Managing Effective Student DiscourseMatt Fisher

LuAnn Malik

Corinne Murawski

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?)

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.

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

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

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

“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 argumentationAdapted from the work of Yackel and Cobb, 1996 and Taking Science to School

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

The Importance of QuestionsTeachers’ 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

The Importance of Questions

Asking questions that reveal students’ knowledge about mathematics allows teachers to design instruction that responds to and builds on this knowledge.

NCTM, 2000

Teachers provoke students’ reasoning about mathematics through the tasks they provide and the questions they ask.

NCTM, 1991

Patterns of InteractionTeacher: What kind of mathematical

relationship does the equation y = 2x + 5 show?

Student: A linear relationship

Teacher: Okay. It’s a linear relationship

Patterns of InteractionTeacher: 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]

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

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

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?

Analyzing QuestionsForm

Closed form seeks a particular answer.

Open form are aimed at promoting description,explanation, solution method, strategies, etc.

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?

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?

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

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

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?

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?

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

Teaching and Learning

Ball and Cohen (2000)

teacher

content

contexts

student(s)

student(s)

Scouts and TentsTake 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?

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.

Questions for Student A

Questions for Student B

Questions for Student G

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.

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?

Ms. V’s Class

Debrief the classroom enactmentUse 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?

Before you leave… Complete the session evaluation. This is

session D. Take a copy of the Gomez article from the

table by the door.