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OCR for page 227
SMALL GROUP DISCUSSIONS a. :~ DIAL 1 ~ Video highlights of the small group discussions provide further insight into the discussion and issues raised. In particular, the discussions dealt with observations related to two of the questions considered by the small groups: Lesson design and teacher knowledge. Question 2: How do teachers use mathematics together with other kinds of knowledge and skill in order to connect students with mathematics? Language related to the enactment of a lesson. Question 3: How do skilled teachers learn about and make use of their students' knowI- edge and capabilities to help them learn mathematics?

OCR for page 227
SMALL GROUP DISCUSSION TRANSCRIPT CLIP ~ Conversation Relatec! to the Use of Mathematical KnowlecIge lapanese Participant Consider what the objective and aim of this lesson is going to be. And also we have to think about before, the children have learned what...beforehand...already~ And then we have to predict what the reactions of the children will be. And also what kind of ideas they are going to submit. And if there are different opinions, then how am I going to summarize those In working on those activities, we utilitize our knowledge in mathematics, and also our pedagogical knowledge as well; so linking those two knowledges, and then creating a lesson plan. So lesson plan preparation is very important. U.S. Participant And there's one way to help them begin to realize that there are cans there. and how to fill in those cans. I, , , . . I, , . That becomes a very useful tool for one, understanding the mathematics themselves and two, helping their students understand the mathematics. So, I think we in agreement there. C IP 2 The Role of the Lesson Plan U.S. Participant 1 And on the leh-hand side of the lesson plank lapanese Participant Yes. That is the more detailed part. U.S. Participant 1 What is that about It includes. lapanese Participant The lesson part you have aim of the lesson. That aim could be, could be your chief focus. Translator Should be more in detail. Japanese Participant More detail. And accordingly to the plan, you need to have the process of evaluation. U.S. Participant 1 How will you know when you lapanese Participant If aim comes, evaluation should be consistent. Therefore, if you have aim, you have evaluation. Japanese Participant 1 U.S. Participant 1 Objective and evaluation. Teacher sets the aim. And the teacher evaluates. By himself APPE N DIX H

OCR for page 227
Japanese Participant 1 U.S. Participant 1 Japanese Participant 1 Yeah, I mean... Whether the students... For instance, this part I mean to let them understand, say, for instance...the definition of square. And then, evaluation means Jo they understand, (the Jefin tion) properly or not. HI. .. I r I .. . . I h Is Is a kind ot checking point. U.S. Participant 2 And will it say how the teacher will know thatch In other words, a student says, "The teacher's goal is for students to understand the Jefinition of square." Does a teacher in the evaluation part say how he will know whether they dog Japanese Participant 2 At this point, very important to take a walk U.S. Participant 1 Walk grounds lapanese Participant 2 Between Jesks. U.S. Participant 1 Walking among the Jesks. C UP 3 Planning U.S. Participant It's about decisions; decisions. I mean, if you watch the interaction in Deborah's class that you're constantly making Jecisions. Should I follow this points Should I Jo this Should far are we going to god And you have to make all these decisions on the fly. You may have an idea where you're going, but it is still... Whereas I think, for many of our Japanese teachers my impression is that they have much more anticipated... It isn't that they aren't willing to be spontaneous; they're happy to be spontaneous and so are the students. But there's a lot more of it that has a structure in it. C IP 4 Role of the Teacher Translator Group Translator U.S. Participant 1 Japanese Participant 1 APPE N DIX H N - O - E N - E (correcting translator) R - I - A - G - E Got it. Kneading with bread, rights Similar to the ideaon the blackboard and teacher try to integrate, compare, and discuss the idea togetfinalconclusion to lesson. So, we have special term forin summing up

OCR for page 227
Japanese Participant 2 Neriage means goes up, I mean Translator To raise it. Group To raise it up. Japanese Partcipant 2 Which imply you can not stay same level as student...because you are teacher. You have to try to level them up. U.S. Participant 1 This is a different word from the one you just saint Group Yes. U.S. Participant 1 What is the different spelled worry U.S. participant N - O - E - R - I - A- G - E (misspelled) lapanese Participant 1 Try to describe whole class whole class discussion. And a teacher orchestrated. Orchestrate. Orchestrate. lapanese Participant 2 Conduct, conduct. lapanese Participant 1 Then to to try them to get higher level, particularly mathematically. And they also, I think matome could be a special term. Group Matome. Matome. Matome. U.S. Participant 1 M - A Translator M - A - T - O - M - E U.S. Participant 1 Summing ups Group Summing up. U.S. Participant 1 What Joes it means Does it literally mean summing lapanese Participant 1 Yes, well ! mean, yes. U.S. Participant 1 What else is it used for in Japanese Japanese Participant 2 (Matome. Matome.) Wrap up session. Wrap up. Concluding session, closing. lapanese Participant 1 Translation: So the VCR that Deborah has showed us; has shown us the neriage portion. That means the one to one interaction between the teacher and the student. Alright~ But I have seen no wrap-up portion. Group Matome~ Matome that's right, matome. Japanese Participant 1 No, no, no! ! Translation: So, we have to have a group discussion in class in order to have neriage. Okays Translation: But, Japanese teachers tend to avoid a situation, where we have only one to one correspondence and interac- tion between the teacher and one of the students. We would like to have a group discussion. Japanese Participant 2 Teacher, student, student, student, student, and teacher. Teacher, teacher, student, student, student, teacher. U.S. Participant Yeah, we didn't see very much of that. APPE N DIX H