I would like to start out next year by creating a classroom community. This year I noticed a lot of burnout towards the second half of the year. Basically, I want to see what kinds of games/activities worked for people. I would like my students to develop agency because many of them come into the math classroom resigned to fail or barely pass. As an example, the first class the students could answer some basic questions about themselves and then pass the focus to the next student of their choice (rather than the instructor passing the focus). I know another teacher who starts her class by giving a 2-minute simple riddle, which allows all students to participate and be able to contribute.
I agree with @Tommi that creating community is bigger than one activity. I do a number of things at the start of semester, but building community is also in the way I teach, every day of class. (I teach college, currently online via zoom.)
You might check out Francis Su's blog, which is related to his book, Mathematics for Human Flourishing. I also found the article "Todxs cuentan: building community and welcoming humanity from the first day of class", by Federico Ardila–Mantilla, inspiring, especially his use of music. (I still haven't done that, but I definitely want to.)
I think helping students understand the beauty of math is helpful, and I ask my students to read these articles:
- Conversation between Steven Strogatz and Grant Wiggins
- Article by Ian Stewart
- Lockhart's Lament (by Paul Lockhart)
In terms of equity, I recommend Whistling Vivaldi, by Claude Steele. It explains the concept of stereotype threat and the research behind it. One intervention that seems small but helps a lot is to ask students to write about their values at the beginning of a course.
I also think it helps when they think about how to learn math, and I ask them to read a number of articles about that, including this one by Jamylle Carter which emphasizes building community.
As we work together in class:
- I pause often to check for understanding,
- I notice the spark of right thinking in wrong answers,
- I accept them where they are and thank them for asking questions,
- If they can't answer a question I've asked, I ask an easier one, and provide scaffolding via questions, to get them to where they can answer the original question.
Do these practices build community? I'm not sure. But they do build safety, which is a first step toward building community.
In the age before covid, back when we were still human, I found breaking the class into groups and having them solve about a half dozen problems on the board was moderately successful in getting them involved. You need a lot of board space and a few minutes before class to write up problems. I would give them 10-20 minutes to attempt, then I'd spend the rest of the class either affirming or denying their answers. I pepper in criticisms of notation etc. as appropriate, ideally striking a friendly posture. I don't do these quizzes all the time, and I don't do them at all in the upper level classes. Sometimes lecture is the most efficient manner to competently cover material.
Another approach, keep a stack of 3x5 cards with their names and randomly select them for questions as you go. This doesn't work as well in my estimation, many kids these days are pretty introverted w.r.t. math class. It's not always wise to antagonize their shyness directly. In contrast, with the groups, everybody is getting out of their comfort zone so it's less personal.
All of this said, every class is different. There is no substitute for just talking to each of them individually to try to forge some small friendship and/or understanding of why they are in your class and what are their aims in seeking higher education. ( I don't recommend this last paragraph for large lecture sections !)
There's a lot of good answers here - just to add one tactic that's worked well for me, consider adding low-stakes assignments that allow students to use skills they don't ordinarily think of as part of a math class. In one of my classes this last year, I included a weekly discussion post as part of the class, usually centered around a philosophical question related to what we were doing in class that week; one of the earliest discussions was about the question of whether math is something that is "discovered" or "invented".
Since this wasn't a philosophy class, the assignment wasn't graded in any strict way - if a student wrote a post that showed engagement, and replied to someone else's post in a way that showed engagement, they received full points. And the discussions were, overall, a very tiny portion of the course grade. But what I noticed was that, apparently as a consequence, I had many more of the less-mathematically-comfortable students bringing their whole selves to class - students who were used to thinking "oh, I'm really a literature person, there's nothing for me to offer in a math class" (or similar) had started to feel like there really was something for them to contribute. The result was a much more energetic and engaged atmosphere than I usually see - even though we were meeting over Zoom!
Rather than trying to figure out a trick to use, you might want to see what are the core activities in the classroom and what, if anything, you can do about those. The family life etc. of the pupils can also have a huge effect, especially in corona times, but there is less you can do about those.
The main ideas in the literature I have met are that activities should allow the pupils to investigate and discover things and be open-ended. For stuff in English you might want to read Boaler's book on Mathematical mindsets. It is very American, but if you can read it in spite of that, it has many good ideas to this effect. Otherwise you might want to look at any recent books in the curriculums of your country's teacher training institutes.
You might want to de as little explaining and lecturing as possible, while have the pupils work, alone and in groups, as much as possible. The problems should be accessible to everyone, but contain depth at the same time. Avoid routine calculations and closed problems with only a single right answer.
Of course, you might already be doing all of this; in that case, please edit your question with a description of what you are doing at the moment!
My experience is at university level so it may not fit your requests.
During my online course I planned and did the following:
- opened each lecture with one musical piece that was chosen by students. They all agreed it helped them gaining concentration and momentum
- asked them, with a small reward on grades, to write a log journal - one page at least per week - with personal comments on what they liked/disliked, found interesting, and in general reflecting on their learning experience. This had to be sent privately to me, with the agreement that (obscuring names) I could have used and commented this material in classroom as well.
- gave the opportunity to jointly work on a small project in groups of 3. Projects were chosen by a list. My course was on differentiable curves and each project should produce as outcome computations of the curve invariants as well as comments on why the chosen curve was interesting/connected to other parts of math/historically relevant. Again small leverage on grades.
- asked them to jointly produce, again in small groups, commented set of notes that I will use in next year class. So produce material to be used by junior students in future classes.
All this was quite effective and (together with a couple of video-parties at moments in which I felt they were losing momentum) helped in creating an active participation in (virtual) classroom.
One thing that I did in the past (not virtual) was the following: I would open each lecture with 5 minutes recalling an argument of their choice with the agreement that they were supposed to choose the argument and agree on it before me entering the classroom. Again this somewhat worked.
I hope I'll be able to reproduce some of this in presence next year. But it has been a hell of work, to say it clear.