I've been working on developmental math redesigns for years and now am developing a version of the Carnegie Quantway course Mathematical Literacy for College Students at my college. I was a part of the initiative when it began between AMATYC and Carnegie. The course is at the developmental level and only has an arithmetic prerequisite. The idea is to take one semester and build the numeracy, proportional reasoning, algebraic reasoning, and function sense (along with some stats and geometry) to be successful in a college level stats or general education math class.
We're a few weeks into the pilot and it's been interesting. Students are so ingrained in believing that unless it looks like this: Solve 3x - 2 = 5(x-6) that we're not doing math. We use online homework for the skill development only and focus on problem solving, critical thinking, and connections. Everything we do, we apply. Students resist some because this approach is so different. We do have direct instruction but the class period moves from whole group to small group and back and forth over and over. When we need to understand a skill, we have a mini-lecture.
Basically, students want it boiled down to "here's a skill, do 30, test on a few similar." But in the U.S., we've trained them to think that way. I'm not blaming anyone. I'm as guilty as anyone of teaching the traditional curriculum (algebra, trig, calculus) that way but I really feel like it does students a disservice. It's saddening to see what we've made students believe math is. It is not just a stack of skills to be learned. So not only is the course difficult for instructors to envision, it's hard for students as well. We're working on it though. They are engaged and do work well in class. They just resist some because they think we're not doing math.
I teach this class like I teach statistics in that the goal is always application and critical thinking; technology and skills are just tools to help us get there. When this approach is used, resources like the Khan academy can facilitate the classroom. If a student wants to see a skill taught again or practice a skill multiple times (and possibly more than we have time for in class), that is where programs like Khan can shine. They can assist our classrooms. When they replace the human element of the instructor, I think that's where the problems can begin.