There are four major learning outcomes for the course:

Students will be able to productively discuss mathematics in a group setting
Students will be able to write detailed solutions using appropriate mathematical language
Students will be able to identify areas in mathematics and other fields where Calculus is useful
Students will be able to generate solutions to unfamiliar problems

How do we achieve these goals?

For #1, the team work provides you with regular opportunities to discuss and present mathematics both formally and informally. The weekly write-ups for selected team problems hone your skills for #2. Throughout the course we discuss applications of calculus to different fields (#3).

Generating solutions to unfamiliar problems (#4) is one of the hardest (but most important!) outcomes to achieve. We approach this in three steps:

i) Fundamentals: These are the building blocks of our more complex techniques, most of which appear towards the beginning of the course. We discuss and practice these in class. You'll see practice problems for this category in the Khan Academy problems sets.

ii) Synthesis: At the next level, we focus on combining the building blocks into more complex techniques by breaking problems in smaller pieces, then solving each and combining the results. A key component is matching the most effective techniques to the problem at hand. As with the fundamentals, some Khan Academy problems sets contain problems at this level but most of your practice will come from problems like ones we do in team work during class.

iii) Mastery: Eventually, we reach the highest level of mastery when you'll be able to take a problem, pull it apart, craft a method of solution, execute it, and interpret the results. Important components of this include discriminating between competing solution methods, evaluating the effectiveness of techniques in different contexts, and competently interpret the results. Team work will be the most common place that we build and practice skills at this level.