Incorporating Group Work  Into Your Class
 


● Contents.

Acknowledgments
What is Group Work?
What Are The Benefits of Group Work?
Getting Started
TPA Page
How to Grade?
Potential Problems and Possible Solutions
What Should You Do While Your Class Works in Groups?
Optimal Time for Group Work


● Acknowledgments

This collection of group works and teaching tips on how to incorporate group work in your Math 1011Q class, is under continuous construction.
Come back often to check what is new, and what has changed. I also would greatly appreciate feedback from you on any of the group
activities and teaching tips. E-mail me, please.

Some of the group works for Chapter 1 to 6, available as pdf files at the click of the mouse in Part II, were constructed during the  Fall
Semester of 2004, for Math 101. I  thank everyone on the Math 101 e-mail list who has sent me feedback. In particular, I thank Luke Hodge
and Stefanie Hartman, who taught other sections of Math 101, and gave me the benefit of their observations and opinions both before
and after trying the group works in our classes. The group work of Chapter 4: Which Honda Should You Buy, is Luke Hodge’s contribution
to the collection. Luke also helped me write up some of the teaching tips. The other group works evolved as the changes in the Math 101
took place: first as additional group projects for the experimental version of Math 1011Q (which was offered as Math 195Q in the academic
year 2005/2006), and then for Math 1011 (under its old number, Math 104Q) and finally into the present collection. The idea for the Team
Performance Agreement (TPA) originated from the book by Tom DeFranco and Charles Vinsonhaler: PPROBLEM SSSOLVING, Thomson
Pub. 2004. The TPA page provided in this section is a modified version of theirs. In Fall 2006, I benefited from the input of Su Liang who taught
the other section of Math 1011, and last year the course evolved with input from Eli Glatt, Deivid Faulin, and Su Liang. In particular, the cute
group work of Chapter 7: Run Fido, Run! was developed by Eli Glatt and Deivid Faulin in the summer of 2008. Thank you all!

The ideas for the group works in this collection come from many sources, too many to mention. When I borrowed more then a general idea 
I cited the relevant source. The group works mentioned in Part II for which there are no pdf files, come from Martin-Gay’s  Intermediate
Algebra book. A very valuable source of extra exercises, group works, and imaginative test problems is the Instructor's Resource Manual
of Martin-Gay’s  Intermediate Algebra book. I highly recommend that you order a desk copy.

I have written an article about Math 1011Q which you might find interesting. It contains an overview of the course, including the motivation behind
its particular content and pedagogy.  Here it is: Preparation for Sciences: Integrating Intermediate Algebra and Mathematical Modeling.

● What is group work?  

Group work is an activity in which the class is split into groups, three to four students to a group.  Each group works as a team to complete an
activity of typically five to thirty minute.  The groups work independently with almost  no interaction from the instructor.  As a rule, when
I assign a project for group work, I allocate class time to complete a part (but never all) of the project, and require that  each group completes
the project out of class, and turns in one report per group.


● What are the benefits of group work?

Among the benefits to students are: Learning how to work as members of a team; learning to use classmates as learning resources;
opportunity  to communicate mathematics to others and learn in the process of teaching, or of being “peer tutored”; fosters team-self discovery
of material; opportunity for positive social interaction in the classroom, as opposed to chatter; breaks up the tedium of  listening to a long lecture;
generates more engagement with the material and puts more energy into the classroom.


Benefits to the instructor include:  All of the above, especially having a more energetic, interested, and participatory class; less homework
to grade (collect only one project from each group); gives you a chance to observe how your students approach problems.


● Getting Started.

You may give your class the opportunity to form their own groups or assign them.  Many students are too shy and self conscious to form their
own group, but friends often sit close to each other. The teacher may use these facts to start group work by asking students to pair up for group work
with the person sitting next to them. This results in small, two people, groups for the first and second group work projects. Occasionally larger groups
get formed this way. You should monitor that the initial groups have no more then four students  each, the optimal group size. Once they formed 
groups the teacher should tell them to introduce themselves to each other, and exchange e-mail addresses and phone numbers.  The first assignment
should give them time in class to get started on the group work, and make sure they need to be in touch after class to complete the assignment.
Ask each group if they have made arrangements for meeting out of class to complete the assignment, before they leave the classroom. Ask them to
submit one work per group.

