In music, there are three kinds of durations: beat elongations, beat divisions, and beat equivalents. The beat being elongated, divided, or equaled is called the tactus; it is the one being tracked as the pulse or “heartbeat” of the music.  Beat elongations are durations longer than the tactus, beat divisions are durations that are shorter than the tactus, and beat equivalents are durations that are equal to the tactus. Dotted rhythms typically involve pairs of notes that together equal some whole number of beats. For example, a dotted quarter note is a beat elongation, because the dot extends the duration beyond a single tactus beat, which in this example shall be the quarter note. A dotted quarter note is typically followed by an eighth note, which is a beat division, because it is less than the duration of the tactus.  Combined, these two durations occupy a time span of two tactus beats. Dotted eighth and sixteenth pairs are comprised of two beat divisions that combined fill a time span of one beat, and dotted half note and quarter combinations are comprised of a beat elongation and a beat equivalent, and have a combined time span of four whole beats.

With this in mind, we can observe that dotted rhythms always complete a whole beat, and always involve two of the three kinds of durations. Now let’s see how we can apply this to teaching dotted rhythms in a way that is clear and helpful to students.

1. Have students tap the tactus with the heels of their feet. Raising the heels up throws the body slightly off balance, necessitating a shift of balance and weight. This allows the beat to be felt in the body.
2. While keeping the pulse with the heels of their feet, have students chant a series of beat equivalents.
3. Add notation of quarter notes as students continue to keep the pulse and chant.
4. While keeping the pulse with the heels of their feet, have students chant a series of beat elongations that end on the next beat and are each followed by an eighth rest.
5. Add notation of dotted quarter notes, each followed by an eighth rest as students continue to keep the pulse and chant.
6. While keeping the pulse with the heels of their feet, have students chant a series of beat elongations that end on the next beat and are each followed by a beat division.
7. Add notation of dotted quarter notes each followed by an eighth note as students continue to keep the pulse and chant.

By this point, students will recognize that the dot indicates an elongation of the duration, and that the note that follows completes the whole number of beats, in this case two. Notice that this technique begins with sound, then introduces sight. Also notice that no mention of mathematical relationships has been mentioned. Once students can accurately chant the dotted quarter and eighth note combination from notation, then, and only then, is it suitable to explain the math. Music theory should never be taught before sound and sight. Mathematical  relationships are evident in music, but the performer does not.consciously use math to perform music. Instead, people use perception of beats and durations in time. Only for beat elongations longer than four tactus beats do performers need to count beats, and even then it is not always necessary when the duration’s placement within a group or phrase is known.

The same technique can be used for teaching dotted eighth and sixteenth with two additional steps. Because both the dotted eighth and the sixteenth are beat divisions when the quarter note is the tactus, students must learn the sixteenth note divisions of the quarter note beat. For this, a combination of drumming and chanting is helpful.

1. Using drums or body percussion, have students drum four sixteenths followed by a quarter note. The quarter note will be used to provide stability at the end of the dotted rhythm.
2. Using drums or body percussion, have students drum four sixteenth notes followed by a quarter note while they chant the first and fourth sixteenths, and the quarter note.
3. Using drums or body percussion, have students drum one eighth, two sixteenths, and a quarter note.
4. Using drums or body percussion, have students drum one eighth, two sixteenths, and a quarter note while they chant the eighth note, the last sixteenth, and the quarter note.
5. Using drums or body percussion, have students drum a dotted eighth, a sixteenth, and a quarter note while they chant the same.
6. Using drums or body percussion, have students drum a dotted eighth, a sixteenth, and a quarter note while they read the rhythm notated on a staff.

By the time the students get to the last step, the division of the quarter note beat into sixteenth notes will be automatic, and the dotted eighth and sixteenth note rhythm will be accurate. I do not show the notation for the preliminary steps, because I want that division to be accessible in memory for reading the dotted rhythm, and for no other purpose at the moment. Once dotted eighth and sixteenths are securely learned, I go back and show them the notation for the other rhythms used. I find this order works best.

Dotted half notes can be taught with simple beat counting, though I prefer to not allow my students to count, instead learning to recognize pairs of beats without counting, and then finishing the second pair of beats with a separate note. The steps for learning dotted rhythms can be repeated at any time to reinforce prior learning. The sixteenth note steps can also be combined as a rhythm exercise, so that part of the class drums all four sixteenth notes while others drum dotted eighth and sixteenths. I strongly advise not doing this until after the rhythms are securely learned, but then it makes good practice and reinforcement. African complementary drumming also fits well into the study of dotted rhythms.