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I am currently teaching calculus and I thought it would be a good idea to do some kind of limit (and later derivative/integral) calculation tournament. The thing is... The students only seem to give their best if the activity is an actual assessment so I was wondering how can I prepare a tournament as a fair assessment.

The main issue is that as an assessment I want every student to be able to get the maximum score (otherwise it wouldn’t be fair), however since it is a tournament only one student can get the first place...

So I was wondering how one can organize a tournament in a way that is fair for all students? There are some remarks to take in consideration:

  1. There should be a prize/incentive for attaining a better place in the tournament compared to the other students.

  2. Everybody should be able to get the maximum score.

  3. There should be some kind of rule which determines whether a student is out the tournament or not.

  4. Every student needs to participate.

  5. The whole tournament shouldn’t take longer than two hours; I can’t spend too much class time on that.

So with those remarks in mind how would you guys organize a tournament? I'd like to compile some suggestions before planning it.

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    Why isn't a regular quiz / in-class test fine? Do you have in mind some other requirements that would make it not suitable? – Federico Poloni Jun 3 '18 at 8:48
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    I think technically speaking "give them a mandatory exam/quiz like usual, and grade it like usual" satisfies all of these. – zibadawa timmy Jun 3 '18 at 9:04
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    While you and many others just see a tournament as a frame for an exercise or display of skill, it’s a format that has a huge tendency (and arguably was designed) to appeal to sensationalist, martial, and other primitive instincts – which should have no place in academia. Quite a few of my fellow students had abhorred such events in school for this reason and would have been hugely demotivated by such an event – not only for the exercise itself, but also for studying in general. You cannot control such associations and the possibility that it brings out the socially worst in your students. – Wrzlprmft Jun 3 '18 at 9:34
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    I think the techniques in this article on competitive, team-based learning by Kristine M. Trego could be adapted to your purposes. Trego is a Latin professor, but I think elements like the discussion of separating the incentive of low-stakes competition from the grade earned for participation, balancing such incentives against "the pressure of performance and responsibility for work outcome", and how to allocate time to the competition would be useful to you. – 1006a Jun 4 '18 at 15:46
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    @Wrzlprmft other primitive instincts – which should have no place in academia The worst primitive instinct in academia, IMHO, is the "ownership one" (It was I who...). There is a whole culture and legal structure about it and nobody seems to do anything to discourage that. Pure competition for symbolic rewards (rather than for better positions, salary raises, promotions, etc.) just to measure your strength against others is actually very healthy. If one cannot stand losing occasionally, it is he who should work on his character, not the others who should pamper him. – fedja Jun 5 '18 at 14:44
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Eager et al. describe how they use flipped classrooms to teach a mathematical biology course. As part of their course, they use "competitions" to motivate students. They discuss some of your concerns in a method paper:

One of the difficulties in teaching a class via the flipped classroom is how to properly assess and examine student learning [3]. Because the class is very modeling focused, and modeling is a time-consuming process, traditional exams are very difficult to administer in a course like MTH 265. The authors’ solution to this problem is to do away with traditional exams in favor of both individual quizzes and group mathematical modeling competitions. The individual quizzes involve the students choosing two small modeling questions from a group of three questions and solving them with help from their class notes, homeworks, past computer programs and video lectures. These quizzes are given over a 55-minute time period. The questions in these quizzes are structured in such a way so that, after the student chooses which two problems to work on, he or she can solve both questions in a combined 40 minutes—meaning that some (but not all) of the modeling process is given to them. These exams provide the students with an incentive to learn the material on their own (which is nontrivial in a flipped course with a large group component), as well as the motivation to become proficient in using some of the elementary skills a mathematical or quantitative biologists would need to possess (e.g. diagram building, script writing/amending, elementary algebra and calculus, scientific writing).

