It is biological a root. Just like the one I showed in the link. .
The way I showed is surly faster as the way you try it. But it is your Cephalotus und always handling it again is the worst method.
You will read a lot of advice which are basically a myth. If somebody grows them with success for many years his method might not be bad, but usually there are very successful growers which do all the no-go stuff and succeed. So the explanation for success is very often faulty.
In this picture are roots and rhizomes
http://www.foxoles.dsl.pipex.com/Resour ... 1AF4B9.jpg
The reddish part is a root the lighter parts with triangular scaly dead leafs at the outside is the rhizomepart.
A carrot is a root, ginger is a rhizome. Both store energy for the plant.
@ lethal traps the thin root grows out of the thick root. Thats what usually thin roots do. It can grow out of a rhizome too and after some time it will be a thick root like the one shown. A thin root has normally not enough energy to grow a new rhizome, so a thick root is better. Even carrots habe thin roots in the ground.