I am a 15-year-old girl. I've been playing the piano for about 7 years, now, and this year will be my second year teaching.
I have a couple questions for the more experienced teachers out there: 1) What way do you find most helpful to help students understand the concept of 'staccato' notes, and 2) to understand the concept of 'eighth notes'?
I would also be interested in any good handouts that you could recommend
Thanks!

I'm not a teacher, but I think it should probably be easy to teach staccato notes.

Just show the student, on the piano, the difference between regular and staccato ... maybe just a scale, or an excerpt from a piece of music. Be very dramatic and exaggerated when demonstrating! Then ask the student to play a few of his own, to see if he or she understands.

I've been playing the piano for 6 or 7 years now, and I think it's probably easier just to explain 8th notes as notes "twice as fast as quarter notes." It's basic, but it'll probably work. Especially if the student has a basic knowledge of fractions.

To teach staccato notes, I think it's important to stress about a very flexible wrist. There are three basic movements of a player's wrists: (1) arc-like (2) up and down (3) rotation. It is the up and down movement that apply when we play staccato note(s). the player's hand and fingers shouldn't be too far away from the keys as if to strike the key from high above (which may produce harsh sound), instead they should exercise their flexible wrist - the up and down motion - to allow the weight of the finger gently press the key and then "bounce" upward. I think the concept of "bounce" will relate well with beginners.

As to understanding the concept of "eighth notes", I have read some recommandations that it's better not to introduce eighth notes until the pupil is very secure in his/her understanding of basic notes value(quater, half, whole notes, 4-4 time, 3-4 time) as well as quite secure in reading notes one octave from either side of middle C . I actually has just start teaching one of my pupil to do counting of eigth notes using word syllable instead of doing the traditional way 1-a 2-a 3-a 4-a etc. So my method goes 'man-go, 2 3 4' for 2 eighth notes follow by 3 quarter notes. I hope this may help with the accuracy of their rhythm and seem to be a less tedious way to count, but in any case the theortical part of it should be mentioned as well. For example by using the note value pie chart.