>>> I went to the physics department and asked for a list of types of mathematical mistakes that are common.
A couple of ideas. First, ask the students. Second, see if you can join in the grading of physics exams, as an observer.
20 years ago, I spent a semester as an adjunct, teaching electrodynamics in the electrical engineering department at a big university. The same semester, I also taught two sections of the freshman college algebra course.
I'm going to make some educated guesses here. The math that's used in physics isn't really high level, but because you're using math en route to something else, you have to be fluent enough that it's not an obstacle to understanding the physics concepts. So for me, just being able to crank through algebraic manipulation using odd symbols and getting it right were important.
My EE students used a handful of basic differential equations that were actually given short shrift in the math curriculum, namely simple linear equations that are conveniently solved using complex exponentials. An example would be any kind of wave phenomena. Being able to bounce back and forth between time space and frequency space got my EE students hung up.
I agree with you about the college math topics. As I understand it, certain topics have to be covered in order to meet the accreditation requirements, which makes it hard to develop new curriculum at the lowest levels where it's the most needed.
I think that for students who aren't going to be STEM majors, I'd rather spend the same course time getting them fluent with Excel. That's how they're going to do math anyway.
A couple of ideas. First, ask the students. Second, see if you can join in the grading of physics exams, as an observer.
20 years ago, I spent a semester as an adjunct, teaching electrodynamics in the electrical engineering department at a big university. The same semester, I also taught two sections of the freshman college algebra course.
I'm going to make some educated guesses here. The math that's used in physics isn't really high level, but because you're using math en route to something else, you have to be fluent enough that it's not an obstacle to understanding the physics concepts. So for me, just being able to crank through algebraic manipulation using odd symbols and getting it right were important.
My EE students used a handful of basic differential equations that were actually given short shrift in the math curriculum, namely simple linear equations that are conveniently solved using complex exponentials. An example would be any kind of wave phenomena. Being able to bounce back and forth between time space and frequency space got my EE students hung up.
I agree with you about the college math topics. As I understand it, certain topics have to be covered in order to meet the accreditation requirements, which makes it hard to develop new curriculum at the lowest levels where it's the most needed.
I think that for students who aren't going to be STEM majors, I'd rather spend the same course time getting them fluent with Excel. That's how they're going to do math anyway.