Class dynamics

A month ago, I took over 2 maths classes which were both not in a good state: their previous teacher had been giving unsatisfactory marks the entire classes, and they were discouraged with maths and generally in a bad mood. The first class was loud and complaining loudly, the second quiet, sulky, their complaints more bitter.

Now I have given the classes away again, and I am still thinking a lot about what happened in the lessons.

In the first one, the loud one, I think I managed to achieve a small progress with a very simple trick:

We had an exam, and after I had returned it, I let the students demonstrate the solutions on the blackboard. For each part of the exam, I picked the weakest student who had still managed to solve it.

The effect was astounding: the class was totally silent listening to a weak student explaining an exercise that part of them had not been able to solve. The weak students suddenly looked taller, even those that I had not asked to solve exercises, and they all started to participate in class and volunteer for solving exercises on the blackboard. It was a huge surprise to me. Somehow it turned around the entire dynamics of the class. One of the weakest students, who I had praised for being the only one to see a second solution in one of the exam exercises, later surprised me with making up a difficult exercise for the class herself, and solving it flawlessly on the blackboard. Perhaps not unexpectedly, all of these weak students who suddenly improved had been girls, who are likely to be better at maths then they seem. What I learned from this is how hungry the students are for praise, even they look disinterested.

Of course, at the same time, I have to admit, the strongest (male) student of the class started acting up, disrupting the class by laughing loudly or making stupid comments, which is probably not surprising: he’s role as alpha student was being questioned.

With the second class, I am less happy and still thinking about what I could have done better. There was a really strange piece of dynamics going on. Whatever I tried to explain, there were two girls at the back of the class, let’s call them Rita and Sina, clamouring loudly and in very annoyed voices that they did not understand, asking stupid questions, and urging me to explain the thing again and again. Rita was especially bad, her face was angry and bitter, her questions especially repetitive.

I remained patient and tried to explain again and again, until another math teacher told me that they sometimes use this trick to slow down the class, so that less material can be covered. I was not fully convinced of this though, because the two of them looked really, really desperate and angry at me for not explaining it better. But in the end I had to tell them that I could not explain the same thing four times.

In any case, in the exam, Rita achieved the maximum score, although she was acting up during the exam, bothering others and annoying me.

Sina, on the other hand, was by a large margin the weakest student of the class. So apparently what both of them had communicated turned out to be Sina’s lack of understanding and frustration; Rita apparently had understood everything perfectly well.

Somehow, instead of managing to explain some things to Sina, Rita supported Sina in her anger and frustration, and gave her the feeling that it was not hers, but the teacher’s fault if she could not follow.

After the exam, Sina came to me teary-eyed, saying that this had been her worst mark yet, and begging to repeat the exam. I said this would be the decision of her next teacher.

I am still wondering what I should have done to break this dynamics, or what a good teacher would do next. Probably those two should stop sitting next to each other, because it is damaging Sina. I just do not understand why Rita is not able to help her even a little bit. Maybe, solving the Rita/Sina problem would put the entire class  in a better mood and make them less sulky.

It is weird how much the faces of the students are still with me, even now that I know I won’t see them anymore. Especially Rita’s cold stare is still following me and I am still trying to figure out why she used this tactics. There was also a guy in the first row, who also wrote a very good exam, but had such a sad, resigned face that it is hard to forget it.

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8 Responses to Class dynamics

  1. kolytyi says:

    As a child, I wanted to be a teacher. No wonder: my mom, my grandparents, my cousin, my aunt and her husband, the wife of my uncle were all teachers. It was a very hard decision whether I should study maths or literature and linguistics. In the end, I started to study mathematics but not as a future teacher but as a future mathematician (the latter is much-much harder and challenging). It was a complete disaster because it turned out in 2 weeks that I didn’t had good enough basics from the high school (I had only 3 maths lessons a week, the other students 6-8). Thus, I turned back to the original idea and made a degree as a maths (and philosophy) teacher. I gave private lessons which were really successful. For example, the son of my boss had the worst results at school but after a month he had the best marks. The key point of this effectivity was the method: The How to Solve It by Georg Polya: https://notendur.hi.is/hei2/teaching/Polya_HowToSolveIt.pdf, http://www-history.mcs.st-and.ac.uk/Biographies/Polya.html. It was one of the biggest revelations for me when I looked into this book in a book shop when I was 17 years old and saw the questions my math teacher always asked my class on the cover. The questions he asked us and let us ask during problem solving seemed to be totally spontaneous. But they weren’t! We felt that he is able to look into our minds and make us discover things alone and solve problems easily, almost automatically on the basis of a few simple heuristics. And the whole class had that feeling, the weakest pupils and the cleverest ones alike.
    Despite this, I haven’t become a teacher. After I graduated, I couldn’t find a job at any school and, after some other attempts, I became a linguist. Recently, I cannot imagine myself as a teacher. I think I have some kind of autism. Thus, while I could make really good private lessons, I has always been unable to make anything useable in front of a whole class. As I found out I cannot see the single class members but only a mass. Nevertheless, my model of linguistic theorizing is based on Polya’s method – thus, it belongs to my most important intellectual resources till today.

