While this exercise may not work for younger students or those with smaller hands, those it does work for tend to have a new outlook on reaching for an octave. Students looking to the keyboard for hand position shifts can occasionally interrupt a steady tempo they have established. This can be a challenge when they are first introduced to playing an octave. Regardless of whether it is to play a harmonic or melodic octave, many students of a certain age can reach the interval and just don't know it yet. To help them realize this I do the following exercise.
First, I have the student raise their hand as if they were trying to get someone’s attention, for instance a teacher at school. Next, I ask them with their eyes closed to make a fist with the raised hand. Third, with eyes closed they are told to stretch their fingers apart to form an imaginary octave in the air. Finally, with their eyes still closed I ask them to drop their hand to the keys and play an octave. For those who comfortably reach the octave, most are either successful or miss by one key. After a few repetitions, those who miss improve in accuracy. Quickly they realize they can keep their eyes on the music and just need to trust their newly found ability. Then we try the exercise with the other hand and then finally both at the same time. Now tempo being affected by looking at hands becomes a thing of the past. Of course, if students have to move from one harmonic octave to another, such as in a leap of a third or greater, that is an entirely different issue to overcome, one in which this exercise does not apply.
Why not challenge your students with an octave etude such as Toccata or Scherzo from NMP? Both solos can be found in the Vignettes for Solo Piano book.