I hope you— students and teachers— are using my Reed method for playing rock beats. I think it's one of the better things I've come up with— it's just a more musical way of learning that basic vocabulary, and easy for players of all level to get, when you explain it the right way. We should be having a print or e-book available covering that, fairly soon...
But here's an add-on to that basic method, this time using the “Syncopation” section of the book Syncopation— the part with the jazz-style notation. The reading is harder, and there are some things about the exercises that require a little bit of creative interpretation. What you end up with is a very modern, melodic, improvisatory way of playing a rock feel, with a lot of displacements, which reminds me of Joey Baron's playing on the Bill Frisell tune Child At Heart.
To quickly review the basic rock method, using pp. 10-11 of Reed: reading the stems-up, melody part from the book, re-voice the part as follows: play the 2 and 4 on the snare drum; play everything else on the bass drum; add 8th notes on the hihat or ride. That's it— see the link above if you need more explanation.
From here on out, use the 1-line exercises starting on p.33, and the long exercises starting on p. 37 (38 of the new edition). To start, just play the exercise with the usual rock method— play the 2 and 4 on the snare, everything else on the bass drum; if there is nothing sounding on the 2 or 4 of the melody rhythm (either it's a rest, or there's another note holding through the downbeat of 2 or 4), add a snare drum hit on that beat. So you'll have a steady backbeat on the snare drum all the way through the exercise. Here are the first three lines of the famous Syncopation Exercise 1:
Next you can work up the exercises using only the notes given in the exercise (plus hihat)— no added snare drum hits. This will be a little more broken up, and you'll have some creative decisions to make: there are plenty of measures without a 2 or 4 sounding, but we don't want to lose the snare drum. So we'll displace it, playing the snare on the closest written note to 2/4— usually either the & of 1/3, or the & of 2/4. Often both are available, so you can decide to favor one or the other. Here are the same three lines of Exercise 1 putting the displaced snare drum hits on the & of 1/3:
And again, with the displaced hits on the & of 2/4:
It may be difficult to get all the reading (Syncopation Exercises 1-8) perfectly together each of those ways, and it may not be necessary— this is just to show you the available options while playing down the exercises. You'll probably end up favoring one over the other. I like the & of 1/3 way because you end up doing a samba/bossa nova-type rhythm in the bass drum quite often. In fact, by altering your touch, you could use this exercise to open up your bossa/samba— to wean yourself from the repetitive bass drum rhythm, for more modern playing.
You can do this at any normal rock tempo, I think it works better faster— quarter note = 150-200. If that's too fast for you, try 130 as your training tempo, or your first goal tempo. For a different musical effect, and to save your chops at the faster end of the tempo range, you can instead play quarter notes on the hihat (closed or open), or the ride cymbal: