1. Managing Effective Student Discourse
Matt Fisher
LuAnn Malik
Corinne Murawski

2. Managing Effective Student Discourse
Why is high level classroom discourse so difficult to facilitate?
What knowledge and skills are needed to facilitate productive discourse?
Why is it important? (i.e. Why do we care?)
Students are reluctant to engage/ classroom environment not comfortable for students to take risks
Coverage of material - Not enough time for students to respond via discussion
Beliefs about what it means to teach
Question whether discussion promotes learning
Lack of skill in posing questions for discussion – or lack of awareness of the questions you actually ask
Teachers afraid of losing control of the class (of the thinking)
Vocabulary/ meaning often challenging to students. Teachers afraid they won’t understand students’ ideas
Teachers have preconceived notions of “the answer” and are not open to other possible responses
Establish a classroom environment supportive of risk taking
Deep content knowledge
Listening and patience
Good questioning skills
How to use a wrong answer in pedagogically productive ways
Keep the mathematical goal of the lesson in mind

3. Teaching is HARD WORK!
Orchestrating classroom discussion that builds on students’ thinking places specialized pedagogical demands on teachers and requires an extensive and interwoven network of both pedagogical and content knowledge.
It’s hard to teach such skills and as a result orchestrating meaningful discussions is not often the focus in pre-service or on-going professional development.

4. A Brownie Problem
I invited 8 people to a party (including me), and I had 12 brownies. How much did each person get if everyone got a fair share?
Later, my mother got home with 9 more brownies. We can always eat more brownies, so we shared these out equally too. This time, how much brownie did each person get? How much brownie did each person eat altogether?
- Corwin, Russell and Tierney 1990, 76
“Let’s start by examining a couple of examples of discourse or discussions in math classrooms to get further insight into why it may be difficult to get to high-level discourse in the math or science classroom.”
[First bullet] “We are going to read a few short excerpts from classes that are working on the Brownie Problem above. Before we examine the transcripts, take just a minute in your small groups to solve this Brownie problem and show your thinking about the problem.”
[second bullet] “Now take just a minute to solve the second part of the problem”
Have one person share their strategy for solving each part on the overhead transparency.
“Now, we are going to read some excerpts from Ms. Carter’s class and Ms. Andrew’s class. The students in Ms. Carter’s class are solving the second part of the problem, when the additional 9 brownies come into play. In Ms. Andrew’s class, they are solving the first part of the problem.”
“Realizing that we are only getting a short glimpse into each of the classrooms, what similarities and differences do you notice in the transcripts?”
Allow small groups to discuss and then share out with the large group

5. Social Norms
Social Norms are things like explaining thinking, sharing strategies and collaborating
These afford opportunities for students to engage in conceptual thinking
Many teachers attempt to establish these social norms
HOWEVER, SOCIAL NORMS ALONE MAY NOT ADVANCE CONCEPTUAL THINKING
“One reason why discourse is difficult is that students may not be familiar with norms for discussions.”
“Did anyone notice any similarities or differences between these two classrooms with regard to the norms or expectations that students seemed to be under in these two classrooms?”
If participants have not already mentioned the social norms at work in the classroom, then get them to look at what the teacher is expecting the students to do with their solutions
Click to get the first three bullets to appear
“Technically, both classrooms have students explaining their solutions. However, there was a difference in what was expected out of the explanation. Can someone say a bit more about that difference?”
Click to get last bullet.
“So, both classrooms has social norms established, but that may not have been enough to get to where Ms. Carter got. So, what else did Ms. Carter have going on in her classroom?”
[next slide]

6. Sociomathematical Norms
Explanations consist of mathematical arguments, not simply procedural summaries of the steps taken
Errors offer opportunities to reconceptualize a problem and explore contradictions and alternative strategies
Mathematical thinking involves understanding relations among multiple strategies
Collaborative work involves individual accountability and reaching consensus through mathematical argumentation
Adapted from the work of Yackel and Cobb, 1996
“She had more than just social norms established. It seems that she might have had what are called sociomathmatical norms established in her classroom. These are things like…” Lay these out to the group
“In the short snipits that we read, do we see evidence of any of these norms at work.” REVISIT TRANSCRIPT TO FIND EXAMPLES OF THESE AT WORK
Emphasize that it takes time to develop these. The older the student, the more time it may take because of their “old ways”

