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Transcript Document

Learning from Lesson Study Debriefings: An Exploratory Study

National Council of Teachers of Mathematics Annual Meeting, Research Pre-Session April 20, 2004 Philadelphia, PA Rebecca R. Perry Mills College [email protected]

Mary N. Leer School District of Lancaster (PA) [email protected]

Catherine C. Lewis Mills College clewis@mi lls.edu

This material is based upon work supported by the National Science Foundation under Grants No. 0207259 and No. 0096509. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Planning Phase

Choose and Discuss Learning Goals for Content Area, Unit and Lesson Plan Lessons(s) that Foster Long-Term Goals and Lesson/Unit Goals

Le sson Stud y

Research Lesson Post-Lesson Activities

Discuss Long Term Goals for Students’ Academic, Social and Ethical Development

RESEARCH LESSON

Actual classroom lesson; attending teachers observe and record student work, speech, behavior.

Lesson Debriefing

Discuss research lesson, focusing on student data collected, goals, and relationship of both to instruction.

Consolidate Learning

Revise and re-teach the lesson if desired. Reflect on what was learned and write it up in report that includes goals, lesson plan, data, and summary of discussion. Begin cycle again, with same or refined goals.

Why Focus on Debriefings?

Given the rapid spread of U.S. lesson study, but limited evidence of effectiveness… • To understand debriefings, regardless of cultural contexts, as opportunities for collaborative reflection on a shared lesson experience; • To uncover what enables some debriefing sessions to elicit deep discussion that seems to build teachers’ knowledge for teaching; • To inform the field and add clarity to lesson study as a vehicle for improving U.S. mathematics instruction.

Research Questions and Rationale

• Question: To what extent are debriefings focused on teaching and learning? How does this happen?

[Teachers are typically isolated (Lortie, 1975) and learning is dependent on individual initiative. Joint debriefings provide opportunities for “ productive disequilibrium” (Ball, 1999), when individuals with different knowledge, skills, ideas, and values interact and learn as their ideas bump up against others’ ideas. Debriefings that focus on teaching and learning are likely to deepen participants’ math knowledge for teaching as a result of greater exposure to these ideas.] • Question: To what extent do debriefings support connections between the specific lesson and the broader domain of knowledge for teaching? How does this happen?

[When participants connect learning from the specific research lesson to existing knowledge from other teaching/ learning contexts, these connections support the development of teachers’ expertise (Leinhardt et al., 1995; Alexander & Murphy; Alexander, 2003; VanSledright & Alexander, 2002) and knowledge integration (Linn, Eylon, & Davis, 2004; Linn & Hsi, 2000). Learning in the lesson study context is valuable because it may support math knowledge for teaching more generally.] 5

Research Questions and Rationale (Cont’d)

• Question: To what extent do debriefings support connections between the three components of instruction -- content, students, teaching/ instructional practice? How does this happen?

[Ball (1999) and the National Research Council (2001) view development of mathematical teaching proficiency as a process of making connections between these instructional elements more expertly and efficiently. Debriefings that demonstrate these connections may illustrate how such connections are made and support participants’ ability to do so themselves.] • Question: To what extent do debriefings highlight student thinking and misconceptions? How does this happen?

[The National Research Council (2001) and Franke et al. (2001) argue that effective teaching is built on a foundation of understanding students’ typical misconceptions and solution strategies and knowing how to respond to such ideas. Debriefings that highlight student thinking - as opposed to those that highlight student behavior - may support teachers’ professional growth and awareness of student thinking.] 6

Research Sites

• 2 debriefings designed to “showcase” lesson study for new learners • Case A - Tokyo, summer 2003*

– Within school lesson study group; – 5th gr. math lesson on identifying odd, even numbers with attention to remainder.

• Case B - Western U.S., summer 2003

– “Experienced” cross-district lesson study group; – 4th gr. math lesson on creating symmetrical designs/ identifying lines of symmetry.

* We wish to express gratitude to our colleagues Akihiko Takahashi and Makoto Yoshida at Global Education Resources for providing not only the opportunity to experience this research lesson in person, but also providing English translations of the debriefing session, lesson plan, and classroom lesson.

