Teaching Rhythm

One of the most significant challenges to teaching rhythm is its relative inextricability from other aspects of music. It's hard to come up with a scope and sequence for teaching rhythm that is not somewhat arbitrary or cultural, since even beatless/tempoless music has temporal aspects to how it is perceived and expressed. Every culture approaches it somewhat differently, and it's difficult to say with certainty if any method is universally better than another. That being said, given the global environment and the openness of many people to foreign approaches to music, I think a blend of several approaches is the most easily applicable across musical situations. This involves teaching European Solmization of Rhythm with an Indian hand-counting method and a (not exclusively) African method of using words from natural language to create rhythms.

My general approach with students is as follows

Explain the concept of a rhythmic cycle and the basic counting (I'd say it's safe to teach this to anyone 8 years or older with normal cognition)
The teacher asks the student to list words (preferrably ridiculous ones) in their native language.
The teacher then translates those words into rhythms with dynamic and agogic accents that parallel their phrasing in the natural language. The teacher plays them and challenges the student to copy.
1. Once the student gets more advanced, the teacher may challenge the student to come up with their own words and play them without copying. The teacher may challenge the student to do this first if they find they are sufficiently advanced and have the tolerance to continue should they fail.
The teacher plays a pulse at a medium tempo (80-120 BPM) and uses a monosyllabic word to teach the student the concept of placement, essentially placing the word on a beat or between a beat. The student then attempts to improvise alternating between playing on and between the beat.
The same process, without a rhythmic cycle, continues with longer words until the student can copy words/phrases of 5 or so syllables in length
The teacher starts a simple rhythmic cycle based on the same pulse. The teacher then translates more words into rhythms, places them in a specific part of the bar and challenges the student to copy correctly. The words and placement get progressively more challenging as the teacher feels the student is ready.
This basic process gets copied over several lessons with different tempi. The first lesson starts with a medium tempo and expands both slower and faster.
When a student performs with acceptable accuracy at 80 and 120, other games may be introduced.

Metronome Mastery

In my experience, there is a remarkable consistency between how professional musicians from different genres and walks of life master timing. This may be due to the trend towards Globalism which musicians are all affected by, though it is remarkable how most famous masters of Jazz, Bluegrass, Funk and many other genres all gravitate towards a few similar principles. One of these principles; the best rhythm players have the metronome inside them. They have internalized the sense of tempo, timing and rhythm to the point where they can play with mechanical consistency even without mechanical guides. Flatts and Scruggs, the influential bluegrass duo, was said to have started a picking groove and to then walk in opposite directions around a house to see if they would still be in sync on the other side. James Morrison, a jazz trumpet player, would have his band play a 12 bar blues, and then stop playing while silently counting the form with their eyes closed and clapping on the downbeat to see if they were still together. Victor Wooten, the influential bass virtuoso, will conclude an advanced set of metronome exercises by walking away from a metronome that is only clicking once every 64 bars, and doing household chores to purposely lose the feel, then trying to point when he thinks the 64 bar downbeat would fall.

The process of reaching this level of master is often not a short or straight line, and the specific techniques applied to different genres can vary. That being said, the value of internalizing timing is incredibly important for players of any highly rhythmic genre, and ideas from many musicians can come together to help you learn what you need to learn to improve your own music.

Very Useful Free Course on Metronome Technique

https://fretboardanatomy.com/course/metronome-boot-camp/

Book on the same subject

http://www.inchronicity.com/

Michael Furstner - Timing exercise and James Morrison Story

http://www.jazclass.aust.com/rhythmcl/rc01.htm