7. “Socioscientific” Norms
Scientific argumentation is about sharing, processing, and learning about ideas. It focuses on ideas, not individuals.
Explanations consist of scientific arguments, not simply procedural summaries of the steps taken or recall of facts.
Different conclusions based on patterns of evidence offer opportunities to explore alternative explanations.
Scientific thinking involves understanding the relationship between theories, hypotheses, and experimental evidence.
Collaborative work involves individual accountability and reaching consensus through scientific argumentation
Adapted from the work of Yackel and Cobb, 1996 and Taking Science to School
Lay these out to the group
Emphasize that it takes time to develop these. The older the student, the more time it may take because of their “old ways”
REVISIT TRANSCRIPT TO FIND EXAMPLES OF THESE AT WORK 7

8. Discourse for Conceptual Understanding
Quantitative analyses indicate that the higher the press in the classroom, the more the students learn
“Press for Learning” was measured by the degree to which teachers
Emphasize student effort
Focus on student learning and understanding
Support student autonomy
Emphasize reasoning more than a correct answer
What do we mean by “press”? If participants have trouble have them think about basketball and a press in that context.
Show second bullet.
What are some examples or non-examples of “press” in each of the classrooms in the transcripts?
The exchange among Sarah, Jasmine and Ms. C highlighted the conceptual focus of the lesson on fair share. Ms. C asked S to explain the importance of having eight halves and why the partitioning strategy using eighths made sense. After J gave a verbal justification, Ms. C continued to press her to link her verbal response to the appropriate pictorial representation and to the symbolic representation.
In Ms. A’s class, the questions she asked yielded general responses without revealing specific info about the student thinking
The four sociomathematical norms on the previous slide help to create a high press for conceptual thinking. How can that be so or why do you think that is so.

9. The Importance of Questions
Teachers’ questions are crucial in helping students make connections and learn important mathematics and science concepts.
Teachers need to know how students typically think about particular concepts, how to determine what a particular student or group of students thinks about those ideas, and how to help students deepen their understanding.
Weiss & Pasley, 2004
A big part of how teacher “Press for Learning” is by the questions they ask on a consistent basis. We would be remiss if we talked about discourse without talking about the importance of the questions that teachers (and students) ask during discourse in the classroom. As you read the transcripts, you likely noted the fact that MS. C was asking lots of questions of her students.

10. The Importance of Questions
Teachers provoke students’ reasoning about mathematics through the tasks they provide and the questions they ask.
NCTM, 1991
Asking questions that reveal students’ knowledge about mathematics allows teachers to design instruction that responds to and builds on this knowledge.
NCTM, 2000
Questions are necessary for both the teacher and the students.
Teachers gain valuable information about students’ understandings and misunderstandings. This information informs the teacher about how to proceed.
Students consideration of questions will help them understand the mathematics better and make connections that will not only help them learn and understand, but also remember.

11. Patterns of Interaction
Teacher: What kind of mathematical relationship does the equation y = 2x + 5 show?
Student: A linear relationship
Teacher: Okay. It’s a linear relationship
A common form of interaction.

12. Patterns of Interaction
Teacher: What kind of mathematical relationship does the equation y = 2x + 5 show? [Initiation]
Student: A linear relationship [Response]
Teacher: Okay. It’s a linear relationship [Feedback]

13. Patterns of Interaction
Although this form of interaction, called IRF, was identified and described over 25 years ago, it is still prevalent in classrooms today
- Stigler and Heibert, 1999
This type of interaction has been shown to lead students through a predetermined set of information and does little to encourage students to express their thinking.
- Cazden, 1988, Nystrand 1997

14. The Role of Questioning in Instruction
Read the vignette on pages 562 – 563 of the article, Unveiling Student Understanding: The Role of Questioning in Instruction
5 minutes – quiet reading time

15. The Role of Questioning in Instruction
What are your impression of the vignette and the discourse that did or did not occur?
What can you say about the “press” in this classroom?
How would you characterize the teacher’s questions?
How do you characterize the students’ responses?
What can you say about what students knew or learned by the end of the episode?
Small group discussion followed by large group share out.

