A single stroke is when you hit the drum with the stick down once.
In the past, many teachers would not teach the double stroke until the player was able to do the single stroke quite well, but it is not practical to have practiced the snare drum for 1-2 years in an elementary school band and not know the double stroke at all.
Once students can hold the stick firmly and start practicing the single stroke, I think it is better to start practicing the double stroke at about the same time.
The way students hold the stick is very important, so please teach it properly before practice.
If they do not hold it properly, their future practice will be completely meaningless.
Please refer to the illustration on the left for how to hold the stick with right hand.
Hold the stick between the pad of thumb and the second joint of bent index finger. Keep other fingers lightly supported and squeeze the stick tightly just as it hits the drum head.
Holding the stick equally with both hands is called matched grip. With this grip, the snare drum should be set horizontally on both sides.
There is also a traditional grip for the snare drum (the right hand is the same as the matched grip), but it seems that many people are practicing with the matched grip these days.
First, practice hitting the snare drum once in time with the metronome.