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Topic: Discourse - Compiled (Long Message)
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Bill Richards

Posts: 25
Registered: 12/6/04
Discourse - Compiled (Long Message)
Posted: Mar 24, 1995 2:22 PM
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A few weeks ago I posted a note seeking input on the topic of discourse. I
received some very helpful responses, which I have compiled below. We
expect to be quoting brief excerpts from some of these responses in our
upcoming program. Thank you very much to those who contributed.


William R. Richards

MICHIGAN GATEWAYS 212 Communication Arts Bldg
The Television Program East Lansing, MI 48824-1212
for Teachers of ph: 517 355-2300 ext 422
Mathematics and Science fx: 517 353-7124

Date: Sun, 12 Mar 1995 9:49:13 -0700 (MST)
Subject: discourse

Hi, Bill, here is some stuff I wrote about discourse in an award
document--I don't know how I did yet--and it may be drier than what you're
asking for, but I'll add some comments at the end.

Discourse is an important way to allow children to hear others' thinking
while exploring their own. Discourse can be encouraged and developed most
naturally in a whole group setting. Children must hear a variety of
opinions and ideas about solving problems in order to build their own
understandings. If students are allowed and encouraged to disagree
respectfully, and to find a variety of ways to solve problems discourse can
occur. The teacher's role in encouraging discourse is varied. The teacher
must ask questions that require students to justify and explain their
thinking. The teacher must ask questions that probe students'
understandings and use of mfathematics. Questions should be posed that help
students to understand a proposed solution and build the confidence of the
participants. Some questions can guide students to greater understandings
about mathematics, and some questions should be posed that cannot be
answererd by the participants, but leave a healthy confusion about a
problem. The teacher has to know when a question in is appropriate and to
whom it should be directed. If a tgeacher uses questions well, a whole
group of children can be taught on several levels at once. Some children
will be encouraged to go further and some will be challenged. Some will
have Montessori's "seeds" planted for them--they will be able to make
better sense of the concepts when they see them again in another place and

The way I "plan" for discourse in my class is just to put out a problem and
ask kids what they think. We discuss what we know and what we're supposed
to find out first. Then kids usually go off and work in pairs, small
groups, or alone (self-selected) with whatever materials we have that
they'd like to use. They come back and present their solutions] to the
whole group. My questions are really key and as I said I ask them based on
the mathematics involved as well as my knowledge of my students. For
instance, we were analyzing a chart we'd made of some data we'd collected.
We 'd been playing a probability game on the computer. There were 30
marbles in a bag and the computer sampled with replacement for 500 trials.
Marble A (there were 3] kinds of marbles in the bag) came up 180 times. I
asked Bevin, who had just told us there wre 30 marbles in the bag, how you
could have 180 for A if there wre only 30 marbles altogether. I knew Bevin
wasn't clear on the concept, but I knew she appreicated a challenge and
thought about the things she heard. She said right away that w there must
have been 180 marbles in teh bag. Other students politely pointed out that
she had just said there were 30 marbles in the bag. Discourse ensued and
Bevin eventually caught her mistake and was able to answer my original

When kids present to the whole group their presentation is often followed
by a Priase, Question, and Polish session by their peers. (This is not
original with me!) I am constantly amazed that mys tudents can come up with
genuine and appropriate positive comments about ANY presentation and that
they are beginning to ask the same kinds of questions I do. Their polish
suggestions still contain such comments as--you should only use one color
of marker because it takes time to switch markers to use more than one
color--to "I would suggest that Martin take a more active role, I didn't
hear him contribute anything to your presentation--to "You might want to
explain how you added those two numbers first becasue I got lost." (By the
way, these are 2nd graders). Presentations have reflected major changes
based on these sessions, by the way.

Of course, the most important part of discourse is to set up a safe
environment where no one is going to be made fun of or humiliated and where
we VALUE mistakes and errors as opportunities to learn. My role is CRUCIAL
here. I must model respect for my students and then insist that they
follow. WE have some terrific discourse in our class and I learn more math
and more about mathematics teaching from my students in these sessions than
probably anywhere else! I will tell you, though, that I have had a LOT of
mathematical training (over 24 hours of graduate credit over the last 3
years) given to me from professors who struggled to encourage discourse in
these classes. I was part of a wonderful NSF/Exxon grant called New Mexico
Fellows for the Advancement of Mathematics Education. Teachers AT LEAST
need to have a feel for where mathematical thinking can lead in order to
conduct and encourage discourse in their classes. AND it really helps to
have it modeled for them.

