Monday, August 1, 2011

What's at the Center of my Classroom? Community, if I'm Lucky...

[This post is part of the July-long Virtual Conference on Core Values, posted a few days late. I highly recommend clicking on over to check out the other posts from the conference, whose thematic question this year was 'What's at the Center of Your Classroom?'.]

I teach math at a community college. My goal is to help the students in each of my classes form a learning community, but I don't reach that goal most of the time. It's embarrassing and discouraging to still be struggling so much after 25 years of teaching.  Maybe writing this post will help me clarify what that community means to me, and how I hope to help my students get there.

What is a community? How many of us really have any experience of what a community is? For most of my life, I have not been a church-goer. (My spiritual values don't mesh well with most churches.) When I lived in Muskegon, Michigan, I got pulled into the Unitarian fellowship there, and I found out what a community was. Sometimes it was just as dysfunctional as many of our families. But like being wrapped in the arms of a super-big family, the folks from the fellowship were there for me when I really needed them. I think many progressives, like me, don’t have much of that sort of experience. I don’t have a church that fits me, but perhaps someday I’ll find that. In the meantime, I want to create a bit of community with my students.

The less concrete communities of math bloggers and math circlers have also made a difference in my life; they've helped me to become more of a mathematician. I love working on math with other people. It's fun to put our heads together to solve a problem, and it's enlightening to see how differently other people will approach it. It has made a huge difference in my life. I want that for my students.

I also know how successful Uri Treisman's work [pdf] was, when he got groups of students to work together on challenging problems, as a way of helping students of color become more successful at UC Berkeley. I've known about his work for many years, and tried to use his model - challenging problems, students working in groups. Something's missing, though, because my results aren't as predictable as his were.

They Made the Class Their Own
I want to tell the story of one of my classes last fall. By a bit of a fluke, I was teaching 3 sections of one course, Beginning Algebra, and nothing else. In 2 of the 3 sections, there were students who interfered with the class running smoothly.*  But in one section, the students really pulled together. There were times when they were frustrated, and sometimes even the most motivated students wanted to blame their failures on me. But mostly, they figured out what they wanted to learn, asked more and more questions, and made the class their own.

Many of them also came in 1 to 2 hours early and worked together, almost daily. The fact that our classroom was empty before class really helped get that rolling. Robert, one of the students, took on the role of teacher, and they were much more comfortable questioning him than they were questioning me in front of the whole class. (I wasn't in the room much, so I had fears that they would trust his statements too much, just like they usually trust mine too much. I'm not sure whether or not that happened.) Robert's life may have been changed by that experience - he may become a teacher himself some day. I hope so. I believe these chosen hours of study helped all the students who participated, but the evidence doesn't show it. I think this class started out with shakier foundations than either of the others.**

The last semester before my sabbatical year, I had another class that really bonded. In that class, Nailah organized regular study sessions but did not lead them. It was much more free-form, with everyone writing problems on the board, asking questions, and offering explanations. That model seems more effective to me, but each class may need to find its own way. (I invented a Community Organizer award to honor Nailah's good work.)

In the Spring I taught Intermediate Algebra, so quite a few of my students came along to the next class (10 from the 1st group, 3 from the 2nd, and 3 from the 3rd). Although that class didn't ever gel as a community as well as my best fall class, it probably had the best pass rate I've ever managed. Our cap is 40 students, but I went over to let in returning students. Overall 38 passed, 11 failed. None of the returning students failed. Although over 20% failed, 38 people passing is a record for me. I'd rather not have the class so big - I never felt like I could really address the whole class at once. But it worked better than I expected it to.

So how do I encourage community, and how do they take it on?
  •  I try to provide a safe atmosphere in which to make mistakes. My syllabus has this: "Some people like to joke around with their friends by putting each other down. Math is too intimidating for that. No put-downs in this class, please." And when I'm correcting someone's mistake, I try to point out the 'part of what they're thinking' that is right.
  • Every day I have people check with a neighbor on a problem they're working on (most days that happens often), and most weeks they work in groups of 4 a few times.
  • They work together to catch me in mistakes - that gets them donut points. I bring donuts once the class has caught me in 30 mistakes.
  • I talk about the research that shows that working together helps students succeed, and encourage them to study with a partner.
  • My students often sit together in the math lab, studying to retake mastery tests.
This doesn't feel like enough to me. I wonder what more I can do. I think I'll tell my students that I need their help figuring out what builds community. I have a hunch they have more experience with living in a tight community than I do.

