Managing Effective Student Discourse

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

2. 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 mindStudents 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. 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 �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] �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��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 WORKLay 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

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.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 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.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 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. 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.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 5 minutes � quiet reading time5 minutes � quiet reading time

15. The Role of Questioning in Instruction Small group discussion followed by large group share out. Small group discussion followed by large group share out.

16. Analyzing Questions

17. Analyzing Questions

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

22. Questioning: Funneling or Focusing

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 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.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.

25. Scouts and Tents 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?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. 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 soluDuring 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.