Studying Classroom Teaching as a Medium for Professional Development Proceedings of a U.S.-Japan Workshop (2002) / Chapter Skim
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Mathematical Knowledge of Teachers Panel
Mathematical Knowledge of Teachers Panel
Pages 99-110
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From page 99... ...
The papers that follow are edited transcripts of their remarks. Moderator: Deborah Loewenherg Ball, University of Michigan Zalman ~ Usiskin, Professor, University of Chicago Deborah Schifter, Senior Scientist, Education Development Center Marco Ishigaki, Professor, Waseda University Miho Ueno, Mathematics Teacher, Tokyo Gak~gei University Senior High School
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From page 101... ...
An entire body of mathematical knowledge is ignored. L~ ~ t.,'d'` ~ There is a substantial body of mathematics that arises from teaching situations in much the same way that statistics arises from data and applied mathematics arises from real situations, and that deserves to be viewed as a branch of mathematics in its own right.
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From page 102... ...
Each might be said to consitute a facet of looking at school mathematics content at a deeper level than is possible for high school students. One focus is on mathematics particularly useful to high school teachers that might not normally be encountered in the standard courses taken by mathematics majors.
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From page 103... ...
Recall the well-known problem in which a rectangular sheet of cardboard is folded into a box by cutting out four congruent squares from each corner. What is the maximum volume of the box that can be created If the cardboard is 12" by 18" and each square has side x, then the box has height x and length and width 12 - 2x and 18 - 2x.
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From page 104... ...
The importance of teachers' mathematics thus goes well beyond the nee(ls of teachers to inclu(le all those who study the learning of mathematics and the mathematics curriculum. Deborah Schifter, Education Development Center When ~ spoke on Sunday, ~ mentioned that one problem with the implementation of the National Council of Teachers of Mathematics Standards is that many MATHEMATICAL KNOWLEDGE OF TEACHERS
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From page 105... ...
My question is, is this understanding shared among Japanese teachers who engage in lesson study? And since it is not shared among teachers in the United States, is lesson study an appropriate context for developing it, or are there other, more propitious settings in which teachers might better develop this disposition toward their work?
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From page 106... ...
It is worth adding that many such teachers, once they discover that their ways of thinking were mathematically valid, go through a period of sadness or anger over lost opportunities, over the many years they could have been doing satisfying mathematics hall they hall the right encouragement. A third common response is illustrated by what happened the first time ~ did an exercise like this with teachers.
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From page 107... ...
They should encourage students, but they should also encourage themselves. Good teaching is 80 percent confidence and 20 percent doubt.
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From page 108... ...
Student teachers come to our school anti try to remember what they (li(1 when they were high school students. This is their understanding of high school classroom activities.
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From page 109... ...
They recognize that they have to learn how they can help students solve problems and understand the mathematics. The student teachers realize that you cannot only rely on textbooks, but rather you have to convey the value and essence of the mathematics with your own wording and with your own understanding.
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