I blogged about the Complex Instruction workshop I participated in earlier this summer. At the workshop we worked some challenging problems and discussed what makes a problem 'group-worthy'. As I plan for the fall, I'm looking for 'group-worthy' problems. I hope that working in groups of 4, and changing groups at least for each unit (about monthly), will help my students become more of a community.

One of the biggest problems is that students resist all this. They want the teacher to 'explain clearly', so they can take good notes, and follow the teacher's steps to do their homework. All this groupwork and figuring things out themselves feels strange to them. In some classes they don't trust me enough to take the risk of working at learning math in a new way. The Complex Instruction paradigm has the teacher give very clear instructions on how to work together - the students get their fix from that, instead of from being told how to 'do the math'. I hope it helps.

I don’t have a satisfying ending for this post, because I’m still trying to find a consistent approach that will help me co-create community with each of my classes.

* Students at our community college have to take one 'college level' math course to move on to a 4-year college. Beginning Algebra is two levels below the 'college level' courses. Most students in this course are not happy about math.
** Pass rates: this group, 18 passed, 20 failed with D or F (yikes!); 2nd group, 25 passed, 11 failed; 3rd group, 21 passed, 16 failed. In the past I've had more students drop, instead of failing. They are not allowed, by the state of California, to drop in the last three weeks of class. With my retesting policy, lots of students on the edge hoped to pull themselves up, and stuck it out to the end. In Nailah's class (mentioned in the next paragraph), before I did as much retesting, I ended up with only 20 students; 13 passed, 7 failed.


  1. I really liked the phrase "but I don't reach that goal most of the time." How refreshing honesty is!

    Many (most?) students I see do not believe in their own thinking, at least not when they are on the board being questioned by me. For them I have tried the following approach.

    "How much is 2 + 2?"
    "OK. Please write it down on the board, 2 + 2 = 4."
    The student does it.
    "Oh, no! That is wrong! 2 + 2 = 5. Please correct what you wrote."
    The strange thing is that many of them change the 4 to a 5.
    "Why did you change the 4 to a 5?"
    "Because you asked me to!"
    "And, ...? Please change it back."
    The student changes the 5 to a 4.
    "Oh, no! That is wrong! 2 + 2 = 5. Please correct what you wrote."
    Sooner or later the student refuses to change the 5 to a 4. When that happens, I say.
    "Please write down: London is the capital of France."
    Some does, some do not.
    By playing this game, in a friendly, positive way, the goal is for them to not being afraid of saying and writing what they believe to be true.
    If they write down x = 1 as answer to the equation x + 1 = 0, my comment to them is "Beautiful!" My next comment is "Please tell me how you got that." By the way, the students are mocking me, in a friendly way, as Mr. Beautiful, which is not something I can hear too often. :)
    This comment was not so much about how to create a math community in the classroom, but more about a prerequisite for this to happen.

  2. Met math mamma writes once again in person since she was my instructor way back in 1998 shortly after I graduated high school. Susan your soul is still as beautifull as then. I pray success to you always, Sincerly, Calvin Matthews. I know you did not remember me, it is alright. I do not remember Math, only history, but all the same I was glad to meet my Muse again from college.

  3. Hey Calvin, will you email me? (mathanthologyeditor on gmail. I wrote it funny so that the 'spambots' won't send me tons of spam.) Thanks for writing me here. I'm honored that you remembered me, and if I return in another 10 years, I bet I will remember you from this encounter.

    I cracked up that you "don't remember math, only history". (Who was your history teacher?) I hated history in high school, and then fell in love with it in college when my women's studies teacher was a history prof, who had us reading original sources.

    Like I told you last night, you made my week.

    I hope you'll keep in touch.

  4. When I say that I do not remember Math, it is to no ones fault but my own. I remember history quite well no matter what time period expansion. History has always been my strong subject; and Math my least, however as we both spoke on 8-9-11, I remember you for being the one person in my early years College whom sparked my interest in Math again. I always aced advanced courses in high School except Mathematics, I skimmed by. You were my one instructor who actually made me give a damn about the subject once more.


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