Post #2 - First thoughts on Calculus

I am currently teaching Calculus for Business Majors. I have only taught Calculus once before - to students at a small private high school in Pittsburgh. Now, I am teaching adults Calculus that are only taking it because it is a required course to get into the Business school at UW-Madison. Most of the students want to major in Business and don't believe that anything they are learning will be useful to them in any way. This makes me sad. Sad because it isn't true. Sad because I haven't convinced them that it isn't true. Many math instructors that teach Calculus shy away from the application problems because they are "harder" than just teaching the straight-up Calculus. Technically, they are correct. But, only in the short term. The real power of Calculus, and math in general, is in how we apply it. By leaving off applications, we are teaching many students to memorize processes and forget it once the semester is over. So, I have tried very hard to put a major emphasis on the business applications in the textbook. However, it is a textbook. The first few weeks of the course were spent training the students to look for key issues with textbook applications. For example, in the textbook, the students are given a function that represents the cost of producing x hundred units of a commodity. So, a major issue for the students is skipping over the fact that x is in HUNDRED units. This issue would never exist in a 'real-world' situation. Because, in a real-world situation, if I was working with a function representing cost of producing something in my factory, I am probably the one that created the function. So, I would be the one that decides the units for x. And, I did not see a single problem in the text explaining how to create the cost function. Does it really make sense to de-couple these actions? Shouldn't we spend a whole Chapter on taking data and developing models? What do you think?