How's that?

Cindy Chapman

Subject: Re: Promoting Discourse
To: (Bill Richards)
Date: Thu, 9 Mar 95 18:04:13 EST

Believe it or not, I began a message to you yesterday, but then I felt it
sounded like it was written by an idiot, so I abandoned the effort until I
had had time to think out what I wanted to say. Unfortunately, I have not
found any spare moments, and here I am back at the keyboard, so the
following is my best "off the top of my head" answer...

>1) What percent of the time does extended discourse occur in your classroom?

I am uncertain of the exact amount of time. I teach fourth grade, so I am
responsible for instruction in all core curriculum areas. I attempted to
pay attention to how much of our time today (3-9-95) was spent listening to
ME, and how much of it was spent listening to each other... I think today's
results might have been influenced by my observing. I know that my students
will learn more from thoughtful discussion with each other, but I am not
sure I always provide the time for that to occur. (That is another story,
though.) Today I noticed that many of my questions were of a redirecting
nature... asking for explanations or reasoning, feigning misunderstanding
to get clarification, (and sometimes not even having to fake it!) My
students are working with decimals (tenths and hundredths), and a few are
having difficulty changing the values of the models we used earlier in the
year (ones, tens, hundreds). The rest seem comfortable, and I notice often
that when someone in a group is off base with an answer, another classmate
will attempt to explain. That interaction makes me think that perhaps my
studetns DO feel they are a part of the learning and instruction.

So, I haven't answered your question in a very straightforward manner have
I? I would like to think that over half of the time my studetns spend
learning about mathematics they are listening to each other, not to me...

>2) How much of this is discourse that occurs as a result of your explicit
>planning (rather than the kind of unplanned digression/opportunity for
>discussion that good teachers have taken advantage of in their classrooms for

Planned? Unplanned? If you mean planned in as much as I actually write out
what I will say, and what the expected responses are, then I would be
honest only if I said NO, they are not planned. If you mean, do I think
about what I will present, and hope for reactions that will make the
information necessory/ important enough to learn, then I could say they are
planned. I know what I want my students to come away from the lesson with,
and I have a strong enough math background to understand the pitfalls that
we might encounter. I can anticipate likely misconceptions, and ask
questions that will bring them to light so they can be dealt with. I also
understand hwo many children acquire math understanding, numeracy, if you
will. I can guide the discussion to help the discoveries happen, as if they
occured by accident. When students think they have made the discovery on
their own, that is a confidence -building experience.

I think good math educators bring those understandings to all lessons. Weak
math educators don't. I am not sure there is a way to plan the discussion
itself, because the studetns are such an unpredictable lot. You never know
what tangent will be sparked, or what bridge will be opened. A good math
educator has to be aware, to flame the fire when the connection is helpful,
and dig a trench when it veers off in the wrong direction. (I listened to
All Things Considered on the way home... a story about a forest fire
fighter... forgive the allusions, please!)

Gail R. Englert

;-) One of the secrets of life is to make
stepping stones out of stumbling blocks.
... Jack Penn

Gail's response to a follow-up message:

Subject: Re: Promoting Discourse
To: (Bill Richards - Michigan Gateways)
Date: Fri, 10 Mar 95 21:57:35 EST

According to Bill Richards - Michigan Gateways:

>What is the level of understanding right now for my students on this topic?

>Armed with this estimate of where the students are at, what are some questions
>I can ask that most will be able to answer -- so they have a comfortable
>footing to start on?

>What are the important leading questions that I should expect to use to guide
>exploration of the topic?

>What are the benchmark points, the things to listen for so that I know we're
>making progress?

>What are the more common misunderstandings/errors that students are likely to
>develop or express, and how will I handle them when they arise?

>Knowing my students as well as I do, what prompts do I use, what opportunities
>must I create, for all to participate?

>Do you think laying out a strategy similar to this would be helpful to a
>teacher who has not done this before? What would you revise?

I think that being able to answer these questions could provide a framework
for instruction. I would caution someone using this format, though, to be
sure they were keeping the focus on teaching the students, rather than
teaching the lesson. It is important for teachers to remember that their
script is just one possibility... they should maintain flexibility.

>What sort of guidance along these lines is provided for you within your
>curricular materials (text, or units, whatever) that helps you through the
>nitty gritty of "real-time decision-making" that well-orchestrated discourse
>demands of you?