After the second group activity, have each member of the group submit to you in writing how well their group worked out, and if they wish to remain
with the same group members. Next class period assign formal groups of three or four students each, taking their opinion into account. Give class time
for the groups to discuss the Team Performance Agreement (TPA) issues, and request that they submit to you a typed and signed “official”
Team Performance Agreement (TPA)

Click on  TPA   to open a pdf file consisting of a one-page handout designed to guide the groups through the discussion of issues necessary for
the TPA preparation.


● How to Grade?

I give a grade on the work submitted.  Every member of the group receives the same grade.  This encourages collegiality, not competitiveness.
 

● Potential Problems and Possible Solutions.

A group functions as four individuals with little interaction. Stress the fact that you will accept only one work for the entire group
(as opposed to four works stapled together). It might help if you ask them to agree on roles for the activity: who will write it up, who will be
responsible for which problem, etc.; or agree on an approach to the problem before starting; or ask them to explain their solutions to each
other.  These types of prompts help break the ice and get the group talking and working together.

A member of the group is not carrying his/hers weight. Part of the learning experience when working in teams is to learn how to handle
difficulties that arise out of the team work. During the preparation of the TPA mention the possibility of such a problem,  and tell them to discuss
it and decide how the group will handle such a problem if it arises. This often helps prevent the problem from arising. If it does not, try to interfere
as little as possible in their decision on how to handle this problem. Listen to the problem and encourage them to voice possible solutions, and to
pick the best of these solutions. In general, to the extent that it is possible, let each group deal with its own discipline problems.

Some individuals hate group work. Have a talk with the student and explain that nearly all jobs involve working with others.  It is an important
and useful skill to have. Insist they work with their group. Most “lone wolves” will warm up to it once they get used to the other members in their group.
 
The group bonds too well and sends a representative to class each week instead of all of them coming to class. This is a toughie,
since you want to encourage both full attendance and group bonding. I have very rarely had students that have poor attendance and excellent grades. 
My first reaction is to talk with the group members one by one, and try to persuade them to attend classes. If this does not work, I would have some in
class activities that carry a grade, or put a group with only one member present at a big disadvantage. Luke Hodge suggested one may, for example, give
a short group quiz with four problems.  If only one member is present, they wont have time to do all four problems.


● What Should You Do While Your Class Works in Groups?

You should circulate, peek over their shoulder, eavesdrop on their conversation, and smile encouragingly. Tell them to call you if they need a little help to
get started or to get unstuck.
 
If many groups are slow to get started on an activity, or get stuck in the same place, ask them all to stop work for a minute and give a hint to the entire
class to help them get going. Sometimes all it takes is for you to read the first problem of the group work out loud, and point out what is relevant and should
be paid special attention to, from the data and questions given in the problem.

It should be a little noisy in the class during group activity. That means they are talking with each other, which is what you want. Listen to the noise they make.
If you hear a hum like a hive of busy bees, it means all goes well. If it is very quiet in the room, this is not a good sign. Prod them to interact, even if it means
asking them to share with each other what exactly they do not understand in the problem. It is a way of getting each of them engaged with the problem, which
will eventually lead them towards a solution. If the talking has turned to things other than the activity, as it may happen when a group is finished, or thinks they
are finished, look over their work.  If it is not done well, tell the group they need to polish it up.  Have an extension to the activity or extra problems on hand
for those that really are finished.  Idle chatter can also happen if the activity is too long.  Most activities should last no more than twenty five minutes.

● Optimal Time for Group Work

Although short, five to ten minutes, group activities can be assigned any time during a class period, I favor longer 15 to 25 minutes group work time at the end
of a class period. This requires only one transition from one type of learning activity (lecture) to another (group work), rather then two transitions. In general, it
 is advisable to avoid the transition from group work to lecture during a class period, as students find it difficult to become relatively passive listeners after being
actively engaged in group work. Also, if the group work occurs at the end of a class period, it provides you with an alternative activity for groups who finish the
assigned group work early. Have them start cooperatively on their regular homework assignment. This encourages out of classroom group work on all homework
assignments, and, by extension, for exam preparation. Both activities are extremely beneficial for strong and weak students alike.

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