I have to calm the uneasiness of students for whom an IBL classroom is unsettling. Today, I wrote an email that I want to be able to remember, because I will probably have to write it again. I have edited this ever-so-gently from what I sent, but really it doesn’t change much. I have not included the student message that prompted this, but I bet you can guess from what I wrote the concerns that it shared.
I understand that you are uncomfortable. What we are doing is not a traditional course structure, and whenever anything is a little different it can take a while to understand and appreciate it.
But I designed the class the way it is for important reasons, and those reasons still persuade me. I am not going to change the basic structure of the class.
Here is what is really going on. I have the following goals for your learning, which are very important to me:
1) you have to learn how to do mathematics independently.
(By the way, the word “mathematics” really means “sharing a clear understanding of things having to do with numbers, shapes, and abstract relationships.”)
2) you have to learn how to communicate mathematics clearly both in conversation and in writing.
3) you have to learn how to judge when some mathematics is correct.
This is what it means to have mastered a subject. A student who can do those things in a linear algebra context has “learned” linear algebra.
None of those goals is served well by the traditional structure where I talk at you and you try to cram facts into your head and then squeeze them back out at exam time. The only real way to learn to do something (ANYTHING) is to try it, often, and get feedback from peers and experts.
So, I have chosen to set up class in exactly this way. You will do mathematics by reasoning through the tasks I set you. You will get practice in communicating: in conversation by presenting in class, and in writing by doing the weekly homework. You will get feedback on these things from your classmates and from me in the form of questions. By taking part in the questioning, you get practice judging if some presented mathematics is correct.
My job is to make you better at mathematics. This is a challenging and uncomfortable thing, for you and for me. But I am pretty sure you can do this. I have seen students struggle and then bloom into better mathematicians because I ask them to do the kinds of things we are doing.
As to the efficiency, sure if I did all the talking, I can go much faster. I already know linear algebra, after all. I have lots of practice doing mathematics, too. But I only got good at it because I spent years doing the kinds of things I am asking you and your classmates to do:
solving problems, talking about our attempts, getting feedback, and judging the quality of work by others for myself.
Hang in there, keep working hard, and you will get more comfortable.