Teaching Calculus with Group Work
Notes from a Talk and Focus Group at CMC Asilomar 2003

• Pair Up
• Quick Dyads. Talk about...
• A change you made in the classroom that you're proud of.
• Something you want to improve in your class.
• As a pair, come up with one reason to do group work and one obstacle.
• Brainstorming
• Reasons to Do Group Work
• changes the authority in the class: students are experts
• collaboration makes it more about what is calculus
• two heads are better than one: more ideas, more thorough
• questions that need to be answered, more answerers
• even-up the basic knowledge in the class (review!)
• peer tutoring: if they disagree, the explainer has to verbalize, that's good.
• We can ask harder questions (NEED TO!); open-ended questions!
• engenders communication
• engages students
• opportunity for exploration
• Obstacles and Issues
• Time (esp for AP)
• Time!
• Time!!
  
• they don't know how to do it well
• sometimes they depend on one group member, hitchhiking
• keeping on task?
• students are driven/self-driven. embarrassing to ask questions
• lots of planning
• one person wanting to do everything
• class status issues
• finding group-worthy tasks!
• holding individuals accountable in group setting
• One Approach (My Class)
• Group Work in My Class
• My Thoughts on Group Work
• successful group work looks like arguing not easy harmony
  
• Free Discussion
  
• Places to get Problems
  
• Calculus projects book from New Mexico State. (Single problems from Apostol)
• Look at f, f', f'' to sort as a group, with eqn and descriptions.
• A short group activity. Use old AP questions. Student responses!
• Projects
  
• Whole grade can be based on these group projects.
• Can Project Idea
• How efficient is the shape of the can?
• Extra Credit Projects
• Find the volume of things (e.g. Ikea weird shapes)
• Good Projects to do AFTER AP Exam
• Let them decide what kind of project
• one group made an iMovie, a rap about concavity and tricks
• They had to write a pre-report
• More guidance next time, maybe, for groups that are off-track at the start.
• Politics of Grading Groups
  
• irate parents?
• individual grades for group project?
• If project is in class, you can watch and prod.
• Group project, but a random individual reports that earn the group grade
• only individual grade was the working with group
• (or pick one problem from each individual paper)
• 'bribe' them with participation credit
• Group assessments. Central connected questions, subparts appear on individual test. It was good! Students treated each other well despite high-stakes.
• Participation Quiz. They can get whatever help they need. Grade is math and the participation(!).
• Working together makes them better thinkers only when there is a rich, hard task where the method matters! Else it might be status-competition.
• Time may feel short, but the AP tests subtle language, e.g. rate of consumption; during or at time= 3 sec??
• This can only be developed with practice communicating.
  
• Look at Resources
  
• CPM Calculus
• Hughes-Hallett Calculus
• others listed at Resources