My tutoring typically started with “debugging” student’s knowledge. The problems were usually deeper that the student reported, and full solution required fixing the underlying problem first.
For example, suppose the student has a problem with quadratic equations. But after doing some background check, it turns out they are quite confused about what happens when there is a minus sign before the parenthesis. Now of course, if they don’t get this right, then no matter how much time you spend explaining quadratic equations, they are going to get half of them wrong whenever the problem starts with something slightly more complicated, that you first need to convert into the standard quadratic equation.
So I kinda imagine the mathematical “tech tree” in my head, and check the previous nodes first, and so on recursively, if necessary. Then gradually build up the correct knowledge.
In school, this would be one student among 20 or 30. There is no time to do this background check with one of them, and definitely not with half of them, no matter how much they need it. Also, you are constrained how much time you can spend at each topic. If it’s not enough for some students, well, sucks to be them, but we must move to the next topic.
(Currently, there is a reform in math education that tries to get the fundamentals right, even if it costs somewhat more time at the beginning, because then kids can progress faster, while actually understanding everything. One day I would like to write a post about it on Less Wrong, but I am not a teacher anymore, and my contact with teachers who use this method is limited because of covid.)
I see. I find that sort of debugging quite enjoyable.
However, I find that students often are very impatient when it comes to traversing deeper down the dependency tree, and instead impatiently just want to “get it working/get the answer” and move on. There are three separate instances in my life that I can think of where I experienced this recently: 1) a backend dev learning frontend stuff, 2) someone entirely new to programming I was tutoring, 3) a college student taking precalc.
My tutoring typically started with “debugging” student’s knowledge. The problems were usually deeper that the student reported, and full solution required fixing the underlying problem first.
For example, suppose the student has a problem with quadratic equations. But after doing some background check, it turns out they are quite confused about what happens when there is a minus sign before the parenthesis. Now of course, if they don’t get this right, then no matter how much time you spend explaining quadratic equations, they are going to get half of them wrong whenever the problem starts with something slightly more complicated, that you first need to convert into the standard quadratic equation.
So I kinda imagine the mathematical “tech tree” in my head, and check the previous nodes first, and so on recursively, if necessary. Then gradually build up the correct knowledge.
In school, this would be one student among 20 or 30. There is no time to do this background check with one of them, and definitely not with half of them, no matter how much they need it. Also, you are constrained how much time you can spend at each topic. If it’s not enough for some students, well, sucks to be them, but we must move to the next topic.
(Currently, there is a reform in math education that tries to get the fundamentals right, even if it costs somewhat more time at the beginning, because then kids can progress faster, while actually understanding everything. One day I would like to write a post about it on Less Wrong, but I am not a teacher anymore, and my contact with teachers who use this method is limited because of covid.)
I see. I find that sort of debugging quite enjoyable.
However, I find that students often are very impatient when it comes to traversing deeper down the dependency tree, and instead impatiently just want to “get it working/get the answer” and move on. There are three separate instances in my life that I can think of where I experienced this recently: 1) a backend dev learning frontend stuff, 2) someone entirely new to programming I was tutoring, 3) a college student taking precalc.