Data Analysis

• Transcribe debriefings, segment into sentences, and code sentence units (2 researchers code both debriefings).

– 1) Teaching and Learning: Teaching and Learning, Debriefing Structure, Other – 2) Knowledge Integration: General Teaching and Learning, Specific Lesson – 3) Instructional Elements: Mathematical Content, Students, Teaching – 4) Student Thinking: Thinking, Behavior, Other • Review coder reliability, refine coding system and interpretation, recode.

Teaching and Learning Knowledge Integration Instructional Student Thinking Elements (Cells Represent % Agreement Between Two Coders) Case A - 1 st coding Case A - 2 nd coding Case B - 1 st coding Case B - 2 nd coding 84.6% 94.4% 81.7% 96.3% 66.3% 90.1% 72.1% 96.0% 54.2% 93.4% 62.7% 94.0% 10.6% 90.3% 34.0% 78.3% 8

Data Analysis (Cont’d)

• Compute code frequencies overall, by role (i.e., moderator, instructor, planning team, observing teachers, outside experts), by individual.

• Examine speaking “turns.” – Chunk statements by speaker, delineating turns and turn-taking sequence; – Examine content of speaker turns, variation across speakers and roles.

Research Challenges

• Different lesson study settings of two sites (e.g., should/ how should years of lesson study experience factor in?).

• “Showcase” context for the two debriefings may have influenced content. (The 20 visiting scholars and teachers from another country may have created a more formal context for the debriefing in Case A.) • Different patterns of speech resulted in different decision rules used to break sentences or include/ indicate interruptions.

Research Challenges (Cont’d)

• Coding challenges – Code definitions too narrowly or too broadly defined, perhaps causing us to overlook information/insights.

– Multiple-coded statements may be informative or may indicate a need to rethink coding categories.

– Lack of attention to issues such as math content strand and grade level.

– Purposeful, perhaps uneven, lack of attention to cultural differences.

– Artificial or unclear coding distinctions. (E.g., is writing a manifestation of student thinking or a behavior? How useful is it to tease out pieces of the complex nature of teaching?) – Coding at “sentence” level confounded by distinction between inferring context from previous sentence(s) or coding on a

prima facie

level.

Participation (Case A vs. Case B)

• Differences – Fewer comments coded (indicating shorter debriefing if comment is seen as a proxy for time), yet only 7% fewer words (indicating longer sentences); – Fewer turns (changes in speakers); – Input from more participants; – More contributions from the Moderator (18% vs. 6%) and higher % of total turns (41% vs. 12%); – Fewer comments and turns by Planning Team Members (12% of total turns vs. 42%); – Administrator present to offer comments.

• Similarities – Similar average number of comments per turn (except outside experts); – Similar % of total comments from observing teachers (% of total turns 8% different).

Participation Summary - Case A

Role

Moderator Lesson instructor Principal Other plann ing team m embers Observing teachers Outside expe rts Total

# people # % of all comments comments # turns

1 1 1 3 98 106 10 66 18.4% 19.9% 1.9% 12.4% 32 13 1 9

Avg # comments/ turn

2.7

4.5

10 7.2

12 2 20 102 150 532 19.2% 28.2% 20 5 78 6.7

49.7

Participation Summary - Case B

Role

Moderator Lesson instructor Principal Other plann ing team m embers Observing teachers Outside expe rts Total

# people # % of all comments comments # turns

1 1 0 4 42 80 N/A 214 6.0% 11.4% N/A 30.6% 16 21 N/A 56

Avg # comments/ turn

2.4

3.8

N/A 3.8

7 2 8 144 219 699 20.6% 31.3% 23 18 134 6.2

12.1

Teaching and Learning Focus

• More than 70% of all speaker comments in both sites were devoted to teaching and learning.

• Discussion of teaching and learning was balanced with structure/ rules for the debriefing (most often used by the debriefing moderator) and social interchanges (used by all participants). This balance facilitates discussion “flow” and creates a collaborative and educative “feel.” – Moderator: I’d like to hear more. How about you, Ms. K.?

