Book: 2.1 #55-58, 86-90; 2.2 #9-10, 17-18, 64; 2.3 #37-48, 79-89 all Even if the problem in the book doesn't ask you to explain your answer, explain your answer for each problem, clearly and thoroughly. Don't get discouraged if you find these questions difficult. They are supposed to challenge you and make you think. That's the reason we're doing them in groups: they are questions that should require some thought and discussion to find all the correct answers. So if you have trouble with them, turn to your group members for help!
Join your group right away (the first week of class, before the first group project begins)! Here are the steps for initially joining a group:
Once you have joined a group, one of the group members should volunteer as the leader for this project. Do this by posting to the group Discussion Board. Whoever volunteers first gets to be the group leader. The group leader gets an extra 10 points on their grade. If no one volunteers, I will appoint a member of the group to be the group leader.
The group leader's first job is to assign a certain number of problems to each person in the group. Each group member should be assigned approximately the same number of problems. They should also get a MIXTURE OF DIFFERENT KINDS OF PROBLEMS. So group leaders, be sure that you don't just give everyone several problems in a row, because they are all going to be alike. Each group member should get problems from several different sections. Be sure to remember to assign yourself problems as well.
The second part of the group leader's job is to assign a deadline by which time all the members in your group should have posted their first try on each of the problems. If the deadline comes and some of the group members have not posted their answers, you should reassign their problems equally to the other members of the group.
Every group member should then work through the problems assigned to them and post their best answers by the deadline given by the group leader to the group Discussion Board. If you work on the problems and just can't figure them out, ask the members of your group to help you. If you do not post your first try at the answers to the problems by the deadline the group leader gives you, your problems will be reassigned to other group members and you will have to do the whole project by yourself or get a 0 for your grade! This is why you must logon to the group webpage right away!
Once your group members have posted their answers to the problems assigned to them on the group discussion board, you must comment on every single problem that a member of your group has worked out. If you think their answer is correct and their explanation is clear and thorough enough, then tell them so. If not, then give them advice about how to make it better. Remember that a part of your grade is based on whether or not you correct and help others in your group when they make mistakes. You must also reply to any substantive comments other group members have made to your work .
You will be graded both as an individual and as a group. To get a good grade you will need to:
Logon to your Group discussion board as soon as the project is assigned, and be sure to log on regularly throughout the week. If you don't login soon enough and your group leader has set group deadlines that you have missed, then you will have to do the project completely by yourself or you will receive a 0!
Make sure the final version of any answers you submit as a part of the group project are correct and contain adequate explanation of your answers. Anytime you submit incorrect work, as soon as you discover your mistakes, resubmit the work with your corrections.
Respond promptly to the group discussion. Be sure you have replied to several other group members’ posts, at different times, with an answer that actually talks with them in detail about the math involved. Remember, just like in the discussion board, answers without substance (for example, responses like, “You did a great job,” and “I don’t understand,” without any other details) will NOT count!
Make sure that you look at everyone else’s work in the group, and if you see someone in your group who is doing something that is incorrect, help them to fix it. Politely point out their mistakes and try to clearly explain to them how to correct them. However, if your fellow group member does not respond to your feedback or does not post corrections in time, you will not be penalized - your job is only to give feedback to each of your group members, but you are not responsible for how well they complete the final answer.
I know that not everyone enjoys working in groups, and that sometimes it can be particularly frustrating when fellow group members don't do what they are supposed to do. But despite these shortcomings, I've still chosen to use group projects in this class, and I'd like to give you a little bit of information why.
Many students assume that the reason professors assign group work, is that the stronger or more experienced students will help the students who know less or understand the material less. And while research experiments have shown that some students do benefit from hearing detailed explanations from their peers, this is not the primary reason that working in groups can benefit students. One of the biggest benefits of group work is actually the other way around: a number of research studies have shown that when you have to give elaborate explanations to fellow students, you learn significantly more. So it is actually the students who do the most explaining that gain the most from group work.
Another issue that often comes up with group work, is that students are concerned how the actions of other students in their group will impact their grade. In this class, when you complete group work, you will have to interact with other students and help them with their answers in order to get full credit. If you don't do this at all in your group, your grade will be quite low. However, if one of your group members does not complete their work, or doesn't respond to your tips on how to improve their answer, this will NOT affect your grade. It is your responsibility in the group to complete your own work, to give other group members feedback, and to respond to the feedback of others, but it is NOT your job to make them do their work. In fact, here is the rubric that I will use on each project in order to determine your grade:
Project Grade (out of 100%):
correctness, detail, and clarity of your final answers: 30%
correctness, detail, and clarity of your explantions: 30%
correctness, detail, and clarity of your feedback to other group members on their answers: 25%
Did you respond to all the timely feedback given by other members of your group on your own questions? 10%
Did you meet all group deadlines? 5%
As you can see, it would be impossible to get a good grade if you just posted your initial solutions and then did not participate in the group discussion; but if another group member does not do their part, this does not affect your grade at all.
And, as always, if your group really gets stuck on something, feel free to contact me for help!
A conjecture is just a fancy word for theory. It's something that you think is true based on your experience but which you haven't actually proved. So when the questions ask you to "State a conjecture," what they mean is just for you to state something that you think is true.
If you don't know how to approach a problem, try looking up the definitions of the operations used in the problem or drawing Venn diagrams.
Once you have written up your answer, ask yourself, "Is every word I use in my answer clearly defined, either by the book/lecture or by me?" If you can find words in your explanation that you haven't defined and which the book and lecture don't define, then define these words before you begin your explanation or reword what you've said! For example, say you that you have written, "A joins B." The problem with this sentence is that no one knows what you mean by "join." Do you mean "intersects"? Do you mean that somewhere we have taken the union of A and B? It isn't clear. Be sure that any words you use when you explain concepts will make sense to your fellow students (and to me!).