I teach beginning band to first-year players aged 10-12. I have always taught 5-stroke and 9-stroke rolls this way: Assuming that we are in a simple meter like 2/4, 3/4, or 4/4, I first divide the notated roll note into 16ths. There are 4 sixteenths in the quarter note of a 9-stroke roll and 2 in the eighth note of a 5-stroke roll. Then, I teach the kids to allow the stick to "bounce" on each stroke, which results in the correct number of impacts on the head. So, a kid playing a 9-stroke roll will use wrists/arms to play four main strokes (that will sound exactly like 16ths); they will let the stick bounce once on each of these main strokes to fill in the remaining notes (which would sound like 32nd notes). Adding the next quarter note after the roll gives 9 strokes total, which sounds correct. Once they learn how to control the speed of the bounce they can execute pretty decent rolls and they are ready to learn more rolls.
Today, however, 2 different students told me that their private drum teacher instructed them to execute the 9-stroke roll with 9 separate strokes (RRLLRRLL R), and no bounces. I'm perfectly willing to accept that as a "band" teacher I may have it wrong, and I'd happily defer to a "percussion" teacher... But if the kids are trying to execute a roll with 9 full motions like this, how will they ever get it to sound smooth at tempo?
Am I teaching it wrong?
This post here seems related... How can double-stroke rolls be faster than single-strokes?