Ms. K.: Thank you for today’s opportunity. [Case A, lines 131-133, series of structuring comments] – Principal: We hope that this research lesson will help us become teachers with the kind of leadership that can serve students and the parents who support them. [Case A, lines 11, social comment] – Teacher R: I would first again like to thank Teacher L for bravely taking on this task. I am a middle school 6 B, Lines 134-137, series of social comments] th math and science teacher. And I was one who was considering taking on this initial research lesson as well. So I was looking at it through the lens of one, a middle school teacher, and two, someone who would be doing this soon. [Audience laughs]. [Case – Moderator: So, [I’d like to take comments from] Teacher L [observing teacher] and Teacher O [observing teacher] and then, I think, Dr. ___ [outside expert]. And perhaps we can continue to discuss it [the lesson] during lunch. [Case B, Lines 436 437, series of structuring comments] • Case A demonstrated slightly fewer social comments (16.7% vs. 24.0%) and slightly more structuring comments (6.1% vs. 4.0%), with structuring comments interspersed more evenly throughout the debriefing.

Teaching and Learning Focus: Strategies and Examples

• We found evidence of several strategies to focus debriefings on teaching and learning: A few focus questions – Planning Team Member: There are three items in shifting [students] from [being] passive to proactive in the lesson’s view point. First, since last year we have been studying about how to change the attitudes of students from passive to proactive.

This time, we thought students would enjoy the problem of seating tickets on a train and finding out if the seat is a window seat, and we decided to use this subject. The question is, did this really help to change their attitudes to be more proactive? Secondly, I think this is this year’s key point of research, is the effectiveness of whole class discussion. We present some equations to consider, and we give a name to each. But I think we need to see if naming was really effective in presentations compared to the traditional ways. We thought it may be a good idea to have a new problem after the children have finished writing journals. Today, we had pictures of airplanes, and a bullet train that goes to the Osaka area. And we wonder if these pictures helped to motivate the children to study more. We would like to ask your opinions. [Case A, Selected lines 17-32] • Multiple (confirming and conflicting) opinions on focus questions; – Observing Teacher [on whether a long form or short form of a worksheet should be given to students]: A student who cannot find the solution will fill the whole area. But I think a student who is capable will also fill in numbers. If the goal is to find circular numbers, they see only a partial list on top such as 4,8,12, and it hits them “Ah, they are multiples of 4.” But it does not go beyond that. To shift their focus to circular numbers, we need the long complete worksheet. They discover one rule and that may make them wonder if there is another rule. In order for them to discover this type of thing, I think it is better for them to see many numbers so they can connect to various complex ideas. [Case A, Lines 232-238] – Planning Team Member: But if we give blank spaces, those students who do not need to fill numbers will also start filling in numbers. More students will rely on it. So, I think one of the important focal points is to make them think about a rule without writing numbers. For this reason, I think the worksheet should not be given. [Case A, Lines 308-311] 16

• • • •

Teaching and Learning Focus: Strategies and Examples (Cont’d)

Data collection assignments and reports – Moderator: So our protocol today is going to be that we’re going to have Teacher L, who taught the lesson, speak first and talk about any comments that she would like to make about the lesson first of all. And then each one of the participants who was in the planning group also had a job today as a data collector during the lesson and they’ll talk about what their observation point was and the things that they observed during the lesson. And we’ll look for a thread or theme of concerns that come out of that that we might want to continue some discussion around. [Case B, Lines 4-6] Summarizing/ paraphrasing by the moderator – Moderator: The question from the 5th and 6th grade group is about the worksheet, which shows the complete seating. Should we use the short worksheet? Was it okay to distribute the long complete worksheet? Is there any opinion? [Case A, Lines 211-214]

[Two teachers respond, after which the moderator continues.]

So, the worksheet is helpful for those students who lack understanding. [Case A, Line 221]

[A third teacher responds, and the moderator summarizes.]

