There are 5 developmental stages, that a child needs to go through, before they can successfully use a mature tripod grip. They need to work through each stage and as their hand, shoulder and arm strength and mobility increases so does the ability to move to the next developmental stage of the grip.
Stage 1. Palmer-supinate grasp
Holds the crayon/pencil in fist (whole hand) like a dagger. They use whole arm movements from the shoulder to mark-make. Due to this whole arm movement they prefer to work on a vertical surface.
Stage 2. Palmer or digital-pronate grasp
Holds a crayon/pencil with the palm of the hand facing down towards the paper. The crayon/pencil is held by all finger and the thumb. The movement comes from the shoulder and elbow. Again, due to the way the arm moves a vertical surface is preferred.
Stage 3. Four finger and thumb grip
Holds the crayon/pencil between the thumb and four fingers with the crayon/pencil nearly vertical up right position. Movement comes from the elbow and wrist.
Stage 4. Static Quadruped or tripod grip
Holds the pencil in very nearly in the correct position however the web space is narrower than it would be if held in a mature tripod grip. This means that the movement is coming from the wrist and large finger movements.
Stage 5. Mature/Dynamic tripod grip