Studying Classroom Teaching as a Medium for Professional Development Proceedings of a U.S.-Japan Workshop (2002) / Chapter Skim
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Appendix E: A Demonstration Lesson: Function Thinking at Sixth Grade
Appendix E: A Demonstration Lesson: Function Thinking at Sixth Grade
Pages 157-176
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From page 157... ...
Lesson Plan Lesson Transcript Shunji Kurosawa, Irk Teacher, Tokyo Gak~gei University, Setagaya Elementary School Postlesson Discusssion Transcript Takashi Nakamura, Professor, University of Yamanahz Postlesson Discussion: Questions and Responses 158 161 168 175
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The relationship is described in graph and equation forms at the fifth-grade level. Now in the sixth grade, the comparison of direct and inverse proportions is use(1 to (1evelop the "function-like thinking process." {2 ~ The situation This lesson is at the stage a step before studying proportions.
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· Create own situations with changing variables. · Were they able to explain the reasons well by using graphs and equations?
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(3) Evaluation Were students able to consider the two changing variables well enough to create a problem?
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This was followed by a sheet with nine black dots. And finally, there was a sheet with thirteen black dots.
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The Triangular area between the lines is getting larger. The size of the cross is getting bigger.
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Whets Teacher: Nothings Whets Waters Waters Student: If the water falls.
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that ghost who had a virus. Kobayashi, how much will the virus be increased aher 5 minutes, if it increases every one and two minutes It is easy to answer for five minutes or six minutes.
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That is what happens one minute later therefore, must add five. Yoshida: Does anybody have any questions regarding my answers Teacher: Kawamura-san Kawamura: ...
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Then, please explain it. Ogawa: I did 1 plus 4 times 48 "Writing} (Ogawa)
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Kurosawa-sensei ended class by asking students to consider "other scenarios that increase" for the next time they met. The sixth-grade lesson was followed by a postlesson discussion with the classroom teacher and the Japanese mathematics educators who were in attendance.
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And for the third goal, I wanted to teach students how to read and under stand the equation that represents how things change. Now, I want to evaluate whether I accomplished these three goals in the class.
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The second point was the concept of a function. The concept of function involves finding how things changethen using examples associated with the change, and finding the "rule of change /' My students used the word "rapidly./' Regarding the use of the word "rapidly/' I would have preferred such terms as "spreading" or "increasing." But they were able to find many words to indicate change.
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If you listened carefully, they said the picture has plane symmetry or line symmetry. Students came up with a number of concepts that are associated with mathematics.
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From page 171... ...
If you listened carefully, they said the picture has plane symmetry or line symmetry. Students came up with a number of concepts that are associated with mathematics.
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The teacher used the word "virus" and that focused the subject at the , · ~ beginning. I think students produced mental images of the virus increasing over time.
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Today's class demonstrated the difficulty but let me explain I did not randomly lead the students towards the problem of the number of dots. The line, distance between dots, size of the "x/', and area all rapidly increasing were related to the number of dots.
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Sakai-san pointed out the presentation of the math problem and the concept of a function as discussed earlier. Do you have any opinions, insights, or thoughts about the lesson as a wholes Participant: In the latter portionhow confidently cilcl students come up with those two answers, and for what reasons Did they think so because the rest of the students got the same answers Is it correct for them to think that they all got the same answer so it should be right2 Teacher: Can we show the charts Is that rights Participant: The chart is acceptable...
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For fourth ~ , grade, it would be okay to post one, then another, and so on so that they could see it increasing. But for sixth graders, I wanted just to show the figure and let them discover how the black Jots increased.
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Observer: What percentage of students actually participated in the teacher's prepared lessons Although I do not have an accurate figure, about 12 or 13 students participated in the process again and again. What percent of the 33 students participated in the process in classy Kurowasa-sensei By what standard can we consider whether the students participated or note Is it a question about whether they came up with answers like 193 or 189 or not.
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