So, it will make it easier for them to discover other patterns. [Case A, Line 240] Written lesson plans that describe pedagogical assumptions, expectations, and rationale – Outside expert, to planning team: So it’s very important to include these shapes [examples that may be used during the lesson] in your lesson plan, so that we can examine these and know what kind of shape we are going to show if you decided before you actually teach. If you want to use student work, what kind of criteria or what kind of shape or design are you actually looking for from students? Please include those [that] kind of information. That [will] really help for the other participants. [Case B, Lines 607-610] Observations about exemplary pedagogy – Outside expert: Many of you talked about [the instructor’s] teaching style. I think there are several points to be thought about. First, [the instructor] praises the children a lot by saying things like, “That’s a good idea.” One more point is that he answers questions by asking questions like, “Why do you think so?” or “What is the reason?” or “Does anyone have something more to add?” [Case A, Lines 450-453] 17

• •

Teaching and Learning Focus: Strategies and Examples (Cont

’

d)

Exchanges between observers and instructor - expressions of confusion about lesson elements (often from a student perspective) and description of pedagogical rationale and assumptions – – Observing Teacher: I was just curious why you chose to begin with them making a design of three blocks. Planning Team Member: Yeah, we had a lot of discussion about this and basically, I think the overriding final decision was driven by the desire to take the kids to the next level. Because … they do activities where, you know, there is a line of symmetry already provided and one kid splits a block and the other kid… It’s a mimicking kind of thing. So it seemed like next step would be that they would be able to recognize, come to the understanding that you can lay a line of symmetry in the middle of a shape and have it be equal on both sides.

– Second planning team member: And I think we felt like if we had started with four blocks then they never would have been pushed. We would have had this matched pair kind of a thing and we might have experienced… We might have felt like “OK, they got it.” But they wouldn’t have gotten what I got when Teacher R says “no, it’s not just matched pairs.” And we wanted to give them that. [Case B, Selected lines 390-426] Low inference observations about the students and instructor – Outside expert: For example, [during] individual problem solving [the student] was doing like (started reading from notes), “Because there are four columns.” “Because there are four columns, 55 divided by 4 and the answer is 13 with remainder 3. So, my seat is not on the window side.”This is what [the student] wrote in the beginning. He solved the problem by himself this way in about 3 minutes. After that, he erased it once again and wrote, “Since the remainder is 3, I know that my seat is on the aisle side.”

[Break in transcript. Expert describes how during lesson teacher intervened with two questions.]

And [then] he [student] said, “Oh, it is divided equally.” In short, at the first stage, I do not know if [the instructor] had decided to put [the student] at the center of the whole class discussion or not, but while [the instructor] was supporting during students’ individual seat working time, he saw what [the student] wrote, and he appropriately [asked two questions] So to have [the student] understand the case when the remainder is one, the remainder is two, the remainder is three, and the number is divisible, to make him pay attention to the window side, [the instructor] asked him what kind of people would sit on the window side after [the student] answered that his seat was on the aisle side, since [the instructor] wanted to make [the student] pay attention to the more general idea than just to his number #55. [Case A, Selected lines 498-515] 18

• •

Challenges to Focusing on Teaching and Learning

Interruptions signify engagement, but may detract from observations about teaching and learning.

– Outside expert: These are [the] only two [students] who made a rotation symmetry at the end of this 60 minute period.

Planning team member: Colin did too.

Outside expert: Oh, really? Second Planning team member: Did what?

Planning team member: Rotational symmetry.

Observing teacher: He copied [student name].

Planning team member: Colin’s… Observing teacher: … And she kept looking at me and I kept looking and she was waiting at the end and she said “he copied me, so I copied him” because she had the sticks on.

Planning Team member: Teacher K, did you see what he did with the sticks? Outside expert: So….

Planning Team Member: But he wasn’t copying?

Observing Teacher: No.

Outside expert: So, a similar student at the end of the lesson, several students made rotation symmetry, not line symmetry. [Case B, Selected lines 626-662] Time allocation among participants during the debriefing may determine what participants gain from the experience. E.g., broader ideas may arise when the debriefing is weighted toward comments from observing teachers and experts not previously involved in planning. In contrast, when the debriefing is primarily devoted to comments from the planning team, the debriefing may involve “teaching” observers about the content of planning discussions.

Opportunity for Knowledge Integration Relating the Specific to the General

• Both debriefings balanced learning about/ improving the specific lesson with learning that relates to the broader domain of knowledge for teaching.

