...the students were not progressing as he expected or would like; in particular, many of them had not remembered how to apply function transformations. He spent the last 15 minutes of the lesson going through the problems with the class at a reasonably quick pace in an attempt to reach his lesson objective.
When we talked about the lesson afterwards, he expressed his frustration, saying: "I never finish what I have planned! Why do they always forget? They don't remember the prerequisites... or perhaps they never understood them in the first place."
We agreed that he would notice when this happened again. We also agreed that I would come in to watch him teach again in a couple of weeks, with a focus on these issues.
This week, I watched him teach an AS lesson where students worked in groups of 4 to sketch graphs according to various criteria in sections of a Venn diagram, a bit like this task. We then talked about the lesson; an approximation to part of our conversation is given below.
What parts of this conversation resonate with your experience? What are the dilemmas here?
Me: Did the task do what you wanted it to?
Wali: I wanted them to think about quadratic graphs, the effects of the coefficients. I wanted them to work in groups so they could talk about them… and I chose a Venn diagram because it was visual so they could see what each other was doing.
Me: So did the task go how you thought it would?
Wali: More or less, yes… A few students didn’t really get involved, I’m not sure what they got out of it. Felicia [a girl who was in the group that I was sitting with] didn’t really say anything.
Me: She spoke three times during the task, but was the most quiet in her group.
(In the group, I recorded that Felicia spoke 3 times, Matheus talked 8 times, Edwin spoke 18 times and Rehman spoke over 30 times in the first 10 minutes. The three boys each wrote on the sheet at various times (mostly Rehman); Feilicia never wrote on the sheet.)
Wali: She often does this, she says: I don’t get it, then sits and does nothing… She’s never asked me a question.
Me: She did something really interesting; after about 12 minutes of the task, she went to get her book, came back and started taking notes.
Wali: Maybe she doesn’t like speaking in front of the class, but maybe she just doesn’t understand what we are doing?
Me: That matches what she said when I spoke to her; she said she was, “Not certain that what she would say was correct.”
Wali: Well, she has a tutor - she waits and asks him questions when she gets home. Maybe she’s not comfortable asking questions in class, but maybe I’m just rubbish at my job! I sometimes think: Why are you here? It’s really annoying.
Me: You find it personally annoying?
Wali: Sometimes I feel that way, yes. I mean, how hard was the task? We went through it before doing it. I put the people who I knew would find it difficult into groups with people who know what’s going on… For these guys to get what is happening I would need to make the task below the level that is required, but it’s gone past this stage now, there’s nothing I can do – it’s too late! They just shouldn’t be on the course. For me, to be able to explain what they need to know, I would need to sit down with them and discuss what they don’t know, such as fractions, solving equations and negatives. I just can’t do it.