This is a very interesting contraption used back when students used full arm movement. Students were taught to hold the pen in a very particular way and not allowed to move their fingers but to only use their arms to form the letters. To discourage finger movement and encourage proper pen position, all kinds of gadgets were developed, and this strange looking pen was one of them. The ovals are where the thumb, pointing and third finger are placed, and this way one knows exactly how the pen should be held.
I admit it is very uncomfortable to hold. The way I hold my pen is completely different. This thing must have tortured some poor student back in the day.