Really this is a piece of texture rubber in which you roll the clove. It's surprisingly effective, and has the advantage of keeping your hands free from the oil. Some cuisines have you not peel the clove at all, claiming this imparts a different flavor. You only need to break off and peel cloves you need. There's less surface area of the garlic exposed with larger pieces.
Smaller pieces are more potent, and crushed or pressed garlic are the most potent.
Pressed garlic especially, since it's easiest to press it directly into the dish you're preparing. Not only to you have garlic in the dish, but also you have more of the oil from pressing it. Chopping and slicing garlic requires a confident hand and practice. To crush it, place the flat of a chef's knife over the garlic, press on the flat, chop the crushed garlic, and repeat these steps until it's the consistency you desire. What a lot of people don't realize is that heat not just changes its flavor, but how you heat it can affect the type of flavor.