What are some topics that you are finding your students need to spend more time on, in order to thoroughly understand?

I am relatively new at teaching so I am finding out suddenly at each lesson what each student is not understanding. They can play the pieces but they had no idea what topic they had just learned. Then I have to backtrack and approach the topic another way.

So far, the more challenging topics have included: V7, the I V7 IV pattern, 6th and 7th intervals, and syncopation.

What have you found more difficult to teach? In order to drill these topics into my students' heads, I'd like to start looking for additional material to supplement their books already being used.

Thank you very much!

Really, it's important to address topics in a logical manner. For example, before they can learn anything about the V7, they must have a grasp of how to build a major chord. Or before talking about a 7th interval, they must have learned 2nds and 3rds and worked their way up. These things are best discussed when encountered in music they are playing. Conversely, it makes little sense to have a student learn a piece with a dotted 8th note and sixteenth rhythm if they have not yet learned 16th notes. This is how piano pedagogy works.

Not only do students need to learn things in proper order, but they need sufficient time to review it before adding something new. So several pieces covering the same new concept would be best. The more they encounter the same concept in different ways (think visual, audio, and kinesthetic/touch) the better chances they have of understanding it.

There are a great number of pedagogy books out there that would help you in this.

I concur. I find that both in my own experience as a student, and watching my students develop over time, these concepts which seem so easy to us now, were quite the mountains to climb back as elementary students. I do make students count out intervals on the piano, form the chords, etc., and it seems to help somewhat, but as they have little interest in chord formation at early stages of music learning, it seems to have little retention. If that makes any sense.

I often feel like Micky Mouse with the brooms (Fantasia). Or something like that.

The only thing I know for sure is that finding the most logical possible order in which to present things is probably about 99% of what makes success, and I keep tweaking, teaching some things earlier, some thing laters, also adding things I have not stressed in the past.

For me the mystery is trying to retrace how I absorbed and mastered things. It's always the same. Anything that I learned when very young seems to have to stages. One, I remember not knowing something, and a first lesson. Then I remember having it mastered. The in between steps disappeared. I know they happened. But I can't remember them.

I also find that I am strongest in teaching things I missed, as a young student, and had to straighten out in my late teens, early 20s, or later. My fingering was very weak, so I am very good at breaking down fingering for students, any age. But I can't explain how I came to sight-read really fast, because I got paid for doing that (as an accompanist) at age 15. And ear-training remains a mystery to me, because I never remember a time when I had any problems looking at a score and hearing it in my head.

Every student is unique. I've taught a student who can play super advanced pieces, passed Level 10 with honors, but can't hear the difference between major and minor chords. Some students play beautifully, but when you present them with the theory book, they totally shut down.

Some students are naturally strong in verbalizing ideas (and thus can understand your verbal directions well), while others are strong in math and have a natural feel for rhythm. It's really a mixed bag for each student.

As a private teacher, you can/should customize the education experience for each student. I tend to focus on the students' weaknesses, though, so their weaknesses can "catch up" to their strengths.

Yes theory! I am not a teacher but a lifelong student. I think when people hear the word "theory" they think of deep scientific thought...like theoretical physics, or something somewhat vague and hard to explain...i.e. "My theory for why this might have happened...." Theory sounds boring. Instead it is a blueprint for how music is structured that is pretty concrete.

It was really never explained to me why there you commonly see a F# accidental in the key of Gmi, that has 2 flats! Or why is does the Bb keep showing up in the key of C, that has no sharps and or flats? How can a group of musicians get up and play the blues in E together without sheetmusic or previous practice? How does one improvise and make it sound good? Then there is transposing....It all requires theory.