(Columns sum to 100%) General comments about teaching and learning (e.g., in other contexts) Specific comments about the lesson Case A 31.9% 68.1% Case B 10.5% 89.3% • Case B participants were more focused on the “here and now.” • Involvement of diverse participants may support knowledge integration and transfer of learning beyond the specific lesson.

• • •

How Diverse Participants Can Support Knowledge Integration

Observing teachers may offer comments from their own experiences.

– Observing Teacher: I know Teacher D uses Investigations [curriculum name], but I don’t know how many of the rest of you do. I thought in the beginning of [using an idea from Investigations of] just having one symmetrical example and only one non symmetrical example might have been… might have been better for them to [see more than one example of each to be able to] say “what’s my rule here?” [Case B, Lines 351, 353] Planning team members may offer comments based on expectations from planning or a prior lesson.

– Planning Team member: …This whole notion that if you cut the shape in half then it’s not a shape anymore or it’s a different shape. And I wondered if it’s the language, the use of the word “cut,” … I just wondered if the discussion had gone to “divide” or “separate” or “match” whether they… that whole notion of the cutting would have been eliminated. Because that seemed to add confusion… and seemed to stifle continuing the discussion about what symmetry really is all about. I mean, I think that always seems critical when we do lesson study is the language that we use and the language that is generated and the language that ends up being the operative language of the lesson and the learning. [Case B, Selected Lines 227-232] – Instructor: In the trial lesson, I was thinking about starting the lesson by talking about where the children would go during the summer vacation, which , I thought, would lead to the talk about the train and the train ticket. But the children just got so excited and started talking about the trip to the US, to Australia, etc. So, I thought I needed to avoid this somehow today.

[Case A, Lines 41-43] Outside experts may offer comments about lesson materials, curriculum guidelines, typical student solutions, and mathematical ideas.

– Outside Expert: Before this change (in the ministry’s guideline) was made, even numbers could be defined as multiples of two, but now the even numbers are those which have no remainder when divided by two, and the odd numbers are those whose remainder is one when divided by two. [Case A, Line 425] 21

Challenges to Knowledge Integration (Analysis of “Turns”)

• Turns focused only on another teaching and learning situation may be useful for sharing ideas, but may not support knowledge integration because participants must make their own explicit connections to the observed lesson.

– Observing Teacher: I think, if we have the children write journals before expanding the idea, I can get a good idea how much they understand. Today, in my 2nd graders class, I taught about the length, and I had the children write journals. Those who understood well wrote a lot, even how he understood such and such by doing such. But those who had a hard time understanding could not write much. By having the children write journals, I think we, the teachers, see who understands and who has not yet. So before extending the subject, to have them write journals is important and effective. [Case A, Lines 277 282] • Turns focused only on the specific lesson may provide confirming/ conflicting evidence, but may not support knowledge integration because participants must fill in their own instructional implications.

– Observing teacher: There could be some students who were converting the orientation in their heads by changing from the vertical to horizontal picture or vice versa. I thought it may have been easier for children to see the numbers if one orientation was consistently used. Well, but [student] unexpectedly made the first presentation and the numbers were listed horizontally. This may actually have given an opportunity for the students to look at it differently. [Case A, Lines 178-181] – – Planning Team Member: But just by looking at my notes here and remembering the lesson, I have to say that what I noticed about the teaching that went on was here was a lot of validation of students’ responses, a lot of questions asked so it wasn’t as, I don’t think, as teacher led. The students were able to respond quite a bit. [Case B, Lines 61-62] Observing Teacher: I was standing next to a girl, who wrote in her journal, “I’d like to think about the three-row seating situation,” and I thought that was good. So, when the instructor introduced three numbers, I was impressed to see that the girl looked so glad. [Case A, Lines 273-274] 22

•

Support for Knowledge Integration (Analysis of “Turns”)

Turns that connect the specific research lesson to other contexts or knowledge domains may support knowledge integration because verbalized observations about the specific lesson explicitly validate or challenge existing knowledge.

