My approach is two-fold. First, I insist that all my students have strong basic skills. Second, I require my students to do high quality teamwork with a group of peers on a open-ended problems. In all cases, I use the best technology available.
Resource delivery: All course resources flow from a course website that I write in HTML. It has a simple, flat layout, and students can go anywhere from there with one click.
Basic skills: I use a combination of automated homework using ALEKS and MapleTA, plus traditional hand-graded homework. Automated online problem sets provides students with instant feedback on their work. All my automated homework is implemented as mastery assignments meaning that they must work simpler problems correctly before moving on to harder problems. I use a combination of ALEKS for precalculus skills and MapleTA for calculus skills. There are types of questions that are too complex or awkward to automate, so I rely upon written problem sets as well.
Application domains: Quantifying problems in different application domains is a great challenge for students, and I have used the Sakai server's wiki to help students learn. Students need practice identifying variables, quantifying process and analyzing open-ended problems, and I have designed a course activity to develop these skills.
I post a collection of images from the web depicting scenes involving change. A team of no more than four will explore the topic captured in an image. Then, I lead them past three milestones or stages to complete their team project.
Stage 1: Students describe the image applying quantitative terminology (angle, distance, function, time) from this course to the image. Students explain how the variables are connected to the image.
Stage 2: Students draw from their quantitative descriptions, write down equations that express their descriptions. They learn how to pose precise mathematical questions that will lead to insights in a "real world" problem.
Stage 3: Students develop calculus "word problems" built around their descriptions and the picture.
I assign a score to each team's work project, and then each team goes through a peer assessment process at each stage. Students receive the project score scaled by a peer assessment. The peer assessment is a measurement of individual intellectual, writing, professional and leadership contributions to the team.
