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Topic: Discourse in Mathematics
Replies: 10   Last Post: Aug 30, 2001 3:48 PM

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Judith Koenig

Posts: 50
Registered: 12/3/04
Re: Discourse in Mathematics -- leading questions
Posted: Apr 4, 2000 11:25 AM
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Dear Pam,

Since I am the teacher who is quoted as asking leading questions with
my class, I thought I would respond to your inquiry.

Encouraging discourse in a class is extremely difficult. We (teachers)
struggle with issues such as: when do we allow our class to discover
things; when do we tell them stuff; when do we ask open questions;
when do we ask leading questions; when do we answer their questions;
when do we question their answers. The list goes on and on and on.

Along with all these issues are reality factors including the length
of a class period, the curriculum, lost teaching time due to school
activities, absenteeism, homework requirements, student attention
span, differences in student preparation, etc.

Whenever possible. I like to ask very open questions. In the cylinder
lesson, we graphed the relationship between radius of the base and
resulting volume. It would be wonderful to be able to ask students to
tell me all that they observe about the table and resulting graph.
However, not all students have the same background information. Also,
as a teacher, I feel pressure to arrive at a certain point in the
process by the end of class. Not to say that I object to leaving a
problem hanging in the middle and return to it the next day. This is
not always possible or practical.

Leaving a problem too open-ended could result in extensive time being
spent on this one problem at a cost to the curriculum as a whole. With
all the explorations that I do, there comes a time when we need to put
some closure (there is never final closure in mathematics) to the
topic at hand and move on.

With all these considerations, and more that I'm not taking the time
to elaborate on, leading questions are often the best course of

Although I may be sounding defensive, I'm not feeling that way. I'm
frustrated that you aren't able to see the full picture in our
classrooms. What was captured in the videopaper, was a small
micro-capsule of what goes on. One of the main reasons that I joined
this group is to learn more, improve my teaching and student learning
and grow professionally and personally. Your involvement in this
project will serve to enhance our work. Speaking for myself, I
encourage you to add your comments to our discussion. We appreciate
all interest in our paper. Not one of us feels that we have it all
down pat. Your queries help us learn and, in turn, help our students.

thank you,

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