The mathematical modeling competitions stemmed from the successful 24-hour Wisconsin Mathematical Modeling Challenge at UW-L, as well as the success of similar activities in other mathematical biology courses [8]. These competitions complement the individual, inclass quizzes by providing students with more open-ended modeling problems and a longer timespan to produce their solutions. These modeling problems can ofen be introduced with only a few paragraphs of text—with few or no equations. The students, in groups, then have 24 hours to come up with an appropriate model for this system, as well as answer the biological question posed. The group of students with the best solution is rewarded with perfect homework scores until the next modeling competition. The class has either an individual quiz or a modeling competition at the end of every other week for a total of three individual quizzes and three modeling competitions during the semester worth roughly 30 percent of each student’s final grade.

Full citation (in case link breaks): Eric Alan Eager, James Peirce & Patrick Barlow (2014) Math Bio or Biomath? Flipping the mathematical biology classroom, Letters in Biomathematics, 1:2, 139-155, DOI: 10.1080/23737867.2014.11414476

As a disclosure, I have collaborated with Eager and gave guest lectures in his Bio Math course about my own research.

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Here is a suggestion. It has its advantages and disadvantages and I haven't tried to implement it myself, but you asked, so here are my 2 cents.

There should be a prize/incentive for attaining a better place in the tournament compared to the other students.

Apparently you are not willing to give out extra points or anything else that might influence the grade. Then just make a few nice drawings, write "The first (second, etc.) place in the calculus tournament" with the date and your signature over them, laminate, and attach some silly little prizes (a box of pencils, a figurine, a notebook, etc.) to each. It'll cost you 40-60 bucks and a few hours of drawing, but it'll work.

Everybody should be able to get the maximum score.

If you have 10 students, prepare 30 tasks and hand them out one by one. For every task the first one to complete it gets 10 points for the task (counted towards the grading score) and 31 minus the number of the task (from 30 to 1) to determine his rank (the first problem is worth 30, the second 29, etc.; the rank is the sum of values of solved problems). Once a student solves three problems, he is not participating any more. You run the tournament until either everyone is out, or nobody can solve the current problem, or the time is out.

There should be some kind of rule which determines whether a student is out the tournament or not.

Addressed above.

Every student needs to participate.

Well, with this scheme at some point he'll be the only eligible competitor if everybody else is done, but if he just cannot do the task anyway, it is his problem. I think it is fair enough.

The whole tournament shouldn’t take longer than two hours; I can’t spend too much class time on that.

That depends on how many and how good the students are and on the difficulty of the problems assigned. Also, do you want just answers or explanations? You can replace the factor 3 by 2 in this scheme, but with more than 20 students it becomes somewhat problematic to implement in under 2 hours. What I expect is a fierce competition with quick answers in the beginning, followed by a slower run once the top students are out, followed by a bunch of dropouts staring mindlessly at the problem (or at the ceiling) forever (unless you impose a time limit on each problem). One partial remedy for this unevenness would be to present hard problems first and to decrease the difficulty along the way.

  • Can you please state more explicitly whether you suggest that tasks are handed out one after the other? – Wrzlprmft Jun 5 '18 at 8:01
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    A big problem I see with this scheme is that you rank all students, so you do not explicitly state who is the best, but also who is the worst, second worst, etc. Ending with such a position would be very demotivating for some students. – Wrzlprmft Jun 5 '18 at 8:07
  • @Wrzlprmft Really? If they are so sensitive, they have nothing to do in the university (or in any professional setting). I know the feeling of being the last. It makes you clench your teeth, set the engines to full steam, and go ahead as fast as you can at the expense of "social life" and other nonsense. But, of course, you can just decrease the problem value only to 15 and then keep it level, so all students at the low levels are formally tied. – fedja Jun 5 '18 at 14:28
  • @Wrzlprmft Yes, one after another. The first one to solve gets the credit and then the next one is given. You can try 2-3 at a time too but then it becomes a bit of a lottery. – fedja Jun 5 '18 at 14:33
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    I agree with you that one has to learn how to deal with failure and certainly with not being the best. But being the last has quite another flavour. I cannot remember any situation in academia where somebody was officially declared the last. I also cannot think of any situation in professional life where this would happen, other when a public shaming component is intended. — [Being last] makes you clench your teeth, set the engines to full steam, […] – This does not apply for the vast majority of struggling students I know. – Wrzlprmft Jun 5 '18 at 19:33

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