Đang chuẩn bị liên kết để tải về tài liệu:
The Mathematics Pre-Service Teachers Need to Know

Skill and automaticity with numbers is only part of the story. Students must also bring abstraction into play. This is also very commonly an uncon- scious process. There are huge numbers of choices for what to emphasize and what to exclude in real problems so as to focus on the core of what matters. Indeed, it is often far from clear what the core actually is. As was the case before, one has to practice to facilitate abstraction. How? One explores the situation, focusing on one area, then another, and accu- mulates sufficient data so that non-verbal tools in the brain can sort things out and focus on. | The Mathematics Pre-Service Teachers Need to Know R. James Milgram Department of Mathematics Stanford UNivERSiTy Stanford California 94305 E-mail address milgram@math.stanford.edu The author was supported in part by a Grant from the U.S. Department of Education. Any opinions findings conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the United States Department of Education. Copyright 2005 R. James Milgram. Permission granted to reproduce for educational purposes and distribute for cost of reproduction and distribution. For my students at the University of New Mexico and Skip Matthes. To my wife Judy my son Jules my daughter Jean and dedicated to the memory of Martha my .