Here is a little history and information I have learned about graphite pencils.
Important things to know about pencils:
You can sharpen your pencils in a few ways. The easiest and most common is with a Pencil Sharpener. Like many tools, you get what you pay for. I like a pencil sharpener with a built-in container to hold the shavings. This makes it less messy. The problem with sharpeners is that they can loosen over time and get dull, thus being less effective. Electric pencil sharpeners seem to hold up well but if you are not near an outlet they are not practical.
Often I will use a knife to sharpen my pencils, especially when I work outdoors. Knives always give you a point that is sharp. For some people it is hard to work the knife just right without cutting off too much wood or graphite. This can also be a messy way of sharpening if you need a waste basket for the shavings. To sharpen with a knife you stroke the knife away from you, like whittling a stick.
Sandpaper can also be used to do fine sharpening of the graphite. I find this a bit messy and do not use this method much. I would rather spend my money on a decent pencil sharpener.
Problem - Graphite in pencil breaks often when sharpening
If your graphite keeps breaking as you are sharpening it, this is because at some point your pencil was dropped and the graphite inside shattered. Be careful not to drop your pencils on hard floors and surfaces.
Your pencil should be held with what is called a dynamic tripod grip. The tripod grip means that there is equal pressure on the pencil from the tips of your thumb, pointer finger and middle finger. This grip gives the most flexibility while drawing.
I hope this information was helpful.
Keep using your Artist's Brain.