When I first began my CÉGEP mathematics courses, one of the things I noticed that was new was how my teacher would give “motivation” to what we’re doing. Basically, the idea was to give us a reason for why we were doing something, instead of just throwing it out in the blue.
This was a welcome change from what I originally did in secondary school. There was some motivation for what we were doing, but most of the motivation was left up to us to find. We simply went from one subject to another. With my teacher in college however, there was nearly always some sort of motivation embedded into the lecture. Some of it might have went over our heads, but my teacher always made sure to give us some reason for what we did.
I’m still a student, but I’m also a tutor, and so I can see how both sides of the relationship see motivation. As a student, I like to know why I’m doing something or what the end goal is supposed to be. As a tutor, I know that giving students direction while learning new concepts is key to keeping their attention (and the inverse means a lack of interest). Therefore, I try to look for ways to motivate the line of reasoning I pursue with them in mathematics. It turns the learning experience from just myself giving information to the student to an experience where the student can feel like they are along for the ride.
And from personal experience, it’s a lot more fun to learn when you feel like you are an active observer with the teacher, instead of merely listening and taking notes.