University of Minnesota

This is a non-lecture class, so there are no notes to be copied from someone if you miss class. There is really no way to make up a missed class. Also, your best thinking and learning will occur during class time. If you don't come to class and participate in problem solving activities, it is unlikely that you will pass the course. There will be about 30 problem solving activities for which you will turn in work to receive credit. Working effectively in small groups is a major skill you will learn by your active involvement in all class activities. Your good attendance will make the whole class work well.

During class time you will be involved in any of the following activities:

1. Solve problems or work on assigned activities in pairs or small groups.

2. Participate in large group discussions.

3. Write out problem solutions and strategies, descriptions and explanations of statistical ideas.

4. Have your statistical learning assessed.

Outside of class you will:

5. Read the text, answer study questions, take notes on material.

6. Complete written assignments and student projects.

In this course we will teach you math the hard way. The hard way for you, and the hard way for us. We do not do this because we are mean and nasty, but because it is the only way for you to develop the types of skills that will be useful to you in later courses and, more important, in later life. In high school you may have learned math by memorizing certain rules and techniques. That approach will no longer be adequate. In this course you will have to learn to determine the rules on your own and to design your own techniques. These skills are important both in higher mathematics and in everyday mathematical problem solving. At first you may find our questions frustrating and have no idea how to answer them. But if you make a serious effort you will find your confidence gradually improves as your skills develop.

You will be asked to do a lot of cooperative work. This may cause you to wonder why, when you are already confused, we ask you to work with other students who are just as lost. There is a very good reason which the following analogy may help to illustrate.

Suppose when you first arrived on this campus you were given precise written instructions on how to get to this classroom. If you followed these carefully each day, how much would you learn about the campus? Without such instructions you have to explore, you get lost, and you make mistakes, but you learn a lot more. The example may be even clearer if you think of driving across a state by superhighway following road signs. You may get through it fast, but you have seen little and learned less.

Since we are going to ask you to find your own way through some of the mathematical terrain we cover, you are going to need all the help you can get. Classmates can tell you about their experiences -- where they got lost, and sometimes, what they found out. Together you can learn more effectively and have more fun doing it. Finally it is in discussing problems and in arguing back and forth that you learn the most. If you do not participate fully in this aspect of the course, you will miss the most important part.

We will be tough with you and we will give you hard assignments, but we also know you wouldn't be here if you found math easy. Don't be afraid to ask questions or to tell us about special problems you are having. We do want to help, no matter how silly you may think your problems are. We are confident that if you work with us, together, we can teach you the material in this course regardless of how bad your previous mathematical experience has been.

Give it a try and your efforts will be rewarded.

(This section was adapted from materials used at University of Massachusetts, Amherst.)

1. Informal Groups: These may change everyday. These are "turn to your neighbor" discussions to:

* Summarize the answer to the question being discussed.

* Give a reaction to the discussion.

* Relate the new information to past learning.

2. Formal Groups: Sometimes in these groups you will divide up the work, work together to solve a problem or apply a statistical method, or work on long-term projects. You may also use these groups to review material, compare homework assignments, teach each other information, encourage and support each other, inform each other about information if a class has been missed, and evaluate the group process.

* Moderator/organizer: Assigns tasks to groups, moderates discussions, oversees that the assigned task is being carried out, helps keep group on course.

* Summarizer: Summarizes discussion or group solution to a problem.

* Recorder: Writes down what summarizer says.

* Strategy suggester/seeker of alternative methods: Says, "Could we try this method?", "Is there another way to solve this?"

* Review/mistake manager: Says, "What went wrong?", "What can we learn from this?"

* Encourager: Encourages participation from all group members, using probes such as: "What do you think?", "Can you add to that?"

* You are always responsible for your own work.

* You must be willing to help any group member who asks.

* You may ask the instructor or TA for help when everyone has the same question (all hands are raised).

* You must achieve a group solution for each problem.

* You must make sure everyone understands the solutions before going on.

* Listen carefully to each other.

* Share the leadership.

* Make sure everyone participates and no one dominates.

* Observe groups, listen, assist as needed.

* Question group about conclusions, solutions, ask what are you doing and why.

* All people learn at different rates, and there are many different ways in which people best learn. Recognize and accept these differences and be respectful of each other.

* You will learn statistics more effectively by asking questions, answering questions, helping each other, and analyzing your mistakes.

* Statistics problems can often be solved in several, correct ways. You can learn from each other by comparing different solutions.

Group is given a concept or procedure to discuss and then write-up. The discussion should include:

* A verbal description or explanation of the concept or procedure.

* An example.

* At least two different types of problems involving the concept or method and a solution for each problem.

* A few other related concepts or procedures.

* What's confusing about the concept or procedure, where might someone go wrong (or be confused).

1. Name one thing that the group (or someone in the group) did that helped you accomplish your assigned task.

2. Determine if someone in the group is pulling the group behind. Discuss how to overcome this problem.

1. Set the task so that students are clear about the assignment.

2. Explain the intended outcome of the activity.

3. Help students understand what they are to learn and do in completing the assignment.

4. Ask the class questions to check that they understand the assignment.

5. Explain criteria for success.

Davidson, Neil (Ed.) 1990. Cooperative Learning in Mathematics: A Handbook for Teachers. Menlo Park: Addison Wesley.

Johnson, David W., Johnson, Roger T., & Smith, Karl A. (1991). Cooperative Learning: Increasing College Faculty Instructional Productivity. ASHE-ERIC Higher Education Report No. 4. Washington, D.C.: The George Washington University, School of Education and Human Development.

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