COOPERATIVE LEARNING GROUPS
Working in teams is becoming
ever more common in the workplace, and there can be many advantages
to team efforts for students as well.
Practice in communicating about mathematics --- talking about
mathematics and formulating difficulties and suggestions in one's own words ---
is itself worthwhile. Then too,
students can provide each other with immediate help and feedback.
Group discussions help students:
- explore alternative problem-solving strategies,
- discover new insights,
- clarify misconceptions, and
- think more critically about their own work.
Weaker students can help the group by asking questions, forcing the
group to clarify its thinking. Stronger students can help the group by
explaining
key concepts to others. In fact, the best way to learn is to teach what you
know to
someone else. The process of organizing, verbalizing, and elaborating on one's
knowledge helps to achieve a deeper level of understanding. Finally, it is
not a bad thing to have allies in this enterprise of learning calculus.
You will be assigned to teams of three or four
students for the purpose of doing the group homework assignments.
There will normally be one group homework assignment a
week,
and each team will need to meet at least once, and perhaps more
often, for each assignment.
You should come up
with group solutions to the assigned problems that you all agree on ---
continue to discuss a problem until you all agree on its solution. You
need to be sure each member of your group understands how to solve each
problem and how it relates to the concepts presented in the text and
can demonstrate that knowledge in class if called on. Each group will
write a single
report to be handed in for grading. Everyone is expected to participate
by reading the assigned material, attending group meetings, helping each
other, asking for help when needed, critically evaluating the group's
work, correcting mistakes, encouraging each other, etc.
The following roles must be assigned to specific members of your
group. These roles must be rotated after each assignment so that
everyone shares
the responsibility for each role.
- Organizer. The organizer is in charge of setting the time and
place of the meeting and getting the group together.
- Scribe. The scribe records the group's work by writing out the
solution to each problem and an explanation, if appropriate.
- Reporter. The reporter explains in writing what the group did and
how it did it (e.g., note briefly other unsuccessful strategies tried on some
problems). Explain also anything about the way the group worked that was
especially helpful to the group's productivity and what needs to be changed.
- Presenter. The presenter will prepare to present the group's solution to the rest of the class.
I expect each group to produce high quality homework papers:
- show individual steps,
- provide explanations when appropriate,
- use the rules of algebra correctly,
- use correct grammar and spelling,
- use technical terms correctly, and
- give complete answers (for example, provide units
of measurement and label axes).
Your paper should include the names
and roles of each member of your group and the solutions to the assigned
homework problems. The
reporter's contribution will usually be one or two paragraphs long, and it
won't be graded.
An important feature of cooperative learning is that the help you
would normally expect from your instructor or a tutor can often now
be provided by other members of your group. Of course, I
am also still available in office hours, and we have a Math Center
for peer tutoring as well.
Guidelines for Groups
- Assign each member of the group a role. (The roles must then be rotated.)
- Work on the homework problems together in your group. Do not
split up the work --- everyone should focus on the same problem at
the same time.
- Discuss each problem until a consensus is reached on its solution.
Individuals should not accept confusion passively --- ask for
clarification from others.
- If you get stuck, explain to each other exactly what the
question is and what the difficulty is. Oddly enough, a good
explanation of this kind is sometimes enough to inspire an answer.
Ask for outside help only if everyone in the group agrees that outside
help is needed.
- Write the solutions to each problem on a separate sheet of paper.
- Make sure everyone understands the solution. If you can't explain
it, you probably don't understand it.
- Write a group report --- solutions to the problems plus the
reporter's summary.
- When the homework paper has been graded, each member of the group
should look over the corrections.
Please realize how important the group homework can be.
Tackling a difficult
problem, puzzling over and explaining to each other the needed ideas,
and putting them
down in a well-thought out solution can increase both your competence
and your confidence
with the material. Be sure that everyone in your group understands
each solution so that
all may benefit from the effort.