While providing interesting information on similarities within the classes of teachers

who use the same curriculum, this coding exercise did not capture important differences

that we knew to exist between different teachers using the same curriculum. The

differences were particularly evident among teachers using the reform curricula. Our

detailed observations and qualitative analyses showed that the teachers generated very

different classroom environments. In order to capture these differences we chose to move

to a finer grain size and code the nature of teachersâ€™ questions, as our observations

suggested that teacher questions were very important. We developed nine categories of

teacher questions that were derived from an analysis of practice. We did not invent the

categories *a priori*, rather we studied different examples of the teaching in our sample

and attempted to describe and name the different types of questions we recorded. In

doing this, we were informed by other analyses of questions, particularly those of Hiebert

and Wearne (1993) and Driscoll (1999). Table 2 shows the categories of teacher

questions we developed.

Table 2: Teacher Questions.

Question type

Description

Examples

1. Gathering

information, leading

students through a

method

Requires immediate answer

Rehearses known facts/procedures

Enables students to state

facts/procedures

What is the value of x in this

equation?

How would you plot that

point?

2. Inserting terminology

Once ideas are under discussion,

enables correct mathematical

language to be used to talk about

them

What is this called?

How would we write this

correctly?

3. Exploring

mathematical meanings

and/or relationships

Points to underlying mathematical

relationships and meanings. Makes

links between mathematical ideas and

representations

Where is this x on the

diagram?

What does probability mean?

4. Probing, getting

students

to explain their

thinking

Asks student to articulate, elaborate

or clarify ideas

How did you get 10?

Can you explain your idea?

5. Generating Discussion Solicits contributions from other

members of class.

Is there another opinion about

this?

What did you say, Justin?

6. Linking and applying

Points to relationships among

mathematical ideas and mathematics

and other areas of study/life

In what other situations could

you apply this?

Where else have we used

this?

7. Extending thinking

Extends the situation under discussion

to other situations where similar ideas

may be used

Would this work with other

numbers?

8. Orienting and

focusing

Helps students to focus on key

elements or aspects of the situation in

order to enable problem-solving

What is the problem asking

you?

What is important about this?

9. Establishing context

Talks about issues outside of math in

order to enable links to be made with

mathematics

What is the lottery?

How old do you have to be to

play the lottery?