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Discourse  Compiled (Long Message)
Posted:
Mar 24, 1995 2:22 PM


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.
Bill
 William R. Richards 23156wr@msu.edu Producer/Director BillR@wkar.msu.edu
MICHIGAN GATEWAYS 212 Communication Arts Bldg The Television Program East Lansing, MI 488241212 for Teachers of ph: 517 3552300 ext 422 Mathematics and Science fx: 517 3537124 
Date: Sun, 12 Mar 1995 9:49:13 0700 (MST) From: CHAPMAN@APSICC.APS.EDU To: 23156@msu.edu Subject: discourse
Hi, Bill, here is some stuff I wrote about discourse in an award documentI don't know how I did yetand 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 themthey will be able to make better sense of the concepts when they see them again in another place and time.
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 (selfselected) 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 question.
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 asyou should only use one color of marker because it takes time to switch markers to use more than one colorto "I would suggest that Martin take a more active role, I didn't hear him contribute anything to your presentationto "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 Chapman@apsicc.aps.edu
 From: genglert@pen.k12.va.us Subject: Re: Promoting Discourse To: 23156wr@ibm.cl.msu.edu (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 (3995) 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 >years)?
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 genglert@pen.k12.va.us
;) One of the secrets of life is to make stepping stones out of stumbling blocks. ... Jack Penn
 Gail's response to a followup message:
From: genglert@pen.k12.va.us Subject: Re: Promoting Discourse To: 23156wr@ibm.cl.msu.edu (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 "realtime decisionmaking" that wellorchestrated discourse >demands of you?
We have recently adopted an AddisonWesley 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 genglert@pen.k12.va.us stepping stones out of stumbling blocks. ... Jack Penn 
Date: Sat, 11 Mar 1995 08:54:57 0500 To: 23156wr@ibm.cl.msu.edu (Bill Richards) From: priniski@cedar.cic.net (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 email 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 retooling 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 >years)?
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 priniski@cedar.cic.net Rib Lake, WI 54470

To: 23156wr@ibm.cl.msu.edu From: LPETERSON@bnk1.bnkst.edu 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 online). They are very good at promoting discourse in their classrooms (k8) 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 1012 participants are online 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 online. It's been an exciting project. Teachers can sign up for graduate credit, inservice 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 email addresses.
Lucille Peterson <*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*> Lucille L. Peterson Math Leadership Program Bank Street Graduate School of Education Tel: 2128754665 610 West 112th Street Fax: 2128754753 New York, NY 10025 Email: lpeterson@bnk1.bnkst.edu <*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*><*>