We have recently adopted an Addison-Wesley Mathematics text for grades 3 -
5. K - 2 use a math kit, with no text. Both provide a teacher's guide with
extensive information and suggestions for introducing and extending topics.

Beyond the text, my school system provides elementary teachers the
opportunity to become Math and Science lead teachers for their faculties.
These teachers receive special training, and become instructional resources
for their school, and the school system. As a math lead teacher, I have the
opportunity to network with other teachers, and discuss my instructional
techniques with them. I think that has been one of the most valuable means
for me as I changed my methods from traditional instruction (arithmetic) to
a more constructivist approach.

Gail R. Englert ;-} One of the secrets of life is to make stepping stones out of stumbling blocks.
... Jack Penn

Date: Sat, 11 Mar 1995 08:54:57 -0500
To: (Bill Richards)
From: (Mark Priniski)
Subject: Re: Promoting Discourse

Bill ---

I hope you have a successful project. If you want me to expand on anything
here, just respond back and I'll elaborate if I can.

I, Mark Priniski grant Michigan Gateways permission to use all or part of
my electronic mail message dated 3/11, with the subject line 'Re: Promoting
Discourse', as well as my name and e-mail address, in video and print
materials related to the Michigan Gateways television series.

>Here are some questions that we have on this topic, that we hope you have a
>few minutes to reply to.

>1) What percent of the time does extended discourse occur in your classroom?

It depends a lot on the class. I have spent a lot of time re-tooling my
Algebra I class. In this class I would say we spend well over 50% of our
time in discourse. My other classes are quite a bit less, altho my AP
Calculus class comes close

>2) How much of this is discourse that occurs as a result of your explicit
>planning (rather than the kind of unplanned digression/opportunity for
>discussion that good teachers have taken advantage of in their classrooms for

Let's just talk Algebra I (I'm extremely proud of this class)

In this class we go out of our way to discuss mathematics. Almost every
class time is allowed to analyze and evaluate the things we are doing.
(more in the next answer)

>3) If you ARE actually planning discourse, how do you do that?

We spend a large part of our time on mathematical modeling. This provides
the students with the opportunity to discuss not just the solving of
equations, but also the effectiveness of the model chosen. Students
develope their own models for situations, and evaluate their effectivness.
It takes time to do this. We have spent as long as 3 days developing,
evaluating and changing models for one problem. I've found that this
approach encourages students to do mathematics that is relavent to them.

We also spend time discussing use of "tools". All of my students are taught
to use scientific and graphing calculators, as well as computer symbolic
manipulation software. Students are encouraged to evaluate which tools are
most appropriate for any given situation.

Hope this helps. Let me know if you need more.

Mark Priniski Pioneering Partner '93
Rib Lake High School
Rib Lake, WI 54470


Date: 9 Mar 1995 16:21:02
Subject: re: Promoting Discourse

Dear Bill,

I am very interested in your posting about Discourse. I have several
teachers in the Graduate Program here at Bank Street College who are
pursuing their Masters Degrees in Math Leadership. I printed your posting
and will be disseminating it to them (some are not yet on-line). They are
very good at promoting discourse in their classrooms (k-8) and I hope they
will take it as part of their emerging leadership roles to share their
experiences in implementing this part of the standards with the teaching
community at large. It is exactly opportunities like this that I am eager
to share with my students to broaden their engagement outside their own
classrooms. It will take some time to mail your posting to them, but I hope
that their contributions will be *worth the wait*!

We at Bank Street have been engaged in producing Math Learning Forums which
use the internet to bring together smalll groups of teachers to examine the
various facets of the NCTM Standards. Each forum is eight weeks long and
the 10-12 participants are on-line with a faculty member as facilitator.
Each participant receives a relevant video of an actual class in action as
well as readings and 2 activities which they are expected to do with their
classes and discuss on-line. It's been an exciting project. Teachers can
sign up for graduate credit, in-service credit or for personal growth. The
fees, of course, vary with the choices. We have already produced and
piloted a forum on discourse. If you are interested in our results, we have
eight weeks of discussion on this topic alone, the persons in charge of
this project are:
Margaret Honey of the Education Development Corporation and Barbara
Dubitsky of Bank Street College. Let me know if you wish to contact them
and I can let you know their e-mail addresses.

Lucille Peterson
<*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*> Lucille L.
Math Leadership Program
Bank Street Graduate School of Education Tel: 212-875-4665
610 West 112th Street Fax: 212-875-4753
New York, NY 10025 E-mail:


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