Projects FAQ

Ithaca College Calculus Project

Questions About Using Projects

Question: How can using projects improve my course?

Answer: Projects bring out both the relevance and the
unity of calculus. Most of the projects are set in "realistic "
situations. Most also involve more than one calculus topic,
often combining topics in unexpected ways. Students need to
broaden their perspective and synthesize ideas in order to
complete these projects successfully.

Many of the projects have "open-ended " parts---that is, parts
for which there is not a unique correct answer or approach.
These questions encourage the students to brainstorm in their
groups and to view mathematics as a subject with creative
elements.

To complete a project, each team needs to submit a well written
report of its solution. Writing about mathematics may be a new
experience for many students, but it is a valuable one.
Describing the solution of a significant problem pricisely in
words requires a deeper understanding than most students gain
from just solving many problems that are based on examples found
in their notes or textbooks.

Question: How do I organize project assignments?

Answer: We believe that the students learn more calculus
if they work on the projects in teams. Three students to a group
seems to be a good working number, but we have used teams of four
or two students. The number depends on the class size and the
particular project.

We require each team to meet with the instructor soon after the
project is assigned and to present an outline or a top-down
analysis of the problem and their anticipated solution at that
time. This assures us that the groups have met and that they
have begun to think about the problem long before it is due. For
a first project, we often require a second meeting to answer
questions and get an intermediate progress report.

The final report is expected to conform to guidelines we hand out
at the beginning of each semester. A sample is included in
an appendix.

Question: How many projects should I use?

Answer: We have found three or four projects to be an
effective choice for a fourteen-week course. We are
convinced that assigning several projects provides significantly
greater benefit than assigning only one project.

Question: How long do the students work on each project?

Answer: Most projects take two to three weeks for a group
of students to complete. The work is done outside class and is
in addition to any daily assignments that we make for the class.
Our students have a project in progress most of the time.

Question: When should the first project be assigned?

Answer: We believe that it is best to assign the first
project early in the course. This helps students to view the
projects as an integral part of the course experience. It also
helps them to develop significant problem-solving skills that
they can bring to bear on other elements of the course.

Question: How should projects affect the course grade?

Answer: Substantially. We count each project as 10% of
the total course grade, so that in a four-project class, 40% of
the course grade is based on the projects. This is a very
effective way to ensure that the students take the projects
seriously and devote substantial thought and effort to them.

Question: Can I use projects without having the students
work in teams?

Answer: Yes, but at a price. If students are working
together to solve these problems, you can have higher
expectations for the solutions---after all, they had the
advantage of collaborative efforts. More important, working on a
team provides effective peer pressure on students not to give up
trying to solve a problem. For the instructor, there is the
added advantage of fewer projects to grade!

Question: How do I answer questions about a project?

Answer: Just as you would any other graded assignment.
Ask them what they have tried and why. Be sure the project team
has discussed the question as a group and that everyone on the
team has tried to answer it. Then suggest they think about
certain ideas that might prove helpful. Try to steer them in
appropriate directions without "giving away " solutions. If the
same question is raised by a number of teams, it is sometimes
helpful to discuss the issue briefly with the whole class.

Question: How much class time should I spend on projects?

Answer: We spend little or none. Our class efforts are
devoted to making available to the students the tools that they
will need in order to complete the projects successfully. These
include the standard tools of calculus, new approaches that can
be found in the activities, and practice (again through the
activities) in modeling and other problem-solving strategies.
One might spend a little class time after a project is
completed, "debriefing " and discussing how the project leads to
or illustrates general concepts.

Question: How do I grade projects?

Answer: That's a good question. In our courses, the team
receives a single grade on the group parts of the project. In
some cases---for example, "Designing a Detector "---that is
the entire project; in other cases---for example, "Spread of a
Disease "---there are individual parts that receive a grade
separate from the team grade.

It's a good idea to think about how you are going to assign
grades before you make the assignment. After you collect the
reports, scan all the solutions before you begin grading, and
then make a firm decision, again before you begin grading, about
how you will determine the grade.

Because there are significant written reports involved, some
credit should be allocated to the manner of presentation.
Derivations should be explained, graphs and other figures should
be labeled, and language should be used correctly.

You need to observe whether they answered the questions posed and
how well. Be prepared to reward creative ideas.

The reports should improve throughout the term. When you return
first projects, indicate how presentation and reasoning can be
improved for future reports. One way to do this is to give out a
"collage " of good solution pieces.

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

Last Modified: January 8, 2000