What is the difference between procedural and conceptual knowledge in math? I'm having trouble with that in my college class and when I googled it, it all had the same definitions that I still don't understand. Any examples would be great.

Procedural involves working out a procedure, but the students may not understand the reasoning behind a procedure. Conceptual knowledge is understanding the concepts in order to solve problems (so students may use any procedure). A great example is with fractions. Many students can solve fraction problems for a test because they memorize a procedure only to forget two weeks later. Thus, the students have not mastered the conceptual understanding.

The quick answer: Procedural knowledge is knowing what to do. Conceptual knowledg is understanding why you're doing it. So a 5th grader might know that in order to add fractions, he needs to find a common denominator, even though he has no idea why it's important. That's procedural knowledge. But the one who realizes that a common denominator puts gives each increment of the fraction equal weight, thus enabling you to add them has Conceptual knowledge.

Just to add another example. A student could go through the procedure of 560 - 74 and reach the answer 760 (I don't know how but I've seen this type of thing before). They've followed a procedure and think that they've reached the right number because they think the procedure was correct. However if they thought conceptually about it even briefly they would think "Hey! The answer can't be more than 560!" because conceptually that's impossible. As another example you can teach a student to memorize 7x8=56 and they can learn to spout it off but if you said "there are eight plates each with 7 carrots, how many carrots are there? they might have no idea how to work that out.