Team Homework Resources

This course will feature a substantial emphasis on cooperative learning. In class, I plan to facilitate group activities and discussion rather than just repeat the content of the text to you at the board. This means that you will be asked to read the material and attempt the homework before it is "covered" in class.

Written homework is a substantial part of your grade. Each of the team problems will require considerable thought and a complete, well-written solution. You will often find that homework problems are best solved in a cooperative environment. Discussing problems with your classmates is a more efficient way to learn and remember the material.

Each homework problem will be graded on a 1-3-5 scheme. The grade "5" means that the problem was solved essentially correctly, perhaps with very minor inaccuracies. The grade "3" means that there was a substantial gap in your solution and "1" means that the problem was essentially not solved. The grades 2 and 4 interpolate the gaps between 1, 3 and 3, 5 respectively.

First, this is a more efficient way to learn and remember the material. Research shows that people remember:

• ~10% of what they read
• ~20% of what they hear
• ~30% of what they see
• ~50% of what they see and hear
• ~70% of what they discuss with others
• ~90% of what they teach someone else

Additionally, this better prepares you for the "real world" of work. It is quite common to see job announcements from companies looking for applicants who:

• can operate effectively in a team environment
• have good communication skills
• have excellent problem-solving skills

The purpose of having you write detailed and clear explanations of your work is to improve your understanding. The more carefully and clearly you write your mathematics, the more likely it is to be correct, and the more likely you will be to remember the ideas involved. Writing is a crucial part of the thinking process itself. In this course, writing is part of the process of learning.

For the team homework in this course, each member of the team has an important role. These roles are to be rotated each week so that everyone has the opportunity to try each role. The roles are the scribe, the clarifier, the reporter, and the manager.

Scribe: The scribe is responsible for writing up the single final version of the homework to be handed in. This is the only set of solutions which will be accepted or graded. Each member of the group will receive the same grade.

Clarifier: During the team meeting the clarifier assists the group by paraphrasing the ideas presented by other group members, e.g. "Let me make sure I understand, the reason two weighings is not enough ...". The clarifier is responsible for making sure that everyone in the group understands the solutions and/or proofs.

Reporter: The reporter writes a record of how the homework sessions went, how long the team met, what difficulties or successes the team may have had (with math or otherwise). If there is disagreement about the solution of a problem, the reporter should present sketches of alternate solutions and explain the difference of opinion. The report should list the members of the team who attended the session and their roles. The report should be on a separate sheet of paper and the first page of the team's homework solutions. You may use a copy of the sample cover sheet for this purpose.

Manager: The manager is responsible for arranging and running the meetings. If the team has only three members, or if one of the four members cannot attend, the manager should also take one of the other roles. When the homework is returned, the manager sees that it is photocopied and distributed so that each team member's folder contains a copy of the corrected problems.

The goal of team homework is to ensure that everyone learns with and from the other members of the group. This means that when the work is completed and submitted, every member of the group should be able to explain how to solve all the problems. Here are some ideas that past students have come up with to help your group function at its full potential.

Schedule enough meetings, and don't schedule them at the last minute.

Go to every meeting and be on time.

Do the reading and work on each of the problems before the group meets.

Find a way to express varying opinions in a friendly way.

Listen carefully. Don't interrupt and don't tune out.

Make sure that everyone is equally involved.

Avoid making others feel dumb.

Stay on the topic.

Don't rush to finish before everyone understands.

TeX is a typesetting system that allows anyone to produce textbook or journal quality mathematical text. This is the way most of modern mathematics is communicated. If you are considering a career that has to do with mathematics, chances are you will need to learn TeX at some point. While typing up homework solutions is not required for this course, a part of the grade will be determined by the clarity of exposition. Some of your solutions are likely to require revisions, and typing things up is an efficient way to deal with that. Additionally, I will give a (small) bonus for typesetting solutions in TeX. If you want to give it a try, here are two options (assuming you have a Windows computer):

• Option 1. Online LaTeX Editor ShareLaTeX. This one does not require you to install anything on your computer, everything is on the cloud. The documents can be shared with other people. The follownig helpful information together with example documents below should be enough to get you started.
• Option 2. LyX. This is a "What you see is what you get" type editor; great for those starting with TeX. You need to choose "Bundle with MiKTeX download" (LyX is the interface, and MiKTeX is the brain that figures out where things go on the page). If your operating system is not Windows, you will probably welcome the challenge of figuring out how to install LyX; I will be happy to help.
• Option 3. MiKTeX. This should work for those ready to code in TeX on their own computer. MiKTeX is the program that compiles the text you enter and produces a good-looking output. You need to download and install it first. (It is free.)
• Option 3, continued. After you install MiKTeX, you can enter the TeX code in TeXWorks, the editor that comes with MiKTeX. Alternatively, you can find a number of free TeX editors with more features.
• Some examples of TeX code.

You may use the information contained in the study guide for Beachy and Blair. It contains solutions for some of the problems, hints, as well as additional exercises.