> I found teaching Calculus I was able to draw in students so much more if I worked in what problems Newton was trying to solve and why. It gave them a story to follow, a reason to learn this stuff.
Be careful.
In undergrad, I worked as a math tutor at their tutoring institute. We had two calculus classes - one for engineers/science and the other for business/economics.
If you're into Newtonian stuff or it's relevant to your degree, then your approach is all great. What I consistently saw is people in degrees like biology (or even industrial engineering) had a harder time learning because of those physics applications in the book. They came in with one problem: Having trouble with the calculus. And then they discovered they had two problems: To understand calculus they suddenly had to understand physics as well.
You'd get students who were totally adept at differentiating and integrating, but would struggle with the problems that involved physics. Yes, it is important to be able to translate real world problems to math ones, but it's a bigger problem when you don't care about that particular field.
Same problem with the business students. Since all the tutors were engineering folks, they had trouble tutoring the business students because their textbook was full of examples that required basic finance knowledge (and it really doesn't help that financial quantities are discrete and not continuous, adding to the tutors' confusion).
If you can find an application the student is interested in, then by all means, use that approach. For a general purpose textbook, though, it hinders learning for many students who don't care for the particular choice of application the book decided to use.
Be careful.
In undergrad, I worked as a math tutor at their tutoring institute. We had two calculus classes - one for engineers/science and the other for business/economics.
If you're into Newtonian stuff or it's relevant to your degree, then your approach is all great. What I consistently saw is people in degrees like biology (or even industrial engineering) had a harder time learning because of those physics applications in the book. They came in with one problem: Having trouble with the calculus. And then they discovered they had two problems: To understand calculus they suddenly had to understand physics as well.
You'd get students who were totally adept at differentiating and integrating, but would struggle with the problems that involved physics. Yes, it is important to be able to translate real world problems to math ones, but it's a bigger problem when you don't care about that particular field.
Same problem with the business students. Since all the tutors were engineering folks, they had trouble tutoring the business students because their textbook was full of examples that required basic finance knowledge (and it really doesn't help that financial quantities are discrete and not continuous, adding to the tutors' confusion).
If you can find an application the student is interested in, then by all means, use that approach. For a general purpose textbook, though, it hinders learning for many students who don't care for the particular choice of application the book decided to use.