Xunzi, 3rd century BC Chinese philosopher
How my lessons are structured
Once we have identified topics that the student thinks that s/he needs help with, I go through a cycle.
I set the student a problem on the topic. Typically the student cannot do the problem. That’s why s/he came to me in the first place, after all. So, I set an easier problem on the same topic.
By this time I understand how well or poorly s/he understands this topic. If necessary, I give a mini-lesson. Then we try again. I may create and work on examples until s/he understands and can do the original problem. Then we do another similar problem to be sure.
It’s not uncommon that in this process I discover that the student has learned and been using for years false methods that s/he must unlearn. (See my list of math errors on this site. ) The student has been building on sand. So we stop what we were doing, put in the needed strong foundations for progress and then return to the current topic.
Normally I suggest one two-hour lesson per week. Two hours is enough time to get a lot done. I find that one-on-one, I have no trouble keeping students engaged and productive for the whole two hours.
I try to schedule as many lessons as possible on Saturdays, but am also available after school. If the student needs more help or has conflicting commitments on Saturdays, I can be flexible.