I’ve taught and tutored math, and this concept is very familiar to me.
When tutoring, I will do as much debugging and back-and-forth as I can. Whenever possible, I would prefer to spend the time to really help cultivate understanding rather than just helping someone stumble through the homework.
When teaching, there’s a lot of constraints that limit the ability to go back and forth. Not all the students are at the same level, there’s a course curriculum that needs to be covered (as much as possible), and there’s simply not enough time to debug the least prepared student. Even if you attempt to do so, you’ll start to bore the rest of the class and waste their time.
The best balance I’ve managed to strike (in my limited experience) is to do short quizzes on prerequisites get an idea of where the class is, take some extra time on things that too many people have forgotten, give explicit instructions and invites to office hours and/or extra study sessions, and then just try and strike the best pace I can. If I get the “dead fish look” of glazed-over eyes from the class, I’ve lost them and need to slow down, schedule be damned.
One of my instructors in grad school actually took the time on the last day to write up a giant graph of all the major results from real analysis, moving downward as one theorem was used in the proof for another. After he finished, all I could think was “why didn’t he give this to us on the FIRST day of class???” In retrospect, I didn’t appreciate that thought enough, because it could have been useful to give something analogous to my students as a way to concretely check what they need to know going into each lesson or concept.
I’ve taught and tutored math, and this concept is very familiar to me.
When tutoring, I will do as much debugging and back-and-forth as I can. Whenever possible, I would prefer to spend the time to really help cultivate understanding rather than just helping someone stumble through the homework.
When teaching, there’s a lot of constraints that limit the ability to go back and forth. Not all the students are at the same level, there’s a course curriculum that needs to be covered (as much as possible), and there’s simply not enough time to debug the least prepared student. Even if you attempt to do so, you’ll start to bore the rest of the class and waste their time.
The best balance I’ve managed to strike (in my limited experience) is to do short quizzes on prerequisites get an idea of where the class is, take some extra time on things that too many people have forgotten, give explicit instructions and invites to office hours and/or extra study sessions, and then just try and strike the best pace I can. If I get the “dead fish look” of glazed-over eyes from the class, I’ve lost them and need to slow down, schedule be damned.
One of my instructors in grad school actually took the time on the last day to write up a giant graph of all the major results from real analysis, moving downward as one theorem was used in the proof for another. After he finished, all I could think was “why didn’t he give this to us on the FIRST day of class???” In retrospect, I didn’t appreciate that thought enough, because it could have been useful to give something analogous to my students as a way to concretely check what they need to know going into each lesson or concept.
That definitely makes sense about it sometimes not being possible for various reasons, like larger class sizes or time constraints.