There are a lot of questions on the moreTPRS list regarding various participation systems. This is what I do in my classroom.
For me, participation cannot be a graded item. What I mean by that is, that participation, effort, behavior, cannot be calculated into the letter grade of the student. At my school, like many, we have a citizenship grade, and that's where I believe participation, effort, and behavior grades should be placed.
For us, the citizenship grade is broken down into the following marks: O(utstanding), S(atisfactory), N(eeds improvement), and U(unsatisfactory). I believe that a student should earn a satisfactory mark, not be given one. I also believe that, not unlike a citizen of a country, a good classroom citizen not only follows the rules, but also contributes to the overall progress of the class. For that reason, my citizenship grade is broken down into five subcategories: participation, homework, behavior, unexcused absences, and unexcused tardies.
For the participation segment, each student starts with 70 points (needs improvement). They need to have a net balance of 80-89 points at the end of the quarter to receive a satisfactory mark, and 90 or more to receive an outstanding. Students earn points for asking good questions, answering questions, using the target language in and out of the classroom, as prizes for games, etc. I hand these points out in the form of various currencies from Hispanic countries cut out on little slips of paper. It's the student's responsibility to keep track of these and turn them in at the end of the quarter.
Students lose points for various activities that take away from their personal learning or the learning of the class as a whole. I start with minus 2 points for bathroom passes, 3 points for hall passes or talking, 5 points for behavior issues, absences, tardies, 10 points for repeated behavior issues, and 15 points if the student has to receive a referral for their behavior. All of these points can be made up by writing a 100-word essay in the target language using the current vocabulary. I give back 5 points for each essay.
At the end of the quarter, I enter how many points the students turn in into the gradebook. The gradebook then adds these to the 70 they automatically receive at the beginning of each quarter and subtracts any negative points the students received and gives a net total. That net total determines their participation grade which is then averaged with the other 4 components of my citizenship grade to give an overall citizenship grade that appears on their report card.
I like this system because it puts the responsibility of being a good citizen in the hands of the students and it takes the subjectivity out of determining these very subjective grades. If ever questioned, I can tell the student/parents exactly how that grade was calculated and what the student can do to improve it for next time.
If you have a system that works for you, please share it in the comments below!