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Responding to students

The situation

In the preceding episode, Cara and Judy were analyzing a part of Judy's Discussion Sketch. It showed that just before Tyrell spoke, Cara had asked Peter for a number sentence to match the tile array on the overhead projector, and he had offered "6 + 6 = 12." That answer not only gave the correct sum but also matched the way the tiles were arrayed on the overhead projector, in two rows of six. When Cara asked, "Is there any other way I can think about writing this in a number sentence?" Tyrell gave her an answer she hadn't anticipated, and the discussion took a turn. The lesson transcript:

Discussion sketch, Side 2*

Time

Teacher's question or statement

Student's statement or question

Teacher's response

  [Continues from....]    
 

Is there any other way I can think about writing this in a number sentence? Teacher records 6+6=12 on overhead.

Tyrell?

T: You could do 3+3+3+3.

I don’t have three of any groups though, but that would equal twelve. You’re right.

   

J: (calling out) I know six times four.

 
 

I’m wondering not how I could make 12, but how I could use this tile pattern to make a number sentence. Carole?

C: You could do 4+4+4

I could break this up into groups of four. I guess I could. I could do 4+4+4 equals 12.

 

And I guess by the same account, I could also take Tyrell’s idea and break this off. I could make equal groups of 3, couldn’t I. 1,2,3 ... 1,2,3 ... 1,2,3 ... yeah. I would write 3+3+3+3.

   
 

Megan, do you have another way?

M: 2+2+2+2+2+2

Oh, I could do 2 six times.

 

Are there still more ways I could do this?

Jason: I know, I know, I got a really good way.

Jason, what’s another way we could do this?

   

J: 6 times 4

We don’t have 6, four times.

   

Sasha: Oh, I know, I know.

Hmmm? Sasha?

   

Sasha: 6 times 2.

Thank you. Do we have 6 two times. We do. So we can do 6 times 2 equals 12.

 

Peter, do you have another idea?

P: We could do 2 times 6.

Two times six. Remember we talked about this. Two times six is the same as six times two. They’re going to be the same thing. And these all equal twelve. We have so many ways to make 12.

 

[Teacher asks students to take out math books. The page shows a variety of tile arrays. As a class, they write a number sentence for the first two. Then the children complete the third problem independently.]

*Source?

When she asked her question, Cara probably was thinking of "2+2+2+2+2+2=12," "2 X 6 = 12," and "6 x 2 = 12." But the children cycled through several responses that either didn't match the way the tiles were arrayed on the overhead or didn't provide the correct sum. And now Cara is wondering how she might have responded to the students' contributions.

Cara and Judy talk

CARA: You know, what I would really like to do with the rest of our time is figure out some alternatives to evaluating the students' comments. I didn't want to do that; I wanted them to evaluate their own suggestions.

JUDY: I can get into that. One of the forms I didn't print was about teachers' responses; it'll only take a minute to download and print it.

(Judy does that, and returns. They attach the new form to the side of Judy's Discussion Sketch).

JUDY: You lead, and I'll try to be helpful...

CARA: This form is interesting. None of it is rocket science, but it's thought-provoking to have a lot of possible responses all in one place to look at. And there's a lot I could have done instead of evaluating what Tyrell and the other students said.

JUDY: So, let's take my Sketch notes, look at what the kids said and identify some alternative responses...

(They do.)

CARA. I think I'll just put this form with my lesson plans and use it for ideas...

Tools in use

The tool Judy printed was made to lay beside the Discussion Sketch, and to support consideration of alternative responses to students' contributions. [Responses to students] With the tool, they compared the responses that Cara did make to her students' comments with a range of responses that teachers can make to student comments.

The tool includes the option of evaluating student comments, but also several other potential responses including gestures, follow-up questions of several kinds, statements of several kinds, and invitations for students to ask questions of their own. These are discussed briefly in another of our resources. [Alternative responses]

The partnership

While Cara can read the repertoire of alternative responses very quickly, she will need years of practice to learn to produce that range of responses in the real time of a classroom, for the range of the curriculum she teaches. And maintaining a large repertoire of responses also is work; probably, Judy will find some useful options, or reminders of options, in this tool.

While Cara might want to employ any or all of the alternatives shown in "Responding to students," she cannot learn to produce them all at the same time. If Cara leads this conversation, she can make those assessments intuitively; it makes sense for Judy to follow her lead.

Having selected an alternative, Cara still has to figure out how to produce any alternative she chooses--in real time in the intense interaction of a classroom. The partners might conclude their discussion by choosing an upcoming lesson in which to try. With luck, Judy can observe or the lesson can be taped, and their conversation can build cumulatively.

Notice that Cara and Judy can get full use of the tool only if they look closely at Cara's (or Judy's) teaching, and talk about it specifically. Also notice that they accomplish that in a matter-of-fact way, as though it were natural to do so. Perhaps they are just compatible--or perhaps they have negotiated with each other to have this kind of working relationship. [Decide how you will work together]

Using the story

Studies of motivation suggest that, in all grades, students' mode of thinking will be affected by teachers' evaluation practices. If the teacher is asking questions, calling for students' comments and evaluating those comments, then students will have good reasons to focus on the teacher's evaluation and to try to satisfy the teacher. When they set that goal, they are more likely to resort to "shallow processing"--just trying to get a right answer by the quickest means--which will tend to make them appear stupid to their teacher.

But the teacher wants them to set the goal of trying to master whatever they are studying, and so to resort to "deep processing" in which they use their minds in much more intelligent ways, and are more fun to teach. The teacher can promote that partly by using responses other than evaluating the students' comments. So, Cara's desire to generate alternatives to her evaluative responses in her lesson probably is sound.

Motivation research points to some other classroom features that affect motivational states and learning. [See Motivation and learning and Motivating students to learn].

The last episode: What's next?