    • zinemin says:

      Thank you! The book by Polya looks fascinating.
      Problem-solving has always been my own main motivation both at school and in research. I can only really care about knowledge when I can use it to solve problems, and having used it to solve a problem is the only way that I can retain knowledge for longer.
      Consequently I tried to focus on problem solving in my math classes, and I was very surprised about how hard it is for the students to apply the knowledge they actually have to real life problems, like making calculations with interest rates or comparing mobile phone contracts. They have all the tools, and they are able to use them in an extremely limited context, but not for anything slightly more complex. It looks like Polya’s book is exactly about this.
      Yes, I also find giving private lessons a lot more pleasant. Trying to figure out 20 individuals with their problems, and the class dynamics on top of it, is just impossible.

      • kolytyi says:

        Polya has a few other books on this topic, too: for example, Patterns of plausible reasoning, or Mathematical discovery. He has also made videos for maths teachers – perhaps you can find them on the Internet. Similarly interesting are, although it belongs rather to the philosophy of science (or more exactly, philosophy of mathematics) works of one of his students, Imre Lakatos, above all this book: Proofs and refutations. The logic of mathematical discovery. CUP 1976.
        I’m so strongly focussed on the problem solving that I know only what I discovered or analyzed recently – I have a catastrophically poor memory.
        What is really fascinating for me in the methodology of Polya is that the teacher has to the make discoveries during the teaching process, too. For example, it often turns out that the pupil makes 2-3 steps where I thought there is only one. It is always fantastic to see that the pupil thinks it was him/her who solved the problem and not the teacher. And the eyes of the kids when they have understand or discovered something … Despite this, I cannot imagine myself as a teacher any more. I’m too introverted to it, the generation gap seems to be also too big. The question whether I can do research as a linguists till my retirement, however, is shaky.

  2. Rita is a frienemy. I’ve seen it every single year when I taught high school. I worked in a really rough school with metal detectors and without fail there was always a pair (mainly girls): one extremely intelligent, the other not so much. Both would act out. How I handled it as a teacher, I never would explain it four times during class, that’s wasting everyone else’s time. Which you definitely don’t want to do since it seemed like their first teacher wasted everyone’s time to begin with. So after the second time, I would just say “I’d love to see you during office hours so I can make sure you get this concept, but I have to move on right now.” At the end of the class make sure to approach them and remind them of when and where office hours are and that you really hope to see them. Tell them you appreciate all their questions, it shows dedication to their learning and you can’t wait to help them get back on track. But as a teacher you and only you can control what happens during class time. When you have students that act out, they’re trying to take over control. Rita is a control freak, it was not about trying to help Sina. Often gifted students struggle in classroom environments because they dislike authority. Particularly if the authority turns out to be inept (as the first teacher was).

    • zinemin says:

      I agree. You are absolutely right that I need to give priority to the entire class, not to those who act out and challenge me. I remember being annoyed as a students that the loud ones could dominate so much and determine where everything was going, and I was always thankful for tough and strict teachers. Strictness can be a way to make things more democratic in a class. It is just very difficult for me to be strict. I hope I can learn it.

  3. Priyanka says:

    Hello. Back after ages, because suddenly lots of your posts showed up o my timeline. This is a lovely piece, in part because it reflects my own dilemmas when I was first assigned my core group of students (about 30 of them). I am afraid what people say here about Rita is more likely true than not – she uses Sina’s friendship to bolster her own confidence, and as a tool to ensure her competitors in the class lag behind or lose interest. I strongly recommend the calling-to-office tactic myself.

    It’s very nice to read about you teaching, and about you actually caring. I think I speak for many many people when I say I had horrible maths teachers who ruined my great love for my the subject for almost a decade. It’s only now that I have begun making tenuous attempts to get back to it, and I’m almost thirty. So well done you.

    • zinemin says:

      Thank you for this nice comment. :) Luckily I don’t have this class anymore and Rita is probably getting on someone else’s nerves now. But I agree in retrospect I should have been much stricter with her. I hope I will handle this better the next time — I was just not prepared for a dynamic like that.
      It is very sad when a love for a subject gets ruined by bad teachers… it happens a lot with maths and physics. I think the entire way we teach these subjects is problematic. But I also don’t know how to fix it.

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