– Outside expert: We had a discussion about whether it was good to give the children this diagram or not, and I know a kid who wrote in this diagram. [The student] at first wrote in every blank space of the diagram, but he used division and got the answer in the end. I was curious why someone who wrote in every blank space of the diagram at first could use division in the end, and so I was watching him carefully. [The instructor] came by twice during the lesson. [The instructor] asked [the student] if he needed to write in everything, and this remark made [the student] to try again. So when you introduce a problem like this one, it is important to follow up, to help the children see a more general view from where they stand. [Case A, Selected Lines 406-415] – Planning Team Member: Well, I know that in most classes that behavior has to be taught – how do you student-to-student share so that you are focused and on-task. So since this was the third day of school, what I saw in my group was that the partner sharing was not as effective in terms of clarifying thinking. The kids were not as eager to correct one another. [Case B, Lines 73-76] – Outside Expert: And so the discussions at the front of the room, when you brought them to the carpet and just what it revealed about student understanding and misconceptions and conceptions and the obstacles that were coming up for them. You know, you can do a lot of work ahead of time anticipating student responses, but unless you let the students have those discussions you never know whether they’re true. So some things that came up in discussion which I thought were really interesting is the notion that you can’t cut blocks with scissors, so that’s a problem with vocabulary and literal interpretation – of directions… [Case B, Lines 257-260] Observing Teacher: [The instructor] always has the children write journals, so the children are accustomed to writ[ing]. In the format of this journal, there are sections named “Discovery corner,” “Development corner,” and “Application corner.” So, the children are used to writing not only what they find interesting in the lesson, but also things they want to try in [the] future. The accumulation of writing journals made it possible to derive good questions from children, as seen today, I thought. [Case A, Lines 257-260] 23

Reference to the Instructional Elements

• • More than 50% of all coded statements in both sites were devoted to instruction or the instructional plan.

Analyses by role in the two sites revealed somewhat different emphases on the instructional elements, with varying emphasis on instruction and students.

% of Total Codes by Role (Columns sum to 100%) Mathematical content Students Instruction/ instructional plan More than one of the above Overall Outside Experts Case A 3.6% 29.6% 58.7% 8.2% Case B 4.0% 37.6% 51.0% 7.4% Case A 10.2% 30.7% 14.2% 9.4% Case B 4.6% 23.4% 62.6% 9.4% Observing Teachers Case A Case B 1.1% 29.2% 57.3% 12.4% 2.7% 65.1% 28.4% 3.7% Planning Team Case A 0.0% 31.4% 64.7% 3.9% Case B 3.8% 42.3% 46.8% 7.1% • • Our coding system resulted in few connections between multiple instructional elements by sentence (8% overall in both sites).

In both sites, connections between instructional elements were made frequently within speaking turn (58.5% of all turns demonstrated connections in Case A; 43.4% of all turns demonstrated connections in Case B).

• •

Strategies for Connecting Instructional Elements

Involve diverse participants with different types of knowledge and strategically allocate time during the debriefing to address intended learning goals of the debriefing, e.g., – Instructors and planning team members may offer comments about e.g., expectations for the lesson, comments about the effectiveness of specific pedagogical decisions, or comments about whether the research lesson provided useful information about a lesson idea. – Observing teachers may offer comments about e.g., aspects of the lesson or instruction that they were impressed by, would do differently, or on which they needed clarification. (If focus questions are specified, they may also evaluate lesson accordingly.) – Outside experts may increase the likelihood that connections will be made to mathematics. (Because of few comments about mathematics overall, few opportunities exist to connect comments about instruction or students to mathematical content.) E.g., • Outside Expert: In the case of multiples and factors, we see the numbers through both multiplication and division interchangeably. One way to approach this is by using division, for example. One more point is that we pay attention to the remainder, which has something to do with number theory. That is, usually the 5th graders go on dividing, or represent numbers in terms of fractions, or decimals. I think they feel remainders are something inconvenient. But, by paying attention to remainders, one can sort numbers, can view numbers from a different direction. [Case A, Lines 428-433] Have moderator encourage comments about how students typically engage or in this instance engaged with instruction and mathematics. 25

