I correct math work, I often focus on how the student arrived at the wrong answer. Was it a transcription error that changed a plus to a minus sign? Or a simple computation error where they multiplied 2 by 3 and got a number other than 6? Do they need an order of operations review? Knowing how the student got the problem wrong is much more useful than just knowing that it is wrong after the initial acquisition phase.