**The Teaching Gap**

As you will see, *The Teaching Gap* compares mathematics instruction in the United
States, Japan, and Germany on the basis of data collected through the Third
International Mathematics and Science Study (TIMSS). You might be surprised (or
not) that the United States does not compare favorably. But it is important
that you understand that *The
Teaching Gap*
is not about a contest. Rather it is about trying to learn more about us by
examining instruction in other countries. As Stigler and Hiebert say
repeatedly, mathematics instruction is a cultural phenomenon, and coming to
understand one's culture is like a fish coming to understand water. A creature
cannot even notice its all-pervasive environment until it experiences life
outside it. Our educational culture is so all-pervasive that there are
important aspects of it that we cannot notice without experiencing cultures in
which they are different. So, please read *The Teaching Gap* in that spirit -- as an attempt to help us
step out of our culture of mathematics teaching in order to examine it more
objectively.

**Reflective Essay**

Please respond to these questions after reading *The Teaching Gap.*

1)
How
did the book make you feel? How did that feeling evolve from beginning to
middle to end of the book?

2)
Which
style of teaching, or combination of styles, best describes the junior high and
high school mathematics instruction that you received?

3)
What
issues raised in the book have the greatest implication for how you think about
teaching mathematics? Has your thinking changed? If so, how. If not, why?

4) What does *The Teaching Gap* have to say about how German, Japanese, and American
cultures think about students studying mathematics or about the expectations
held of them?

5) Is there a noticeable difference among the countries
in their goals for the mathematics that students learn?