Ithaca College Calculus Project

Questions About Course Organization and Content

• Question: How do activities and projects work together?
• Answer: Both activities and projects help the students
  learn modeling and other problem-solving skills, and both force
  them to be active learners. Working on activities is good
  preparation for working on projects. Some of the same approaches
  are appropriate, although the problems in the activities are
  shorter and done in a more guided setting (the classroom).
  Working on projects helps the students to become self-starters,
  which helps them with their work on the activities.
• Question: How do you teach problem solving?
• Answer: We teach the top-down approach to problem
  solving. That is, we teach the students to break large problems
  into successively simpler pieces until the pieces are such that
  they can find solutions, then to reassemble the pieces into a
  solution of the original problem. We use this approach in
  working on problems and activities in class and expect the
  students to carry the ideas over to the solution of the large
  problems in their projects.

• Question: How will I have time for activities?
• Answer: We have found that incorporating activities into
  our classes does not result in time pressure. One reason is that
  many of the activities tend to be fairly short and can be done by
  the students as they settle in at the start of the class. The
  other is that the activities actually serve as a means of
  developing the course material. The student-involved approach
  replaces some of the formal presentation that we were accustomed
  to do---and does a more effective job. When the students learn
  through the activities, they absorb the material better and
  retain it longer.
• Question: How do I present new material?
• Answer: Quite a bit of new material comes from the
  activities, and still more can be introduced in projects.
  Furthermore, the project/activity approach does not preclude
  including some "traditional" kinds of presentations. We have
  found that using activities predisposes our students to
  participate more fully in even the more traditional classes,
  resulting in more lively classes and more give and take between
  students and instructor.
• Question: How do quizzes and exams relate to activities
  and projects?
• Answer: We include ideas first encountered in activities
  and projects on the quizzes and exams. As we mentioned above,
  this is one way to ensure some degree of participation in project
  work by all members of the project groups. We also feel free to
  ask non-standard questions---questions that do not correspond to
  any template the students have seen---on exams. Such questions
  are in the spirit of original problem solving that we emphasize
  through the activities and projects. Some sample questions are
  in an appendix.
• Question: My students need to have good computational
  skills. How will they learn to perform computations?
• Answer: Much as they always did---through daily homework
  assignments. There is a difference, however. In the traditional
  course, students come to believe that calculus is
  computations. In the new course, students see the subject
  itself---its unity and applications---and regard routine
  computational problems as an easier (and less interesting) part
  of the course.

• Question: How do you teach the logical and theoretical
  aspects of calculus?
• Answer: While the theoretical side of calculus is taught
  less formally than in more traditional models, the emphasis in
  our courses is on conceptual understanding. We believe this
  approach lays a more solid foundation for subsequent study than
  rote memorization of definitions and theorems. We still teach
  the formal definition of continuity, the derivative and the
  definite integral, and significant theorems (the intermediate
  value theorem, mean value theorem, fundamental theorems, etc.).
  We emphasize critical thinking about these concepts and
  understanding their meaning.
• Question: Will I be able to cover all of the material?
• Answer: We do. The activities and projects serve the
  same purposes as, for example, several days studying "word
  problems " and do the job more effectively.
• Question: What is the role of technology?
• Answer: Several of the activities presuppose the use of
  either a computer or a graphing calculator. Some of the projects
  are greatly simplified if some computational device is available
  to help with the calculations and graphs. The Instructor's
  Guide lists what, if anything, is needed for any particular
  activity or project. We do not prescribe any particular choice
  of technology, however. We have always described our materials
  as technology independent. This means that most of the
  activities and projects require no technology at all, and the few
  that do require a computer or graphing calculator are presented
  in such a way that the instructor using the material can choose
  whatever implementation is available.

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This page maintained by: Diane Driscoll Schwartz, Ithaca College
schwartz@ithaca.edu

Last Modified: January 8, 2000