Knowing_and_Teaching_Elementary_Mathemat (1)

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Series Editor’s Introduction to the Anniversary Edition
direction, which is equally valuable in general and much more valuable in elementary
school. She asks, what are the different ways you can think about fractions, so that you can
help kids develop deeper understandings of them? See how many stories you can come up
with to represent the division . It’s a challenge! Indeed, many mathematicians will
soon run out of stories, because we’re not used to thinking about fractions in this way; we
think about them in abstract terms. Yet, these different stories represent different ways of
thinking about division. They help to develop a broad and robust understanding of what
fractions are, and why the operations on them work the way they do. This breadth of knowledge
provides the “support structure” for truly making sense of fractions. Reading the book
allows you to see the rich tapestry of elementary mathematics as it should be understood.
This is new to some, and resonates with others.
In sum, this book offers riches for teachers and mathematicians both; it points the way to
the kinds of deep understandings we want teachers to be able to help children develop. Ten
years after its appearance, it is every bit as powerful and useful as when it first appeared.
Alan H.Schoenfeld
Berkeley, California
July, 2009