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I have a motto, "My class is not an Olympic swimming pool! It is a museum full of the masterwork paintings! Relax and enjoy all of this mathematical beauty which I am drawing on the blackboard!"

By this sentence I mean that in my point of view the best mathematicians are those who enjoy beauty of math more not those who enjoy to be called as a great mathematician.

I don't like the competition atmosphere in my class because students effort to prove themselves as the best mathematicians of the class is contradictory with my teaching philosophy. Also it harms the team work morale of this small society. In this direction I try to avoid any kind of unnecessary comparison between my students because it commences a competition amongst them.

On the other hand I try to encourage them to team works for exploring mathematical wonderland and discovering more and more beauties of the teaching subject. The personal improvement of each student follows from this team works naturally and what is much more important is their ethical improvement during these group activities which learn them how to work together for the benefits of all.

Question 1. How can I encourage my students to work together as a team? What are the practical ways for achieving this goal?

Question 2. Tests in any sense (including exams, quizzes, etc.) increase the comparison (and so the competition) atmosphere of the community of my students. How can I design a test free course with fair enough marks which are acceptable for both students and me at the end of semester? In the other words, is there a more "soft" testing method different from the classic exams with an acceptable accuracy which measures the team work morale of each student?

Remark. I don't believe in numerical marks for measuring students at all. I think it is too simple-minded (and sometimes too harmful) to refer the abilities of a human just by a number. But unfortunately it seems this inappropriate method will be the common method of almost all math departments at least in the short future because there is no other known effective substitute for it.

Please explain your ideas and suggestions even if they are strange, unnatural and completely new.

  • Have you considered giving group tests? These can be tricky to set up, but my experience with them in university was overall quite positive. – David Ebert Apr 12 '14 at 22:16
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    Disagree with "relax and watch the movie". Instead, you should look at sports or music training. Math is difficult because of the structure of the human brain. We are much better at listening to human interest stories (history, literature) than we are to doing math calculations. In order to progress in math, some real effort is needed. Obviously this effort needs to be individual. (Consider swimming, do I get better by watching someone in the pool?) – guest Oct 06 '18 at 18:32
  • @DavidEbert - My experience is that giving the students individual tests produces a lot of team work. – Pere Jun 22 '20 at 19:34

4 Answers4

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Well, the method of Randy Pausch (or perhaps of Disney Imagineering) seems to be a perfect answer to your questions. It is worth noting that his course was practical, hence the approach might not work for more theoretical courses.

  • There were multiple projects during the semester (for Randy Pausch it was 5).
  • Tight deadline (i.e. two weeks to design, implement and test).
  • Randomly chosen teams (4 people per team), change per project.
  • The projects would be presented at the end.
  • Students would give their peers marks on "how easy it was to cooperate with them".
  • There would be a teamwork-feedback after each project.
  • The peer-evaluation would be transformed into a ranking during the final presentation (from what I understood, it was not a part of the grade).

There are more details given in his famous last lecture, a lot of worthy content, inspirational and deeply moving; I recommend it very much!

I hope this helps $\ddot\smile$

To anyone who had actually attend one of his courses, or knows more details from any other source:
I would greatly appreciate sharing your experiences/information.

dtldarek
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    Throwing together random teams is torture. The will need to cope with the equivalent in their professional life later on, true. But keep it in check while studying. – vonbrand Apr 13 '14 at 14:07
  • @vonbrand It did work in his case. I don't know, perhaps it is the point, that is, in other conditions people don't have the incentive to work out compromises with others they don't particularly like. On the other hand, in this approach they do, it's in their best selfish interest to get along and stop "the torture" as you had put it. – dtldarek Apr 13 '14 at 19:37
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Elizabeth Cohen and Rachel Lotan of Stanford University have written about an approach called Complex Instruction that supports students working together and learning from each other.

Some of the principles involve:

  • Group worth tasks: The tasks must be challenging enough so that you need to work with others, cannot be solved easily on your own
  • Assigning different roles and responsibilities to different students (again, promotes interdependence)
  • Assessing both the process of working together and the final product -- group and individual accountability as well

This approach also involves addressing issues of status -- who is the "smart" one -- as when the tasks are challenging, different people can contribute something (a new way to see the question, a unique representation that allows for a connection) so that different people are smart in different ways, and we all need each others' forms of smartness.

Mandy Jansen
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Getting people to really work together is hard. Encourage them to form study groups, so they start working together on small projects (solve individual problems), learn how to organize themselves (where, when to meet, what to prepare). Make them organize a short seminar on some topic (contact invited speakers, but have them handle the rest). Encourage independent groups/clubs, even in totally unrelated matters. Ask for help organizing welcome for new students.

As in everything, you learn not by seeing how it is done, but by doing (and making your own mistakes on the way, preferably where they don't matter much).

vonbrand
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Groupwork sucks. In any field groupwork is used because it is necessary - you need to row in sync to make the boat go faster, or you need four people to carry a coffin - not because people actually enjoy it. Do not introduce groupwork where it is not needed. Comparison is good. Competition is good. As long as you don't grade on a curve your students should be all right (because grading on a curve sucks).

Rusty Core
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    As is, this is more of a comment with an opinion than an answer. If you want to challenge the question, consider adding more detail and sources on why groupwork sucks and competition is good. – Tommi Oct 05 '18 at 09:04
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    Not exactly a mathematician but close... You may enjoy https://www.cs.utexas.edu/users/EWD/transcriptions/EWD05xx/EWD575.html – Rusi Dec 11 '21 at 02:25