16. Analyzing Questions Form Closed form seeks a particular answer.
Open form are aimed at promoting description, explanation, solution method, strategies, etc.

17. Analyzing Questions
Look at the specific questions from the vignette and think about the form.
How does the form influence what is learned by the teacher about student thinking?
How does the form influence the level of discourse in the classroom?

18. Analyzing Questions
Read the vignette (example 2) on page 485 of the article, Questioning our Patterns of Questioning
How does this vignette compare/contrast with the previous vignette?
Think about the form of the questions. How do they affect the outcome of the discussion?

19. Questioning: Funneling or Focusing
Funneling occurs when a teacher asks a series of questions to guide students through a procedure or to a desired result.
Teacher engages in cognitive activity
Student merely answering questions – often without seeing connections

20. Questioning: Funneling or Focusing
Focusing requires the teacher to listen to student responses and guide them based on what students are thinking rather than how the teacher would solve the problem.
Allows teacher to learn about student thinking
Requires students to articulate their thinking

21. Questioning: Funneling or Focusing
Again, consider the vignette (example 2) on page 485 of the article, Questioning our Patterns of Questioning.
What questions would you ask to move from funneling to focusing?

22. Questioning: Funneling or Focusing
Read example 2 (revised) on pages 487 – 488.
What are the key differences between the example as funneling and the example as focusing?
How might this be applicable in your classrooms?
Do funneling versus focusing questions have any potential influence on the discourse?

23. Science Writing Heuristic
Originally a framework rooted in “writing to learn” and
Elements work well for verbal discourse also:
beginning questions
procedure development
claims and evidence
reading and reflection

24. Teaching and Learning Ball and Cohen (2000) teacher content student(s)
Instruction
teacher
content
student(s)
student(s)
Teaching in school and teaching in professional development involves dynamic relationships among the teacher, the students, and the content. Teaching in school can be thought of as a set of relationships between teacher and student, student and content and teacher and content as illustrated in the diagram. These dynamic relationships require the teacher to know the content, not just the specific content of a lesson, but a deeper understanding of where that content resides in the curriculum, what is important for students to know, and how students come to learn it. These relationships are influenced by the context. The teacher also needs to know about her students in particular and student thinking and learning in general. She needs to know how students learn the content–how she brings the student and the content together to create a learning environment.
contexts
Ball and Cohen (2000) 24

25. Scouts and Tents Four tents will house 12 scouts.
Take a minute to think about this problem on your own:
Four tents will house 12 scouts.
If there are 40 tents, how many scouts
will have a place to sleep?

26. Scouts and Tents Student Work
As a group, choose 3 student strategies that you would want to have shared in a whole class discussion.
How would you characterize each of these strategies?
In what order would you have these students share?
What questions would you ask the student as they are working at their desk?
What questions would you ask the class as they are sharing their solution?
When you decide on how you would order the work, write your choices on the chart paper up front.
How are B and E the same and different?
How are C and F the same and different?

27. Questions for Student A

28. Questions for Student B

29. Questions for Student G

30. Enactment of a Classroom Episode
Ms. V. teaches a combination fourth- and fifth-grade class in an elementary school in a mid-sized urban city in the Midwest.
She had recently participated with other teachers in professional development programs designed to help teachers understand and build on children’s mathematical reasoning.

31. The White House held an Easter egg hunt on Monday
The White House held an Easter egg hunt on Monday. For every 16 children that staff hid 20 pink eggs. If there were 36 children, how many pink eggs did they hide?
During the two weeks prior to the episode, the student had been solving problems like the Easter egg hunt problem. (Read the problem)
The strategies used by the students showed their different levels of understanding and development of proportional reasoning.
Pictures representing all the information from the problem, ratio tables using a doubling and adding strategy, and number sentences repeatedly using the doubling and adding strategy were the most common solutions the students presented in this class.
From their solu

32. Ms. V’s Class

33. Debrief the classroom enactment
Use the transcript to site evidence as you answer these questions…
How would you describe the social interaction?
How would you describe the discourse forms?
Do you think the mathematical goal of the lesson was achieved?

34. Before you leave… Complete the session evaluation. This is session D.
Take a copy of the Gomez article from the table by the door.