I have been teaching students for the past 6 and $\frac{1}{2}$ years- in all levels of college undergraduate math (decent bit of physics too). I have found that analyzing learning and all the ways to understand mathematics, in particular, is a very necessary first step. (See above posts!)

To the OP: I believe your conclusion is correct, the process you outlined alone doesn't constitute a proper lesson. One commonality I see that most students crave but don't always realize, is a narrative. Some do and ask: how do we know these things?, why are we doing this?, etc. Narrative may facilitate a crucial step in teaching after all the analyzing of how we present mathematics is done. After we have given the types of lectures, assignments and one-on-one advice that we think are the most effective, we may have missed packaging it all up in a narrative.

Depending on the context; giving an arc of where we have been and why we must do it this way, to get us to where we are going next, is a good way to motivate a desire to delve deeper.

More explicitly, you want students to be able to do the algorithmic process and also understand how or why it must be done that way. That way ultimately they may view mathematics more axiomatically as they see a need for consistent definitions and theorems. It is then that they will understand this is necessary in being able to know if one is correct or not logically. I am often quite upfront in saying this is how you will learn this material for now. I tell algebra, trig, and calculus students the things they should simply memorize for the time. Usually with the backing: [Of course these things must not be taken for granted, but can be proven rigorously using only logic. We will not be doing that for this course or even in your later courses. However, at a certain level, after you have learned the how you must treat with the why. This is where you will go in math.]

When there is particular confusion or curiosity I will engage in a small discussion about abstract ideas. The further students are in math the more I think they will feel comfortable hearing that what they are doing now is just a very small piece of the whole of mathematics. Often these abstract connections help students and serve as glue to get them engaged in what they are doing now.

I have been teaching students for the past 6½ years- in all levels of college undergraduate math (decent bit of physics too). I have found that analyzing learning and all the ways to understand mathematics, in particular, is a very necessary first step. (See above posts!)

To the OP: I believe your conclusion is correct, the process you outlined alone doesn't constitute a proper lesson. One commonality I see that most students crave but don't always realize, is a narrative. Some do, and ask: how do we know these things?, why are we doing this?, etc. Narrative may facilitate a crucial step in teaching after all the analyzing of how we present mathematics is done. After we have given the types of lectures, assignments and one-on-one advice that we think are the most effective, we may have missed packaging it all up in a narrative.

Depending on the context; giving an arc of where we have been and why we must do it this way, to get us to where we are going next, is a good way to motivate a desire to delve deeper.

More explicitly, you want students to be able to do the algorithmic process and also understand how or why it must be done that way. That way ultimately they may view mathematics more axiomatically as they see a need for consistent definitions and theorems. It is then that they will understand this is necessary in being able to know if one is correct or not logically. I am often quite up-front in saying this is how you will learn this material for now. I tell algebra, trig, and calculus students the things they should simply memorize for the time. Usually with the backing: [Of course these things must not be taken for granted, but can be proven rigorously using only logic. We will not be doing that for this course or even in your later courses. However, at a certain level, after you have learned the how you must treat with the why. This is where you will go in math.]

When there is particular confusion or curiosity I will engage in a small discussion about abstract ideas. The further students are in math the more I think they will feel comfortable hearing that what they are doing now is just a very small piece of the whole of mathematics. Often these abstract connections help students and serve as glue to get them engaged in what they are doing now.