Student Thinking Focus

• The majority of student-related statements were about student thinking (67% and 56% in Case A and B, respectively), higher percentages than we expected. – Observing Teacher: …what I saw in my group was that the partner sharing was not as effective in terms of clarifying thinking…I based that on a specific…observation of …[student A] specifically noticing that [student B] had divided a shape correctly one way and incorrectly another way. … One of them was still unclear on the concept, and I base that on again watching… [Student A] had created when they were doing the three blocks and many, many patterns on there…and after the discussion, he went back and actually – it was very purposeful – he went straight to that one design and played around with it until he figured out that what he needed to do was even change one of the blocks. [Case B, Lines 75 – 86] • The remaining student-related comments, about behavior, referred to lesson goals to varying degrees and were often connected within turn with other types of comments. When connected with other comments about student thinking, instruction or mathematics, comments about student behavior provided useful background. Without such connections, such as the one below, these comments about student behavior seemed to “fall flat” (i.e., add little to the discussion) and were rarely responded to by others. – Observing Teacher: And all he [student] was doing was being silly on the carpet - poking another kid and trying to get the other kid away from you, which it didn’t work. [Case B, Line 371] 26

Differences in Comments on Student Thinking (by Participant Role)

• We found evidence of different types of student thinking comments by participant role.

• At least two-thirds of the Instructors’ student-related comments were about thinking (78% and 67%, respectively, Case A and B) and frequently about how students responded to their instructional decisions or about their own inner dialogue while teaching: – Instructor: And I had the picture in my mind at [student A’s] turn, that she would present the interesting alternative way. But in the lesson, [student B] started by saying the digit 1 would repeat. And I thought “Oh, no. What should I do?” And they started saying it increases or decreases by 5. [Case A, Lines 68-71] 27

• •

Differences in Comments on Student Thinking

(by Participant Role)

– Comments by observing teachers and planning team members about student thinking frequently included observations about student thinking in relationship to instructional decisions or expectations. When verbalized, these comments could be compared and contrasted to comments by the instructor on the same topic.

Observing Teacher: And then they went back [to their desks after class discussion] and what I saw at my table was that it [the discussion] generated a lot more designs. I was thinking “oh wow this is great.” But then I noticed they were all the same design: They were all two blocks the same, one block… in the middle... [Case B, Lines 96-100] – Student thinking-related comments by outside experts included evidence in response to focus questions (case A only) or ideas brought by other participants or (as below) observations that could be used by all observing teachers to guide their future instruction.

Outside Expert: Another point was when he [the instructor] introduced the last question, and asked the children why they used division, and they answered because they found it easier, or easy to understand. In general, it is the teacher who says it is easier to use division, as the summary of the lesson, but [the instructor] chose the students to say that. He drew everything that the students can say from the students. [Case A, Lines 390-392] 28

Considerations For U.S. Lesson Study

• • • • • Consider overall learning goals for debriefings: is focus on hearing from planning team about lesson rationale and expectations or is focus on hearing comments/ opinions from observing teachers?

Preparing a written lesson plan describing rationale, assumptions, expectations may limit the need for explanation by planning team and reserve time for “live” lesson specific comments from observers.

Consider limiting debriefing length and focus to target a few ideas deeply rather than many ideas superficially.

The moderator plays a strategic role in determining learning outcomes for all. He/ she should think carefully about his/ her role in clarifying norms for participant involvement, e.g., encouraging participants to make explicit connections and express implications for teaching and learning; limiting comments to one “big idea” per turn; having participants focus on student thinking or strategies.

Comments about instruction/ teaching should not be avoided; on the contrary, it may be useful to ask questions of the instructor/ planning team. However, such comments may be less likely to be perceived as evaluative when they are made in reference to specific questions about the lesson, allowing the focus to become about instruction generally, not an individual’s instruction in the specific instance.

Considerations For Future Research

• Collect and analyze a more diverse set of debriefing examples.

• Examine comments and questions brought by individuals in different roles (e.g., outside experts) to determine how these guide the discussion. • Share results with participants involved in these debriefings to determine the power of the coding scheme to capture events.

• Refine/ expand coding system (e.g., relationship of debriefing comments to lesson goals, plans for revision).

• Examine idea of knowledge integration more deeply, to understand whether references to general/ broader domain are apt or over-generalizations.

• Examine code correlations and meanings (e.g., more generally).

Student thinking is implicated in both comments about the specific lesson and comments about instruction • More closely examine the pre-conditions and debriefing structures that foster a student thinking focus.