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Setting tasks during discussion

The situation

As explained in the first episode, Judy had visited Cara's classroom at Cara's invitation. Judy used the Discussion Sketch form to record interaction during a discussion Cara led. After the discussion, Cara was somewhat frustrated by her students' seeming failure to recall a concept--"columns"--that she had taught previously. Since we probably couldn't read Judy's hand-written notes taken during class, here's the transcript of Cara's discussion with her class about "columns":

Discussion sketch, Side 2*

Time

Teacher's question or statement

Student's statement or question

Teacher's response

9:38

Teacher begins by asking students if they remember what it means to be in a row. She asks students to put their thumbs up if they think a row goes up and down and sideways if they think a row goes across.

Class is about evenly divided between up and down and sideways.

I’m glad I brought this up. A column goes up and down and a row goes from side to side. I always remember because if you ever see a column on a house, they go up and down.

   

What’s a column?

A column on a house. Some large houses have columns, like on the porch.

 

A row goes from side to side.... I’m going to show you a design. I’m going to make a design with my tiles. I want you to tell me about it using rows.

Teacher puts a 6X2 array made of pattern blocks on the overhead.

Various children calling out numbers.

I'm not done yet.

 

I want you to tell me how many rows there are in my design.

Various children call out “12.”

 
 

How many are in each row? I might be trying to trick you. How many tiles are in each row? Remember a row goes from side to side.

C: Oh, a row

C: six

C: two

 

9: 42

Put it up on your fingers. I’m hearing people call out. I’m seeing ... How many tiles are there in a column? Put that up on your fingers. You have to use both hands.

   
 

Oh, I just gave you a hint. How many tiles are there in a column? A column goes up and down.

James?

James doesn’t respond.

 
 

How might you tell me about this if I couldn’t see this? How could you tell me about this? Devin, if I couldn’t see this, what could you tell me about it?

D: What?

 
 

If I couldn’t see this ...

D: You wouldn't be doing anything.

 
 

But you could tell me what it looks like? What does it look like?

D: In the dark? In the dark?

 
 

If I couldn’t see this and you were telling me about it, what would you tell me?

D: I don’t know.

 
 

Look at it. What does it look like? How could you describe it to me?

(5 second pause)

If I asked you, what’s on the overhead right now, what would you say?

D: Tiles?

 
 

What kind of shape are they in?

D: Square?

They are square. They’re in a rectangle.

 

How many rows are there?

D: Two

There are two tiles in each row.

 

And there are 1, 2, 3, 4, 5, 6 rows. Going across we have two columns.

   
 

I’m wondering if it would change if I turned my paper. [Turns the transparency so the array is 2X6.]

   
 

Now how many are in each row? Ben? How many tiles are in each row now?

B: Six.

 
 

And how many tiles are in each column now?

B: Two

 
 

[Turns the array around again.]

So if I was going to write a number sentence about this, what might I say? Peter?

P: Well, you might count the first column and double it.

So I would count the column and then add that to it? So how many are in our column?

 

So how many are in our column?

P: Six.

 
 

So I would use six

P: Plus

Plus six.

   

P: Equals

Equals 12.

  [The discussion continued from there]    

Cara and Judy talk

Judy (looking at a tool she just laid beside her Discussion Sketch): What task are you setting?

CARA: I’m asking what a column is.

JUDY: Yes, but what kind of thinking are you asking them to do?

CARA: Remember, I guess. Recall what we studied the week before.

JUDY: Okay, recall information. The other thing that I think is important here is that you set the task for the whole class. When you asked them to use their thumbs, everyone had to respond. (Writes this in). Now, the tool asks, “What task did the students appear to perform?” They tried to answer your question, but they didn’t really know.

CARA: No, half of them got it wrong. I thought they'd remember that.

JUDY: I got down just a little bit of your response. I wrote, "Columns like on a house."

CARA: Yeah, I said that columns go up and down like on the porch on a house.

JUDY: Do you think that helped?

CARA: Actually, I don’t think most of them knew what I was talking about. Maybe I need to come up with something else to help them remember.

JUDY: Maybe you could look for columns in pictures.

CARA: Or even on the houses across the street. I think there’s some there.

JUDY: That might help.. . .

The tools in use

Cara and Judy have been working both with the Discussion Sketch and an accompanying tool on questions and students' mental tasks [Questions and mental tasks] The point of this tool is that learning is an active process that depends heavily on the students.

One way teachers attempt to set tasks for students is by asking questions during discussion. Cara had done that. But asking a question is not always a straightforward process. Often, students can perform a different task than the teacher intended to set. So this tool asks, "What tasks do your questions set for students, and what tasks do the students actually perform in response to your questions?" The tool employs a common taxonomy of students' mental tasks, and a related resources offers a list of questions related to the tasks you want to set. [Setting tasks]

Partnership

In their discussion of "columns," Judy and Cara might have missed an opportunity. It appears that Cara's students have not grasped the seemingly simple concepts of "columns" and "rows." Perhaps that suggests that the concept is not as simple as one might think.

Also, Judy has accepted Cara's idea that tall objects like the columns on some houses will help students grasp the concept of "column" in an array of counting tiles on an overhead. But the example of houses seems to provide no analogy to rows at the same time, and columns and rows at the same time are what defines the array. By suggesting pictures of houses, Judy has encouraged Cara in what might not be a useful analogy.

The point is this: Our partners don't need us to help them think what they already are thinking. Perhaps, since Judy and Cara have been working together only for a few weeks so far, Judy thought criticizing the columns analogy would be a bit pushy. That might be right. On the other hand, politeness leaves Cara with the seemingly failed analogy to columns on houses.

Using the story

Teacher questioning is pervasive. We ask questions to find out what students know or think at the beginning of instruction, to get students to do things from which they might learn and to estimate whether they have learned. Thus, it is crucial for all teachers to ask constantly what students actually do, in their minds, in response to our questions.

The "questions set student tasks" tool is completely open to any subject and any grade. You define the situation, you decide what tasks the students actually perform in response to your questions and you decide whether those were the tasks you wanted them perform. [Questions and mental tasks]

The next episode: A discussion with students turns into a recitation.