Group Work in MAT191

There are many purposes for group work and much research to show its benefits. In this course, groups will be used to enhance the learning experience by providing a network to support your mathematical progress, a forum for discussion and debate of mathematical ideas and concepts, a set of collaborators with whom to expand your knowledge and understanding, and a measure of accountability for keeping up with the course work. In addition, it is hoped that group work may make math more fun and that some group members may become friends.

Groups of four will be assigned and will work together until reassignment, which should occur soon after each exam. It is very important that group members be respectful and helpful to each other. Group work will be beneficial to the highest achieving students, because they will need to be able to explain ideas clearly to others. As every teacher knows, the best way to truly learn a subject is to teach it. Group work will be beneficial to average students, because working with others helps us reinforce our strengths and improve upon our weaknesses. In my experience, the level of understanding of average students rises tremendously when they talk and work together. Group work will be beneficial to struggling students, because they will have an extra forum for help and explanations. Often your peers will be better than instructors at putting ideas into terms you can understand.

Group Meetings

Groups need to meet at least twice each week, and should plan on meeting for at least one hour each time. Each meeting should have the following structure:

• Discussion of Individual Exercises. During this time, the group should check that each person completed his or her individual exercises. Groups may want to compare answers or discuss difficult problems. Students who have questions need to ask them. Students who understand need to explain. By the end of this time, each group member should be up to speed on the current exercises.
• Discussion of current material. This section may be interwoven with the discussion of individual exercises. Group members should discuss the reading from the text and the content of the lectures. Be sure to ask all of your questions! Make sure that others in your group answer your questions. If they can’t, bring those questions to me. Don’t forget to point out ideas that you find fascinating! Math can be great, and you should celebrate that fact during your meetings.
• Discussion of group homework problems. During this time students will work together to solve the group homework problems.
• During the meeting, the director (described below) should be filling out the meeting sheet.

Note: Many students believe that group work “lowers” their grade. Surprisingly, I have never had a student whose grade has been “lowered” by group work. Because the groups are changed throughout the semester, hard working students always stand out and slackers always sink to the bottom.

Getting Four People to Work Together

How do you get four different people to work together? One way (the way we will use) is to assign each person a different role. Each week each group member will have one of the following roles. Roles must rotate week to week. The roles are as follows:

• Coordinator—The coordinator is in charge of scheduling the meetings and reminding group members of meeting times and places. He or she is also in charge of making sure that group members behave respectfully of each other and that each member has a chance to talk.
• Clarifier—The clarifier makes sure that everyone understands the material. In particular, it is important that each group member fully understand the solutions to all group homework problems.
• Director—The director keeps the group on task, fills out the meeting sheet, and generally makes sure that the meeting is mathematically productive.
• Scribe—The scribe takes notes at the meeting and writes up the homework problems for submission. Only one write-up will be accepted per group. Though the scribe is in charge of writing, it is the responsibility of every group member to okay the final product before turning it in.

Making Group Work Work

In order to make group work fruitful and pleasant, it is imperative that you do the following:

• Come to meetings prepared and ready to work. You need to have done the reading and the individual exercises. You should bring a sheet with your written comments and questions about each. You should also bring your textbook, calculator, and anything else you might need. Be sure to read over and think about the group problems before you get to the meeting.
• Listen carefully and with respect to each other. Everyone’s ideas are important, and it is vital that each person understand the material. Do not be dismissive of what others have to say.
• Criticize ideas, but do not criticize people.
• Everyone has the right and responsibility to contribute to the homework. You must share your ideas and your questions, and you must allow others to do the same. If one group member dominates the discussion, every group member loses.
• Ask for help when you need it. Giving help can be just as informative as getting it.
• Give help when requested. Giving help can be just as informative as getting it.
• Make decisions by consensus, not majority rule. Do not try to intimidate others into agreeing with you. Don’t agree with something you don’t understand.
• Come on time and stay on task during meetings. Each member’s time is as valuable as any other’s. Do not make your group wait for you to participate.
• Be flexible when scheduling. Scheduling group meetings can be difficult. Be open to changing minor scheduling conflicts in order to meet with your group.
• End on a positive note. Review what you have accomplished. Thank your group members for working with you. Even if you had a difficult session, thanking each other will leave you all feeling better about the experience.

Writing Up the Group Homework Problems

Writing up the group homework problems may not be like writing up any math problems you have done before. These problems are intentionally more interesting and challenging than the individual exercises, and the write-ups will reflect this more sophisticated nature. In addition to including correct and complete symbolic work, your solutions should include

• A statement of the problem. This should be paraphrased from the book, not recopied!
• A mathematically correct explanation aimed towards other students in the same course who haven’t yet read or done the problem. Do not write the explanation for me, as I already know how to do it. This explanation must involve words! You need to write in complete sentences. Use correct punctuation. Be sure to spell-check.
• Use of a graph, a table, and/or a formula whenever it would enhance the explanation.

The group homework should be a work of art. You will need to put thought and effort into each write-up to make it as good as possible. Each group member must read and okay the final product before its submission. If it is not possible to reach a consensus on a given problem, two solutions for that problem may be submitted. In that case, the scribe must include a discussion of the merits of each.

The Honor Code and Group Work

The meeting sheets, which you will attach to the front of each group homework assignment, request that you do two things. First, you must comment on the effectiveness of each group member. Second, you must only include a group member’s name on the final product if that group member was present at the meetings and contributed to the work. In order to comply with the honor code, this information must be true and accurate. In addition, the homework write-up must be a product of the work of your own group members. You may not copy any part of any other group’s work. Nor may you copy any part of any work done for any other section of MAT191.